{"id":8467,"date":"2023-12-08T16:25:38","date_gmt":"2023-12-08T10:55:38","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=8467"},"modified":"2023-12-08T10:16:32","modified_gmt":"2023-12-08T04:46:32","slug":"envision-math-common-core-grade-3-answer-key-topic-12","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-3-answer-key-topic-12\/","title":{"rendered":"enVision Math Common Core Grade 3 Answer Key Topic 12 Understand Fractions as Numbers"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 3 Answer Key<\/a>\u00a0Topic 12 Understand Fractions as Numbers<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 3rd Grade Answers Key Topic 12 Understand Fractions as Numbers<\/h2>\n

Essential Question:<\/strong>
\nWhat are different interpretations of a fraction?
\nAnswer:
\nThere are five different <\/span>interpretations of fractions.
\nExplanation:
\n<\/b>\u00a0Fractions<\/b> as parts of wholes or parts of sets.
\n<\/span>Fractions<\/b> as the result of dividing two numbers.
\n<\/span>Fractions<\/b> as the ratio of two quantities.
\n<\/span>Fractions<\/b> as operators.
\n<\/span>Fractions<\/b> as measures.\u00a0<\/span><\/p>\n

\n
\n
<\/div>\n<\/div>\n<\/div>\n

\"Envision<\/p>\n

EnVision STEM Project: Fossils and Environment<\/strong>
\nDo Research Use the Internet or other sources to find out more about what fossils tell us about past environments. Research and make a booklet of fossils found in your state. Find at least 5 fossils and use one page for each fossil. Include where each fossil was found and what type of environment each location is now.<\/p>\n

Write a Report: Journal Include what you found. Also in your report:<\/p>\n

    \n
  • List the types of food each of the 5 creatures ate when they were alive.<\/li>\n
  • Explain whether each of the 5 creatures on your list could live in today’s environment.<\/li>\n
  • Find the lengths of different fossils to the nearest half inch. Record the lengths in a line plot.<\/li>\n<\/ul>\n

    Review What You Know<\/strong><\/p>\n

    Vocabulary<\/strong>
    \nChoose the best term from the box. Write it on the blank.<\/p>\n

      \n
    • halves<\/li>\n
    • thirds<\/li>\n
    • inch<\/li>\n
    • yard<\/li>\n<\/ul>\n

      Question 1.
      \nIf a shape is divided into 2 equal parts, the parts can be called _________.
      \nAnswer:
      \nHalves<\/p>\n

      \"Understand<\/p>\n

      Question 2.
      \nThe width of an adult’s thumb is about 1 _________.
      \nAnswer:
      \nInch<\/p>\n

      Question 3.
      \nIf a shape is divided into 3 equal parts, the parts can be called _________.
      \nAnswer:
      \nThirds<\/p>\n

      Skip Counting on the Number Line<\/strong><\/p>\n

      Skip count on the number line. Write the missing numbers.
      \nQuestion 4.
      \n\"Envision
      \nAnswer:
      \n125, 130, 135, 140, 145, 150, 155
      \nExplanation:
      \nAdd 5 to each number present on number line.
      \n110 + 5 = 115
      \n115 + 5 = 120
      \n120 + 5 = 125
      \n125 + 5 = 130
      \n130 + 5 = 135
      \n135 + 5 = 140
      \n140 + 5 = 145
      \n145 + 5 = 150
      \n150 + 5 = 155<\/p>\n

      Question 5.
      \n\"Envision
      \nAnswer:
      \n240, 260
      \nExplanation:
      \nAdd 20 to each number present on number line
      \n180 + 20 = 200
      \n200 + 20 = 220
      \n220 + 20 = 240
      \n240 + 20 = 260<\/p>\n

      Equal Parts<\/strong><\/p>\n

      Question 6.
      \nCircle the shapes that show halves.
      \n\"Envision
      \nAnswer:
      \n\"\"<\/p>\n

      Question 7.
      \nCircle the shapes that show fourths.
      \nAnswer:
      \n\"\"<\/p>\n

      Measurement<\/p>\n

      Question 8.
      \nHow long is the nail to the nearest inch? Explain how you know.
      \n\"Envision
      \nAnswer :
      \n2 inches
      \nExplanation :
      \nThe nail is in between the 1.5 marks and 2 inch mark
      \nso the nearest inch the nail is 2 inches<\/p>\n

      Pick a Project<\/strong><\/p>\n

      PROJECT 12A
      \nHow long would it take to drive across the Florida Keys?
      \nProject: Make a Map
      \n\"Envision<\/p>\n

      Answer:
      \n\"Miami<\/p>\n

      The\u00a0Florida<\/strong> Keys<\/b>\u00a0Overseas Highway\u00a0is\u00a0113 miles in length, joining the mainland of\u00a0Florida<\/b>\u00a0(starting in\u00a0Florida<\/b>\u00a0City, just south of Homestead) to\u00a0Key\u00a0West. If you drove directly from\u00a0Key\u00a0Largo to\u00a0Key\u00a0West, it\u00a0would take\u00a0you roughly 2.5 hours, traveling\u00a0distance\u00a0of 100 miles.<\/p>\n

      PROJECT 12B
      \nWhy are there so many different floors in a building?
      \nProject: Create a flooring design
      \n\"Envision<\/p>\n

      Answer:
      \nA floor<\/b> is the bottom surface of a room or vehicle. Floors vary from simple dirt in a cave to many-layered surfaces made with modern technology. Floors may be stone, wood, bamboo, metal or any other material that can support the expected load. The levels of a building are often referred to as floors, although a more proper term is storey.<\/p>\n

      \n
      \n
      There are a few basic steps to\u00a0creating a floor\u00a0plan:<\/b><\/div>\n
      \n
        \n
      1. Choose an area. Determine the area to be drawn.<\/li>\n
      2. Take measurements. If the\u00a0building<\/b>\u00a0exists, measure the walls, doors, and pertinent furniture so that the\u00a0floor<\/b> plan will be accurate.<\/li>\n
      3. Draw walls.<\/li>\n
      4. Add architectural features.<\/li>\n
      5. Add furniture<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n

        PROJECT 12C
        \nWhat is the most common hat size?
        \nProject: Collect Hat Size Data and Create a Line Plot
        \n\"Envision
        \nAnswer:
        \nHead sizes<\/b> and shapes differ from region to region. The most common male size is 7-5\/8 and the average hat size for females 7-2\/8
        \n\"\"<\/p>\n

        PROJECT 12D
        \nWhat are the most popular fruits and vegetables?
        \nProject: Draw a Garden Plot
        \n\"Envision<\/p>\n

        Answer:
        \nThe most popular fruits and vegetables are,
        \nFruits like Mango ,Banana ,Apple, Grapes, Water melon.. so on
        \nVegetables like Carrot, Potato, Tomato, Brinjal … So on<\/p>\n

        \"Pin
        \nLesson 12.1 Partition Regions into Equal Parts<\/h3>\n

        Solve & Share<\/strong>
        \nShow two different ways to divide a 2 x 6 region into 6 equal parts. How do you know the parts are equal?
        \nI can … read and write a unit fraction.
        \n\"Envision<\/p>\n

        Look Back! How are the parts of the regions alike? How are they different?<\/p>\n

        Essential Question<\/strong>
        \nHow Can You Name the Equal Parts of a Whole?
        \nAnswer:
        \nEach\u00a0<\/span>equal part of a whole<\/b> is called one-half.
        \nExplanation:
        \n<\/span>One half is expressed as 1\/2 and read as one over two or one upon two.<\/span><\/p>\n

        Visual Learning Bridge
        \nYou can divide a whole into equal parts. What fraction can you write to represent one of these equal parts?
        \nA fraction is a part of a whole.
        \nDivide each green whole into four equal parts.
        \n\"Envision<\/p>\n

        Divide each green whole into six equal parts.
        \n\"Envision
        \nIn the green wholes:<\/p>\n

          \n
        • All parts have an equal area.<\/li>\n
        • Each part is one sixth of the area of the whole.<\/li>\n
        • One sixth can be written as the fraction \\(\\frac{1}{6}\\).<\/li>\n<\/ul>\n

          Convince Me! Critique Reasoning Kim says that the figure at the right is divided into fourths because there are 4 equal parts. Carrie says it is not divided into fourths because the parts are not the same shape. Who is correct? Explain.
          \n\"Envision<\/p>\n

          Answer:
          \nCarrie is correct.
          \nExplanation:
          \nIn the given figure it is not divided into fourths because the parts are not of the same shape.<\/p>\n

          \"Understand<\/p>\n

          Guided Practice<\/strong><\/h3>\n

          Do You Understand?<\/strong>
          \nQuestion 1.
          \nIn the examples in Box A on the previous page, explain how you know the 4 parts are equal.
          \nAnswer:
          \nAll parts are equal.
          \nExplanation:
          \nAll parts have an equal area.
          \nEach\u00a0<\/span>part is <\/span>one-fourth or a quarter of the whole sheet.<\/span><\/p>\n

          In 2 and 3, tell if each shape shows equal or unequal parts. If the parts are equal, label 1 of the parts using a unit fraction.
          \nQuestion 2.
          \n\"Envision
          \nAnswer:
          \nEqual parts
          \nExplanation:
          \nThe area and size of each part of the figure are equal so the figure is divided into equal parts.<\/p>\n

          Question 3.
          \n\"Envision
          \nAnswer:
          \nUnequal parts
          \nExplanation:
          \nThe area and size of each part of the figure are not equal so the figure is divided into unequal parts.<\/p>\n

          Do You Know How?<\/strong>
          \nQuestion 4.
          \nDraw lines to divide the shape into 8 equal parts. Then write the fraction that represents 1 part.
          \n\"Envision
          \nAnswer:
          \n\"\"
          \n1\/8 unit fraction
          \nExplanation:
          \nThe area and size of each part of the figure must be equal .
          \nThen the figure is divided into equal parts
          \nThe total area of the figure is 24
          \nSo we need 8 parts
          \n24 \u00f7 8 = 3<\/p>\n

          Independent Practice<\/strong><\/p>\n

          In 5-7, tell if each shape shows equal or unequal parts. If the parts are equal, label 1 of the parts using a unit fraction.
          \nQuestion 5.
          \n\"Envision
          \nAnswer:
          \nUnequal parts
          \nExplanation:
          \nThe given square has unequal parts, so it is difficult to denote in fraction<\/p>\n

          Question 6.
          \n\"Envision
          \nAnswer:
          \nEqual parts
          \nExplanation:
          \nThe area and size of each part of the figure must be equal.
          \nThen the figure is divided into equal parts.<\/p>\n

          Question 7.
          \n\"Envision
          \nAnswer:
          \nEqual parts
          \nExplanation:
          \nThe area and size of each part of the figure must be equal.
          \nThen the figure is divided into equal parts.<\/p>\n

          In 8-10, draw lines to divide the shape into the given number of equal parts. Then write the fraction that represents one part.
          \nQuestion 8.
          \n6 equal parts
          \n\"Envision
          \nAnswer:
          \n\"\"<\/p>\n

          Question 9.
          \n3 equal parts
          \n\"Envision
          \nAnswer:
          \n\"\"<\/p>\n

          Question 10.
          \n4 equal parts
          \n\"Envision
          \nAnswer:
          \n\"\"<\/p>\n

          Problem Solving<\/strong><\/p>\n

          In 11-14, use the table of flags to answer the questions.
          \n\"Envision
          \nQuestion 11.
          \nWhat fraction represents the white part of Nigeria’s flag?
          \nAnswer:
          \none third[1\/3]<\/p>\n

          Question 12.
          \nWhich nation’s flag is \\(\\frac{1}{2}\\) red?
          \nAnswer:
          \nPoland<\/p>\n

          Question 13.
          \nHigher Order Thinking<\/strong> The flag of this nation has more than 3 equal parts. Which nation is it, and what fraction represents 1 part of its flag?
          \nAnswer:
          \nMauritius has more than 3 equal parts.
          \nOne fourth fraction represents 1 part of its flag.<\/p>\n

          Question 14.
          \nWhich nation’s flag is NOT divided into equal parts?
          \nAnswer:
          \nSeychelles<\/p>\n

          Question 15.
          \nMaryann buys 24 cans of soda. The soda comes in packs of 6 cans. How many packs does she purchase? Write a multiplication equation and a division equation to show your answer.
          \nAnswer:
          \n4 packs of can soda
          \nExplanation:
          \nMaryann buys 24 cans of soda
          \n1 pack of soda cans consist of 6 cans
          \nso :
          \n24 \u00f7 6 = 4
          \nMaryann buys 4 packs of soda cans
          \n6 x 4 = 24<\/p>\n

          Question 16.
          \nMake Sense and Persevere Jim has stickers in an array of 8 rows and 4 columns. He also has a packet of 14 stickers. How many stickers does Jim have in all?
          \nAnswer:
          \n46 stickers
          \nExplanation:
          \nJim has stickers in an array of 8 rows and 4 columns.
          \nNo of stickers in array are:
          \n8 x 4 = 32 stickers
          \nHe also has a packet of 14 stickers.
          \ntotal no of stickers Jim has are:
          \n32 + 14 = 46 stickers<\/p>\n

          Assessment Practice<\/strong><\/p>\n

          Question 17.
          \nDraw lines to show how to divide this square into 8 equal pieces. Then select the fraction that represents 1 of the pieces.
          \n\"Envision
          \nA. \\(\\frac{1}{2}\\)
          \nB. \\(\\frac{1}{3}\\)
          \nC. \\(\\frac{1}{4}\\)
          \nD. \\(\\frac{1}{8}\\)
          \nAnswer:
          \n\"\"
          \noption D
          \n1\/8 unit fracttion<\/p>\n

          Lesson 12.2 Fractions and Regions<\/h3>\n

          Solve & Share<\/strong>
          \nPat made a garden in the shape of a rectangle and divided it into 4 equal parts. She planted flowers in 3 of the parts. Draw a picture of what Pat’s garden might look like.
          \nAnswer:
          \nPat’s garden might look like this.<\/p>\n

          \"\"<\/p>\n

          I can… use a fraction to represent multiple copies of a unit fraction.
          \n\"Envision<\/p>\n

          Look Back! How many parts of Pat’s garden do NOT have flowers? Explain.
          \nAnswer:
          \n1\/4 part of Pat’s garden do NOT have flowers.
          \nExplanation:
          \nAs\u00a0 she planted only 3\/4 of his garden with flowers.<\/p>\n

          Essential Question<\/strong>
          \nHow Can You Show and Name Parts of a Region?
          \nAnswer:
          \nFractions name parts of a whole region.
          \nExplanation:
          \nWhen an object is divided<\/u>\u00a0into a number of\u00a0equal parts<\/u>\u00a0then each part is called a\u00a0faction<\/u>.
          \nThere are 2 parts that make up a faction:
          \n<\/span>Numerator: Which is the number that goes on top of the fraction, tells how many parts of the whole.
          \n<\/span><\/span>Denominator: Which is the number that goes on the bottom of the fraction, tells how many equal parts in all.<\/span><\/p>\n

          Visual Learning Bridge
          \nMr. Peters served part of a pan of enchiladas to a friend. What does each part of the whole pan represent? What part was served? What part is left?<\/p>\n

          \"Envision<\/p>\n

          Answer:
          \nEach part of the whole represent fraction.
          \n2\/6 part is served.
          \n4\/6 part is left.<\/p>\n

          Convince Me! Be Precise Below is a picture of a pie pan. Draw lines and use shading to show that five \\(\\frac{1}{8}\\)-pieces are still in the pan, and that three \\(\\frac{1}{8}\\)-pieces were eaten. Use a fraction to label the part of the pie that is in the pan.
          \n\"Envision<\/p>\n

          Answer:
          \n3\/8 pie in the pan is eaten.
          \n5\/8 pie in the pan is left over.
          \n
          \nGuided Practice<\/strong><\/p>\n

          Do You Understand?<\/strong>
          \nQuestion 1.
          \nIn the problem in Box A on the previous page, what fraction names all of the pieces in the pan?
          \nAnswer:
          \nThe whole pan is divided into 6 equal parts. Each part is 1\/6 of the whole
          \nExplanation:
          \n6 copies of 1\/6 is 6\/6.
          \nSo the whole is 6\/6.
          \nThe unit fraction is 1\/6.<\/p>\n

          Question 2.
          \nMrs. Patel made a cake. What fraction of the whole cake does each piece represent?
          \n\"Envision
          \nAnswer:
          \n1\/8 fraction of the whole cake represents each piece<\/p>\n

          Question 3.
          \nIn the picture in Exercise 2, how many \\(\\frac{1}{8}\\)-pieces were eaten? What fraction of the whole cake was eaten?
          \nAnswer:
          \n2 pieces were eaten.
          \n2\/8 pieces were eaten.
          \nExplanation:
          \nIn the given picture cake is divided into 8 equal parts.
          \nOut of which 2 pieces were eaten.<\/p>\n

          Do You Know How?<\/strong>
          \nIn 4-6, use the figure below.
          \n\"Envision
          \nQuestion 4.
          \nHow many \\(\\frac{1}{3}\\)-parts are blue?
          \nAnswer:
          \nTwo
          \nExplanation:
          \nOut of 3 parts in a given picture 2 parts are blue and 1 part is yellow.<\/p>\n

          Question 5.
          \nWhat fraction of the whole is blue?
          \nAnswer:
          \nTwo third
          \nExplanation:
          \nIn the given picture 2\/3 of the whole is colored with blue<\/p>\n

          Question 6.
          \nWhat fraction names all of the parts in the whole?
          \nAnswer:
          \n1\/3 one thirds<\/p>\n

          \n
          \n
          \n
          \n
          <\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

          Independent Practice<\/strong><\/p>\n

          In 7-10, write the unit fraction that represents each part of the whole. Then write the number of blue parts and the fraction of the whole that is blue.
          \nQuestion 7.
          \n\"Envision
          \nAnswer:
          \nOne part is blue
          \nThe fraction of whole is 1\/2
          \nExplanation:
          \nThe given triangle is equally divided into two,
          \none half colored with blue and the the other with yellow.
          \nSo the fraction of whole is 1\/2.<\/p>\n

          Question 8.
          \n\"Envision
          \nAnswer:
          \n3 parts are blue
          \nThe fraction of whole is 3\/6
          \nExplanation:
          \nGiven hexagon is equally divided into six equal parts,
          \nout of six, three are colored with blue and three with yellow
          \nSo the fraction of hexagon is written as 3\/6.<\/p>\n

          Question 9.
          \n\"Envision
          \nAnswer:
          \n2 parts are blue
          \nThe fraction of whole is 2\/4
          \nExplanation:
          \nGiven circle is equally divided into 4 parts,
          \nout of which 2 are colored with blue and 2 with yellow.
          \nSo the fraction of circle is written as 2\/4.<\/p>\n

          Question 10.
          \n\"Envision
          \nAnswer:
          \n6 parts are blue
          \nThe fraction of whole is 6\/8
          \nExplanation:
          \nGiven picture is equally divided into 8 parts,
          \nOut of which 6 are colored with blue and 2 with yellow.
          \nSo the fraction of given picture is written as 6\/8.<\/p>\n

          Question 11.
          \nDraw a rectangle that shows 6 equal parts. Write the unit fraction that represents each part. Then shade \\(\\frac{2}{6}\\) of the rectangle. Explain how you know you shaded \\(\\frac{2}{6}\\) of the rectangle.
          \nAnswer:
          \n\"\"
          \nThe unit fraction that represents the part of the rectangle is 116<\/p>\n

          Problem Solving<\/strong><\/p>\n

          Question 12.
          \nVocabulary Fill in the blanks.
          \nIn the fraction \\(\\frac{4}{7}\\), 4 is the ______ and 7 is the ________.
          \nAnswer:
          \n4 is the numerator and 7 is denominator<\/p>\n

          Question 13.
          \nGeneralize Divide the grid below into fourths. Shade 3 of the parts. Write a fraction that represents the shaded area. Write a fraction that represents the unshaded area. What can you generalize about your fractions?
          \n\"Envision
          \nAnswer:
          \n\"\"
          \n\"\"<\/p>\n

          Question 14.
          \nChristine has 6 red scarves and 3 blue scarves. Each scarf has 2 stripes. How many stripes does Christine have on her scarves? Write equations to represent and solve the problem.
          \nAnswer:
          \nChristine has 18 stripes in total on her scarves.
          \nExplanation:
          \nNo of red scarves = 6
          \nNo of stripes on red scarves = 6 x 2 = 12
          \nNo of blue scarves + 3
          \nNo of stripes on blue scarves = 3 x 2 = 6
          \nTotal no of stripes = 12 + 6 = 18<\/p>\n

          Question 15.
          \nHigher Order Thinking<\/strong> Draw a circle that shows 6 equal parts. Shade more than \\(\\frac{3}{6}\\) of the circle, but less than \\(\\frac{5}{6}\\) of the circle. What fraction have you shaded?
          \nAnswer:
          \n\"\"
          \nExplanation:
          \nA fraction more than 3\/6 is 4\/6 and a fraction less than 5\/6 is 4\/6
          \nso we have to shade 4\/6 of the circle<\/p>\n

          Question 16.
          \nNumber Sense What is the area of the baseball card? Show your work.
          \n\"Envision
          \nAnswer:
          \nThe area of baseball card is 70 cm.
          \nExplanation:
          \nBaseball card is in the shape of rectangle.
          \nSo the area of rectangle is length X breadth\u00a0 ( l x b )
          \nLength = 10 cm
          \nBreadth = 7 cm
          \nArea = length x breadth
          \n= 10 x 7
          \n= 70 cm.<\/p>\n

          Assessment Practice<\/strong><\/p>\n

          Question 17.
          \nSelect numbers from the box to write fractions to show 3 parts of each of these vegetable trays.
          \n\"Envision
          \nAnswer:
          \n\"\"
          \nExplanation:
          \nThe first plate is divided into 4 parts out of which three parts are removed
          \nThe second plate is divided into 6 parts out of which three parts are removed
          \nThe third plate is divided into 8 parts out of which three parts are removed<\/p>\n

          Lesson 12.3 Understand the Whole<\/h3>\n

          Solve & Shar<\/strong>
          \nMrs. Garcia’s third-grade class is planting a flower garden and a vegetable garden.
          \nDraw a picture of the whole flower garden and the whole vegetable garden based on the parts shown. How did you decide what the whole of each garden looked like?
          \nI can … identify the whole by seeing a part.
          \n\"Envision<\/p>\n

          Look Back! What do the fractions and tell you about the number of equal parts in the whole?
          \nAnswer:
          \nA basic way to interpret a\u00a0<\/span>fraction<\/b>\u00a0is by dividing a\u00a0<\/span>whole<\/b>\u00a0object into several\u00a0<\/span>equal parts<\/b>.
          \nThe denominator\u00a0<\/span>tells how many equal parts<\/b>\u00a0the\u00a0<\/span>whole<\/b>\u00a0is subdivided into.
          \nThe numerator\u00a0<\/span>tells<\/b>\u00a0the\u00a0<\/span>number<\/b>\u00a0of those\u00a0<\/span>parts<\/b>\u00a0that\u00a0<\/span>are<\/b>\u00a0under consideration.<\/span><\/p>\n

          \n
          \n
          <\/div>\n<\/div>\n<\/div>\n

          Essential Question<\/strong>
          \nHow Can You Use a Fractional Part to Find the Whole?
          \nAnswer:
          \nFor finding a fraction of a whole number, we multiply the numerator of the fraction by the given number and then divide the product by the denominator of the fraction.<\/p>\n

          Visual Learning Bridge
          \nAnya and Novi are running in different races. The diagrams below show how much of their races each runner has completed.
          \nDraw a picture of the whole of each track. Write a fraction to represent the whole.<\/p>\n

          You can look at the fraction to find how many parts will make up the whole.
          \n\"Envision<\/p>\n

          You know Anya and Novi have each completed \\(\\frac{1}{6}\\) of their races.
          \nSix lengths of \\(\\frac{1}{6}\\) make \\(\\frac{6}{6}\\), or 1 whole.
          \n\"Envision<\/p>\n

          Convince Me! Reasoning Why is Novi’s track longer than Anya’s track?
          \nAnswer:
          \nNovi’s track is longer than Anya’s track because 1\/6th of the track were of different size.<\/p>\n

          Another Example!<\/strong> The part of a race Rob completed is shown at the right. You can use fractional parts like this to identify the whole.
          \n\\(\\frac{2}{3}\\) is 2 copies of \\(\\frac{1}{3}\\). Divide Rob’s track into 2 equal parts.<\/p>\n

          Three copies of \\(\\frac{1}{3}\\) make \\(\\frac{3}{3}\\), or 1 whole. Draw one more third.
          \n1 = \\(\\frac{3}{3}\\).
          \n\"Envision<\/p>\n

          Guided Practice<\/strong><\/p>\n

          Do You Understand?<\/strong>
          \nQuestion 1.
          \nIf the distance Anya ran was of the length of the track, what fraction would you use to represent the whole track?
          \nAnswer:
          \nThe fraction of whole track = 6\/6
          \nExplanation:
          \nSix lengths of 1\/6 make 6\/6 or whole.<\/p>\n

          Question 2.
          \nWhat is true about the numerator and denominator of each fraction that represents one whole?
          \nAnswer:
          \n<\/span>A fraction represents a\u00a0part of\u00a0<\/span>a\u00a0whole.
          \nExplanation:
          \nThe <\/span>numerator represents\u00a0how many parts of that\u00a0<\/span>whole\u00a0are being considered,
          \nwhile the\u00a0<\/span>denominator represents\u00a0the total number of parts created from the\u00a0<\/span>whole.<\/span><\/p>\n

          \n
          \n
          <\/div>\n<\/div>\n<\/div>\n

          Do You Know How?<\/strong>
          \n3. Draw a picture of the whole and write a fraction to represent the whole.
          \n\"Envision
          \nAnswer:
          \n\"\"<\/p>\n

          Independent Practice<\/strong><\/p>\n

          In 4-7, draw a picture of the whole and write a fraction to represent the whole.
          \nQuestion 4.
          \n\"Envision
          \nAnswer:
          \n\"\"
          \n1 = 3\/3<\/p>\n

          Question 5.
          \n\"Envision
          \nAnswer:
          \n\"\"
          \n1 = 2\/2<\/p>\n

          Question 6.
          \n\"Envision
          \nAnswer:
          \n\"\" 1 = 4\/4<\/p>\n

          Question 7.
          \n\"Envision
          \nAnswer:
          \n\"\"
          \n1 = 6\/6<\/p>\n

          Problem Solving<\/strong><\/p>\n

          Question 8.
          \nRonnie and Gina were shown \\(\\frac{1}{2}\\) of a table. They each drew a picture of the whole table. Whose drawing could be correct? Explain.
          \n\"Envision
          \nAnswer:
          \nGina’s drawing of the whole table is correct
          \nExplanation:
          \nBoth Ronnie and Gina were correct.
          \nbut tables are generally square , rectangle or circle in shape so Gina’s table is correct<\/p>\n

          Question 9.
          \nHigher Order Thinking<\/strong> If the part shown in Exercise 8 is \\(\\frac{1}{4}\\) of a table, what could the whole table look like? Draw a picture and write a fraction to represent the whole.
          \nAnswer:
          \n\"\"
          \nOne whole<\/p>\n

          Question 10.
          \nThe Florida panther is endangered. In 1970, the population was estimated at 20 panthers. In 2017, the population was estimated at 230 panthers. About how many more panthers were there in 2017 than in 1970?
          \n\"Envision
          \nAnswer:
          \nAbout 210 more panthers were there in 2017 than in 1970.
          \nExplanation:
          \nIn 1970, the population was 20 panthers.
          \nIn 2017, the population was estimated at 230 panthers.
          \nSo 230 – 20 = 210.
          \nQuestion 11.
          \nConstruct Arguments Jenna and Jamal are making rugs. They have finished the parts shown. Draw pictures to show each whole rug. Whose rug will be longer when it is finished? Explain.
          \n\"Envision
          \nAnswer:
          \nJenna: I have finished 1\/3 of my rug.
          \nJamal:\u00a0I have finished 1\/3 of my rug.
          \nJamal: My rug is bigger than you.
          \nJenna: How is your rug bigger than mine. Explain?
          \nJamal: My 1\/3 of the rug is bigger than your 1\/3 of the rug
          \nExplanation:
          \nJamal’s 1\/3 rd of the rug is bigger than Jenna’s 1\/3 of the rug
          \n\"\"<\/p>\n

          So Jamal’s rug is longer than Jenna.
          \nAssessment Practice<\/strong><\/p>\n

          Question 12.
          \nThe picture shows \\(\\frac{2}{3}\\) of a granola bar. Which shows the whole granola bar?
          \n\"Envision
          \nAnswer:
          \nOption B<\/p>\n

          Question 13.
          \nEach part below is \\(\\frac{1}{2}\\) of a different whole. Which is part of the largest whole?
          \n\"Envision
          \nAnswer:
          \nOption A<\/p>\n

          Lesson 12.4 Number Line: Fractions Less Than 1<\/h3>\n

          Solve & Share<\/strong>
          \nAt a state park, there is a 1-mile hiking path between the park entrance and the beach. Scenic lookouts are located at points and of the distance from the park entrance to the beach. Show about where the lookout points are located on the line below.
          \nI can… represent fractions on a number line.
          \n\"Envision<\/p>\n

          Look Back! If you know about where the point for \\(\\frac{1}{3}\\) is located, how can you find about where the point for \\(\\frac{2}{3}\\) is located?
          \nAnswer:
          \nThe line is divided into 3 parts,
          \nWe know 1\/3 location on number line.
          \nThe point next to 1\/3is 2\/3, so we know where 2\/3 point is located.<\/p>\n

          Essential Question<\/strong>
          \nHow Can You Record Fractions on a Number Line?
          \nAnswer:
          \nFractions expand our number system beyond whole numbers and integers.
          \nExplanation:
          \nFractions help us to denote any decimal number with higher precision.
          \nRepresentation of Fractions on the number line is important to understand how fractions represent part of a whole.<\/p>\n

          Visual Learning Bridge
          \nMr. Singer is picking up his daughter, Greta, from school to go to soccer practice. Greta’s school is located at \\(\\frac{3}{4}\\) of the distance from the Singers’ house to the soccer field. How can you represent \\(\\frac{3}{4}\\) on a number line?
          \nEvery number on a number line represents a distance from 0.
          \n\"Envision<\/p>\n

          \"Envision<\/p>\n

          Convince Me! Critique Reasoning Jenna and Benito each marked \\(\\frac{1}{4}\\) on a number line. The length of the part from 0 to \\(\\frac{1}{4}\\) on Jenna’s number line is shorter than on Benito at Benito’s. Did someone make a mistake? Explain your thinking.
          \n\"Envision<\/p>\n

          Jenna did a mistake by marking unit fraction on a small number line, compared with Benito number line.\u00a0
          \nGuided Practice<\/strong><\/p>\n

          Do You Understand?<\/strong>
          \nQuestion 1.
          \nMaliya divides a number line from 0 to 1 into 6 equal lengths. What unit fraction represents each equal length? What should Maliya label the tick mark just to the left of 1? Explain.
          \nAnswer:
          \n5\/6 unit fraction
          \nExplanation:
          \n0 to 1 is divided in to 6 fractions
          \nEach 1\/6 unit fraction
          \n\"\"<\/p>\n

          Question 2.
          \nJosh divides a number line from 0 to 1 into 8 equal lengths. What should he label the first tick mark just to the right of 0? Explain.
          \nAnswer:
          \n1\/8 unit fraction.
          \nExplanation:<\/p>\n

          \"\"<\/p>\n

           <\/p>\n

          Do You Know How?<\/strong>
          \nIn 3 and 4, divide the number line into the given number of equal lengths. Then mark and label the given fraction on the number line.
          \nQuestion 3.
          \n2 equal lengths; \\(\\frac{1}{2}\\)
          \n\"Envision
          \nAnswer:
          \n\"\"<\/p>\n

          Question 4.
          \n4 equal lengths; \\(\\frac{2}{4}\\)
          \n\"Envision
          \nAnswer:
          \n\"\"<\/p>\n


          \n<\/strong>Explanation :
          \nDraw a line and make 3 equal parts on number line and then mark 1\/4, 2\/4 and 3\/4unit fraction.<\/p>\n

          Leveled Practice In 5 and 6, divide the number line into the given number of equal lengths. Then mark and label the given fraction on the number line.
          \nQuestion 5.
          \n3 equal lengths; \\(\\frac{2}{3}\\)
          \n\"Envision
          \nAnswer:
          \n2\/3 unit fraction.<\/p>\n

          \"\"<\/p>\n

          Explanation : Draw a line and make 3 equal parts on number line and then mark 1\/3, 2\/3 and 3\/3 units<\/p>\n

          Question 6.
          \n6 equal lengths; \\(\\frac{2}{6}\\)
          \n\"Envision
          \nAnswer: 2\/6
          \n\"\"<\/p>\n

          Explanation :
          \nDraw a line and make 6 equal parts on number line and then mark 1\/6, 2\/6,3\/6,4\/6,5\/6 and 6\/6units<\/p>\n

          In 7 and 8, draw a number line from 0 to 1. Divide the number line into equal lengths for the given fraction. Then mark and label the given fraction on the number line.
          \nQuestion 7.
          \n\\(\\frac{4}{6}\\)
          \nAnswer: 4\/6
          \n\"\"<\/p>\n

          Explanation :
          \nDraw a line and make 6 equal parts on number line and then mark 1\/6, 2\/6,3\/6,4\/6,5\/6 and 6\/6units<\/p>\n

          Question 8.
          \n\\(\\frac{5}{8}\\)
          \nAnswer: 5\/8
          \n\"\"<\/p>\n

          Explanation :
          \nDraw a line and make 8 equal parts on number line and then mark 1\/8 , 2\/8 , 3\/8 , 4\/8 , 5\/8 , 6\/8 , 7\/8 and 8\/8units<\/p>\n

          Problem Solving<\/strong><\/p>\n

          Question 9.
          \nConstruct Arguments Terrance and Dana each drew a number line and marked \\(\\frac{3}{4}\\). Did each person represent \\(\\frac{3}{4}\\) in the correct place on his or her line? Explain.
          \n\"Envision
          \nAnswer:
          \nyes
          \nExplanation:
          \nTerrance number line is a bit smaller that Dana’s but both the number lines are divided into equal parts.<\/p>\n

          Question 10.
          \nA gymnast starts at the left end of the balance beam and does some handsprings. When she is finished, she is at the point shown on the diagram. What fraction represents how far she went on the balance beam?
          \n\"Envision
          \nAnswer:
          \n6\/8 unit fraction.
          \nExplanation :
          \nThe balance beam is divided in to 8 equal parts of same unit lengths
          \nthe point is market at 6\/8 on the balance beam.<\/p>\n

          Question 11.
          \nMark draws a number line and labels the points for 0 and 1. He divides the distance from 0 to 1 into 2 equal lengths and labels the fraction \\(\\frac{1}{2}\\). If Mark divides each half into 2 equal lengths, what fractions can Mark label on his number line?
          \nAnswer:<\/p>\n

          \"\"<\/p>\n

          Explanation:
          \nMark draws a number line and labels the points for 0 and 1 of two equal lengths and labels the fraction and label 0 , 1\/2 and 1.
          \nMark divides each half into 2 equal lengths, each fractions is marked labels on his number line as 1\/4, 2\/4, 3\/4 and 4\/4
          \nas shown in the above figure.<\/p>\n

          Question 12.
          \nHigher Order Thinking<\/strong> Show 3 ways you can represent three eighths.
          \nAnswer:<\/p>\n

          \"\"<\/p>\n

          The number ABOVE the line tells\u00a0HOW MANY PARTS
          \n<\/b>we have (the\u00a0colored parts).The number BELOW the line tells how\u00a0many EQUAL parts
          \n<\/b>the whole is divided into.\u00a0To\u00a0<\/span>find 3\/8 of a number, we multiply the numerator <\/span>3\u00a0by the given whole\u00a0<\/span>number and then divide the product by the denominator 8.<\/span><\/p>\n

          \n\n\n\n
          <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

          Assessment Practice<\/strong><\/p>\n

          Question 13.
          \nWhat fraction does the red point on this number line represent?
          \n\"Envision
          \nAnswer:
          \nOption\u00a0 C
          \nExplanation:
          \nThe above line is of 6 equal parts of each label 1\/6, 2\/6, 3\/6<\/strong>, 4\/6, 5\/6 and 6\/6<\/p>\n

          Question 14.
          \nWhich number line has a red point at \\(\\frac{1}{3}\\)?
          \n\"Envision
          \nAnswer:
          \nOption A
          \nExplanation :
          \nIn the number line has a red point at \\(\\frac{1}{3}\\)<\/p>\n

          Lesson 12.5 Number Line: Fractions Greater Than 1<\/h3>\n

          Solve & Share<\/strong>
          \nThe length of one strip of paper is 1 whole unit. Fold two strips of paper in half. Open the two strips and place them end to end.
          \nHow many halves do you have? Use fractions to name each fold line. Tell how you decided. Draw a picture to show your work.
          \nAnswer:
          \n2 halves
          \n\"\"<\/p>\n

          strip of paper is 1 whole unit. Fold two strips of paper in half,
          \ntwo halves for two strips of papers , if it unfolded and kept end to end open<\/p>\n

          I can … represent fractions equal to or greater than 1 on a number line
          \n\"Envision<\/p>\n

          Look Back! If you added a third strip of paper folded in half, how could you use halves to name the fold lines? Explain.
          \nAnswer:
          \nIf you add a third strip of paper folded in half, as 5\/4 and 6\/4.
          \nExplanation:
          \nOne can represent fractions equal to or greater than 1 on a number line.<\/p>\n

          Essential Question<\/strong>
          \nHow Can You Use a Number Line to Represent Fractions Greater Than 1?
          \nAnswer:
          \nF<\/span>ractions greater than 1<\/b>\u00a0have numerators\u00a0<\/span>larger than their denominators, those that are less <\/span>than 1<\/b>\u00a0have numerators smaller\u00a0<\/span>than\u00a0their denominators; the rest are equal to\u00a0<\/span>1<\/b>.<\/span><\/p>\n

          Visual Learning Bridge
          \nA marsh rabbit hopped \\(\\frac{7}{4}\\) the length of a rabbit trail. How can you show this on a number line?
          \nNumber lines can represent fractions that are greater than 1 whole \\(\\frac{7}{4}\\). 5 is greater than 1 whole, but less than 2 wholes. The whole is the distance between 0 and 1.
          \n\"Envision<\/p>\n

          Divide each whole into 4 equal lengths.
          \nEach length is \\(\\frac{1}{4}\\) of the whole.
          \n\\(\\frac{4}{4}\\) is the same as 1 whole.
          \n\"Envision<\/p>\n

          The marsh rabbit hopped 7 lengths of the unit fraction \\(\\frac{1}{4}\\).
          \nThe point showing 7 lengths of \\(\\frac{1}{4}\\) can be labeled as \\(\\frac{7}{4}\\)
          \n\"Envision<\/p>\n

          Answer: 7\/4
          \nExplanation:
          \nMarsh rabbit hopped shown in the number line.<\/p>\n

          \"\"<\/p>\n

          Convince Me! Be Precise One tick mark on the number line below has been named with the fraction \\(\\frac{2}{3}\\). On the number line the lengths marked are equal. Write fractions for the other tick marks shown.
          \n\"Envision<\/p>\n

          Answer:<\/p>\n

          \"\"
          \nExplanation:
          \nDivided a number line from 0 to 1 into 3 equal lengths. Each unit fraction represents 1\/3 of equal length.<\/p>\n

          Guided Practice<\/strong><\/p>\n

          Do You Understand?<\/strong>
          \nQuestion 1.
          \nName a fraction that is to the right of the tick mark for 2 on a number line.
          \nAnswer: 7\/3
          \nExplanation :<\/p>\n

          \"\"<\/p>\n

          Question 2.
          \nQuinn says that \\(\\frac{10}{8}\\) comes to the right of \\(\\frac{9}{8}\\) on a number line. Do you agree? Why or why not?
          \nAnswer: YES
          \nExplanation:<\/p>\n

          \"\"<\/p>\n

          Do You Know How?<\/strong>
          \nIn 3 and 4, each number line has equal lengths marked. Write the missing fractions.
          \nQuestion 3.
          \n\"Envision
          \nAnswer:
          \n1\/3 and 4\/3 of unit fraction.
          \nExplanation:
          \nMarked on number line.
          \n\"\"<\/p>\n

          Question 4.
          \n\"Envision<\/p>\n

          Answer:
          \n1\/4,\u00a0 4\/4,\u00a0 5\/4 and 7\/4 are marked on number line.
          \nExplanation:<\/p>\n

          \"\"<\/p>\n

          Independent Practice<\/strong><\/p>\n

          Leveled Practice In 5-7, each number line has equal lengths marked. Write the missing fractions.
          \nQuestion 5.
          \n\"Envision
          \nAnswer:
          \n1\/2 and 3\/2 are missing marked on number line.
          \nExplanation:
          \n\"\"<\/p>\n

          Question 6.
          \n\"Envision
          \nAnswer:
          \n1\/4 and 4\/4 or 1 are marked on number line.<\/span><\/p>\n

          Explanation:
          \n\"\"<\/p>\n

          Question 7.
          \n\"Envision
          \nAnswer:
          \n2\/6,\u00a0 4\/6 and 5\/6 are missing marked on number line.
          \nExplanation:
          \n\"\"<\/p>\n

          In 8 and 9, divide the number lines into equal lengths. Write the missing fractions.
          \n\"Envision
          \nQuestion 8.
          \n\"Envision
          \nAnswer:
          \n1\/3, 4\/3, 5\/3 7\/3 and 8\/3 are marked on number line.<\/p>\n

          Explanation:<\/p>\n

          \"\"<\/p>\n

          Question 9.
          \n\"Envision
          \nAnswer:
          \n2\/8, 3\/8, 5\/8 and 6\/8 are missing numbers marked on number line.
          \nExplanation:<\/p>\n

          \"\"<\/p>\n

          Problem Solving<\/strong><\/p>\n

          In 10 and 11, use the number line below.
          \n\"Envision
          \nQuestion 10.
          \nWhat fraction tells how far the swimming pool is from the school? Explain how you know.
          \nAnswer:
          \n1\u2153 mile from school.
          \nExplanation :<\/p>\n

          \"\"<\/p>\n

          Question 11.
          \nHigher Order Thinking<\/strong> The hospital is halfway between the grocery store and the post office. What fraction tells how far the hospital is from the school? Explain.
          \nAnswer:
          \n4\/6 unit fraction.
          \nExplanation :
          \nThe hospital is 4\/6 mile distance from the school, it is located at 4\/6 on number line.<\/p>\n

          Question 12.
          \nTim has 78 board games. He has 10 boxes. Each box holds 9 games. If Tim puts all the games he has into the boxes, how many more games can he fit? Complete the bar diagram and solve the problem.
          \n\"Envision
          \nAnswer:
          \n12 more games.
          \nExplanation:
          \n\"\"
          \nTim has 10 Boxes, each box holds 9 games.
          \nTotal boxes can hold 90 games, but the Tim has 78 games.
          \nRequired games = 90-78 = 12 games.<\/p>\n

          Question 13.
          \nCritique Reasoning Rachel says that she can find (7 \u00d7 5) \u00d7 2 by calculating (7 \u00d7 2) + (5 \u00d7 2) = 14 + 10. Then add to get 24. Does Rachel’s reasoning make sense? Use properties of operations to explain.
          \nAnswer:
          \nRachel’s reasoning doesn’t make any sense.
          \nExplanation:
          \nCommutative Property\u00a0 \u00a0 \u00a0 x + y = y+ x
          \nAssociative Property\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 x + (y + z) = (x + y) + z
          \nAccording to the above two properties (7×5)x2=70 and
          \n(7 \u00d7 2) + (5 \u00d7 2) = 14 + 10 =24.<\/p>\n

          Assessment Practice<\/strong><\/p>\n

          Question 14.
          \nWhat fraction is represented by the total length marked on the number line? Select the correct fraction from the box.
          \n\"Envision
          \nAnswer:
          \n4\/3 fraction on number length.
          \nExplanation:
          \n\"\"<\/p>\n

          Lesson 12.6 Line Plots and Length<\/h3>\n

          Solve & Share<\/strong>
          \nJamie measured the lengths of 6 beetles. She measured each beetle’s length to the nearest inch and to the nearest half inch. She recorded the lengths in the two line plots below. Measure the length of each beetle below to the nearest inch and to the nearest half inch. Record your measurements in Jamie’s line plots.
          \nI can … measure to the nearest half inch and show the data on a line plot.
          \n\"Envision<\/p>\n

          Look Back! What tool did you use to measure the length of each beetle? How did you use this tool?
          \nAnswer :
          \nI used a scale to measure the beetle.
          \nWe have to place the beetle beside the scale and then we have to mark the length of the beetle on a piece of paper.<\/p>\n

          Essential Question<\/strong>
          \nHow Can You Measure Lengths and Use Line Plots to Show the Data?
          \nAnswer:
          \nLine plots, are particularly useful for showing <\/span>measurement data.
          \n<\/span>Explanation:
          \nIf a class of students all\u00a0<\/span>measured\u00a0the length of their pencils, a\u00a0<\/span>line plot would\u00a0highlight the range and frequency of the\u00a0<\/span>measurements.<\/span><\/p>\n

          \n
          \n
          <\/div>\n<\/div>\n<\/div>\n

          Visual Learning Bridge
          \nJulio is measuring some lengths of yarn in inches. How can he use a ruler to measure to the nearest half inch?
          \nLine up one end of the object with 0.
          \n\"Envision
          \nThe fifth \\(\\frac{1}{2}\\)-inch tick mark is closest to the end of the length of yarn.
          \nSo, to the nearest half inch, the yarn measures \\(\\frac{5}{2}\\) inches.
          \nThis length is two whole inches and one \\(\\frac{1}{2}\\) inch. You can write this length as 2\\(\\frac{1}{2}\\) inches.
          \nAnswer:
          \nJulio measured 9 other lengths of yarn in inches:
          \n\"Envision
          \nExplanation:
          \nOne can use number lines to show fractions.
          \nA line plot is a way to organize data on a number line.<\/p>\n

          Steps to Make a Line Plot<\/p>\n

            \n
          • Draw a number line. Show a scale based on the data.<\/li>\n
          • Write a title for the line plot.<\/li>\n
          • Mark a dot for each data value.
            \nAnswer:
            \n\"\"<\/li>\n<\/ul>\n

            Convince Me! Reasoning Suppose you measured a length of yarn that was about 4\\(\\frac{1}{2}\\) inches. How would you need to change the line plot above to record this length?
            \nAnswer:
            \nIt has to extend up to 9\/2.
            \nExplanation:
            \nThe line is extended to right side and the values are increases as shown in the above line plot,
            \nvalues on line is extended up to 9\/2 for 4\u00bd.<\/p>\n

            Guided Practice<\/strong><\/p>\n

            Do You Understand?<\/strong>
            \nQuestion 1.
            \nDraw a line that is 1\u00bd inches long.
            \nAnswer:
            \n\"\"<\/p>\n

            Question 2.
            \nIf a line measures halfway between 3 and 3\\(\\frac{1}{2}\\) inches and you need to measure to the nearest \\(\\frac{1}{2}\\) inch, what length will you record? Why?
            \nAnswer:
            \n3 inches is the nearest inch.
            \n\"\"<\/p>\n

            Explanation:
            \nThe line is nearer to 3 inch mark.<\/p>\n

            Do You Know How?<\/strong>
            \nQuestion 3.
            \nMeasure the length of each of your fingers. List the measurements to the nearest half inch.
            \nAnswer:
            \n1 Index or Point Finger of Length 3\u00a0inches
            \n2 Middle Finger of Length 3\u00bd inches
            \n3 Ring Finger of Length 3\u00a0inches
            \n4 Little Finger of Length 2\u00bd inches
            \n5 Thumb Finger of Length\u00a0 2\u00bd inches
            \nExplanation:
            \nAnswers may vary from hand to hand.<\/p>\n

            Question 4.
            \nMake a line plot to show the measurements of your fingers.
            \nAnswer:
            \nInches of fingers may vary from person to person.
            \nExplanation:<\/p>\n

            \"\"<\/p>\n

            Question 5.
            \nMeasure the lengths of the pieces of yarn at the right to the nearest half inch. Write the length for each piece.
            \n\"Envision
            \nAnswer:
            \nFirst\u00a0 \u00a0 \u00a0 – 3 inches
            \nSecond – 2\u00bd inches
            \nThird\u00a0 \u00a0 \u00a0– 3 inches
            \nForth\u00a0 \u00a0 \u00a0– 2 inches
            \nFifth\u00a0 \u00a0 \u00a0 – 2 inches
            \nExplanation:
            \nLength of yarn may vary.<\/p>\n

            Question 6.
            \nDraw a line to represent another length of yarn. Measure your line to the nearest half inch.
            \nAnswer:
            \n3\u00bd inches length yarn.
            \n\"\"<\/p>\n

             <\/p>\n

            Question 7.
            \nMake a line plot to show the measurements of the yarn.
            \n\"Envision
            \nAnswer:
            \n3\u00bd inches length yarn.
            \n\"\"<\/p>\n

            Problem Solving<\/strong><\/p>\n

            Question 8.
            \nMeasure the lengths of 10 classroom objects to the nearest half inch. Choose objects that are between 1 and 6 inches long. Record your measurements.
            \nAnswer:
            \n\"\"<\/p>\n

            Question 9.
            \nOn grid paper, draw a line plot to show your data from Exercise 8.
            \nAnswer:
            \n\"\"<\/p>\n

            Question 10.
            \nMake Sense and Persevere Raymond weighed his three dogs. The oldest dog weighs 74 pounds. The other two dogs each weigh 34 pounds. How many more pounds does the oldest dog weigh than the other two dogs combined?
            \nAnswer:
            \nThe oldest dog weighs 6 more ponds than the other two dogs.
            \nExplanation:
            \nWeight of oldest dog is 74
            \nWeight of other two dogs (34+34) is 68
            \nSo the oldest dog weighs 6 ponds more
            \n74 – 68 = 6<\/p>\n

            Question 11.
            \nDraw a number line from 0 to 2. Label the wholes. Divide each whole into thirds. Label each fraction.
            \nAnswer:
            \n\"\"<\/p>\n

            In 12 and 13, use the table at the right.
            \n\"Envision
            \nQuestion 12.
            \nHow many more of the shortest paper chains does Rico have than the longest paper chains? Explain.
            \nAnswer:
            \nShortest paper chain length 6\u00bd
            \nRico has 3 shortest paper chains each of length 6\u00bd
            \nExplanation :
            \nIn the table the shortest length of the paper chain is 6\u00bd
            \nThere are 3 shortest 6\u00bd<\/p>\n

            Question 13.
            \nHigher Order Thinking<\/strong> Look at Rico’s measurements. Can you tell if he measured the paper chains to the nearest half inch or to the nearest inch? Explain.
            \nAnswer:
            \nRico’s measurements are to the nearest half inch
            \nExplanation:
            \nIf we look at Rico’s measurements all of the measurements are in inches and nearest half inches,
            \nthere are no one fourth inches.
            \nSo Rico’s measurements are in nearest half inches.<\/p>\n

            Assessment Practice<\/strong><\/p>\n

            Question 14.
            \nJessica used 4 of Nail A, 2 of Nail B, and 3 of Nail C to build a birdhouse. Measure each nail to the nearest half inch. Then complete the line plot.
            \n\"Envision
            \nAnswer:
            \n\"\"<\/p>\n

            Lesson 12.7 More Line Plots and Length<\/h3>\n

            Solve & Share<\/strong>
            \nMonica and her friends measured the lengths of their shoes. Show this data by marking a dot for each length on the line plot below.
            \nMeasure the length of three classmates’ shoes. Add a dot to represent each length on the line plot. What length was the most common?
            \nI can … measure to the nearest fourth inch and show the data on a line plot.
            \n\"Envision<\/p>\n

            Look Back! Are there different ways to record the results of a data collection? Explain.
            \nAnswer:
            \nYes, there are different ways to record the results of a data collection.
            \nExplanation:
            \nWe can use a scale, measuring tape, and so on to measure the data.<\/p>\n

            Essentials Question<\/strong>
            \nHow Can You Make and Use Line Plots?
            \nAnswer:
            \nA\u00a0<\/span>line plot\u00a0is a\u00a0<\/span>graph\u00a0that shows frequency of data along a number\u00a0<\/span>line. It is best to\u00a0<\/span>use\u00a0a\u00a0<\/span>line plot\u00a0when comparing fewer than 25 numbers. It is a quick, simple way to organize data.<\/span><\/p>\n

            \n
            \n
            \n
            \n
            <\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

            Visual Learning Bridge
            \nAnna is measuring the length of her crayons. How can she use a ruler to measure to the nearest fourth inch?
            \nLine up one end of the object with 0.
            \n\"Envision
            \nThe tenth \\(\\frac{1}{4}\\)-inch tick mark is closest to the end of the length of the crayon.
            \nSo, to the nearest fourth inch, the crayon measures \\(\\frac{10}{4}\\) inches.
            \nThis length is two whole inches and two \\(\\frac{1}{4}\\) inches. You can write this length as 2\\(\\frac{2}{4}\\) inches.<\/p>\n

            Anna measured her other crayons.
            \nShe then recorded the data in a line plot.
            \n\"Envision<\/p>\n

            Convince Me! Make Sense and Persevere Nathan also made a line plot to show the lengths of his crayons. Tell three things you know about the lengths of Nathan’s crayons.
            \n\"Envision
            \nAnswer:
            \nNathan’s measured his crayons nearest \u00bcth
            \nMost of Nathan’s crayons are 2\u00bc inches
            \nThe smallest crayon Nathan’s has 1 inch.<\/p>\n

            Guided Practice<\/strong><\/p>\n

            Do You Understand?<\/strong>
            \nQuestion 1.
            \nMeasure the length of this line to the nearest fourth inch.
            \n\"Envision
            \nAnswer:
            \nLength = 3\u00be inches
            \nExplanation:
            \n\"\"<\/p>\n

            Question 2.
            \nDescribe how you would show this measurement on a line plot.
            \nAnswer:<\/p>\n

            Do You Know How?<\/strong>
            \nQuestion 3.
            \nDraw a line plot to show the data.
            \n\"Envision
            \nAnswer:<\/p>\n

            Question 4.
            \nMeasure your pencil to the nearest fourth inch. Show the length on your line plot.
            \nAnswer:
            \nlength of pencil : 3 \\(\\frac{3}{4}\\)
            \n\"\"<\/p>\n

            Independent Practice<\/strong><\/p>\n

            \"Envision
            \nQuestion 5.
            \nDaisy measured the lengths of her toy dinosaurs to the nearest fourth inch. She listed the lengths. Make a line plot to show the data.
            \n1\\(\\frac{2}{4}\\) in., 2\\(\\frac{1}{4}\\) in., 1 in., 1\\(\\frac{2}{4}\\) in., 1\\(\\frac{3}{4}\\) in.
            \nAnswer:
            \n\"\"<\/p>\n

            Question 6.
            \nMeasure the lengths of the toy dinosaurs at the right to the nearest fourth inch. Write the length for each toy. Show the lengths on your line plot.
            \nAnswer:
            \nlength of toy 1 : 1\\(\\frac{2}{4}\\) in.
            \nlength of toy 2 : 2\\(\\frac{1}{4}\\) in.
            \nlength of toy 3 : 1 in.
            \nlength of toy 4 : 1\\(\\frac{2}{4}\\) in.
            \nlength of toy 5 : 1\\(\\frac{3}{4}\\) in.<\/p>\n

            Problem Solving<\/strong><\/p>\n

            In 7 and 8, use the line plot at the right.
            \n\"Envision
            \nQuestion 7.
            \nArty made a line plot to show the number of inches that different snails crawled in a 5-minute race. What was the most common distance that the snails crawled?
            \nAnswer:
            \nthe most common distance that the snails crawled is 9 \\(\\frac{1}{4}\\) inches<\/p>\n

            Question 8.
            \nHigher Order Thinking<\/strong> How many more snails crawled a length more than 8\\(\\frac{3}{4}\\) inches than a length less than 8\\(\\frac{3}{4}\\) inches?
            \nAnswer:
            \nsnails that crawled length less than 8\\(\\frac{3}{4}\\) inches are : 6
            \nsnails that crawled length more than 8\\(\\frac{3}{4}\\) inches are : 19
            \ndifference : 19 – 6 = 13 snails
            \n13 more snails crawled a length more than 8\\(\\frac{3}{4}\\) inches than a length less than 8\\(\\frac{3}{4}\\) inches<\/p>\n

            Question 9.
            \nMeasure the lengths of 10 classroom objects to the nearest fourth inch. Choose objects that are between 1 and 5 inches long. Record your measurements.
            \nAnswer:
            \n\"\"<\/p>\n

            Question 10.
            \nOn grid paper, draw a line plot to show your data from Exercise 9.
            \nAnswer:
            \n\"\"<\/p>\n

            Question 11.
            \nJackson bought 5 books that cost $7 each. How much change did he get from $40?
            \nAnswer:
            \nJackson got $5 change.
            \nExplanation:
            \nCost of each book = $7
            \nCost of 5 books = 5×7
            \nTotal cost of 5 books =$35
            \nTotal amount paid = $40
            \nTotal change he received = 40-35
            \n= $5.<\/p>\n

            Question 12.
            \nUse Structure Use the digits 2, 6, and 8 to make as many 3-digit numbers as you can. Use place value to arrange the numbers in order from least to greatest.
            \nAnswer:
            \nH\u00a0 \u00a0 \u00a0T\u00a0 \u00a0 \u00a0U
            \n2\u00a0 \u00a0 \u00a06\u00a0 \u00a0 \u00a0 8
            \n2\u00a0 \u00a0 \u00a08\u00a0 \u00a0 \u00a0 6
            \n6\u00a0 \u00a0 \u00a02\u00a0 \u00a0 \u00a0 8
            \n6\u00a0 \u00a0 \u00a08\u00a0 \u00a0 \u00a0 2
            \n8\u00a0 \u00a0 \u00a02\u00a0 \u00a0 \u00a0 6
            \n8\u00a0 \u00a0 \u00a06\u00a0 \u00a0 \u00a0 2
            \nAssessment Practice<\/strong><\/p>\n

            Question 13.
            \nTonya is making headbands. She recorded the lengths of all the blue bows she purchased for the headbands. Tonya also purchased 4 red bows with lengths of 1 inch, 1\\(\\frac{1}{4}\\) inches, 1\\(\\frac{2}{4}\\) inches, and 1\\(\\frac{2}{4}\\) inches. Record the lengths of Tonya’s red bows in the line plot.
            \n\"Envision
            \nAnswer:
            \nRed bows are : 1 inch , 1\\(\\frac{1}{4}\\) inches, 1\\(\\frac{2}{4}\\) inches, and 1\\(\\frac{2}{4}\\) inches.
            \nso there are 4 red bows.
            \n\"\"<\/p>\n

            Lesson 12.8 Problem Solving<\/h3>\n

            Make Sense and Persevere<\/strong>
            \nSolve & Share<\/strong>
            \nMarcus, Mariah, and Tony painted a mural. They divided it into equal parts. Marcus painted 2 parts, Mariah painted 3 parts, and Tony painted the rest. What fraction of the mural did each student paint?
            \nThis problem may have missing or extra information. If information you need is missing, make up some reasonable information and then solve the problem.
            \nI can … make sense of problems and keep working if I get stuck.<\/p>\n

            Thinking Habits
            \nBe a good thinker! These questions can help you.<\/p>\n

              \n
            • What do I need to find?<\/li>\n
            • What do I know?<\/li>\n
            • What’s my plan for solving the problem?<\/li>\n
            • What else can I try if I get stuck?<\/li>\n
            • How can I check that my solution makes sense?
              \n\"Envision<\/li>\n<\/ul>\n

              Look Back! Make Sense and Persevere What information was not given in the problem? How did you still solve the problem?
              \nAnswer:
              \nThe number of parts the mural is divided into was not given
              \nAdditional information:
              \nMarcus, Mariah, and Tony painted a mural. They divided it into 8 equal parts. Marcus painted 2 parts, Mariah painted 3 parts, and Tony painted the rest. What fraction of the mural did each student paint?
              \nAnswer:
              \nMarcus painted 2 parts
              \nMariah painted 3 parts
              \nand Tony painted the rest
              \n= 8 – ( 2 + 3 )
              \n= 8 – 5
              \n= 3 parts
              \nTony painted 3 parts
              \nMarcus painted\u00a0 :\u00a0 \\(\\frac{2}{8}\\)
              \nMariah painted\u00a0 :\u00a0 \\(\\frac{3}{8}\\)
              \nTony painted\u00a0 \u00a0 \u00a0 :\u00a0 \\(\\frac{3}{8}\\)<\/p>\n

              Essential Question<\/strong>
              \nHow Can You Make Sense of a Problem and Persevere in Solving It?
              \nAnswer:
              \nThe <\/span>meaning of a problem\u00a0and looking for entry points to its\u00a0<\/span>solution. Helps to\u00a0analyze givens, constraints, relationships, and goals.<\/span><\/p>\n

              \n
              \n
              Visual Learning Bridge<\/span><\/div>\n<\/div>\n<\/div>\n

              Suki divides her garden into 6 equal parts. She plants daisies, roses, and violets. It takes Suki 1 hour to plant the flowers. She plants daisies in 1 part, roses in 2 parts, and violets in the rest of the garden.
              \nIn what fraction of the garden does Suki plant violets?
              \n\"Envision
              \nWhat is a good plan for solving the problem?
              \nI need to make sense of the given information. I need to think about what I can use to help me solve the problem.<\/p>\n

              How can I make sense of and solve this problem?
              \nAnswer:
              \nI can…..<\/p>\n

                \n
              • identify the quantities given.<\/li>\n
              • understand which quantities are needed to solve the problem.<\/li>\n
              • choose and implement an appropriate strategy.<\/li>\n
              • check to be sure my work and answer make sense.
                \nExplanation:<\/li>\n<\/ul>\n

                The information about 1 hour to plant the flowers is not needed to solve the problem.
                \nI can use a picture to help make sense.
                \n1 equal part for daisies is \\(\\frac{1}{6}\\) of the whole.
                \n2 equal parts for roses is \\(\\frac{2}{6}\\) of the whole.
                \nThere are 3 equal parts left for violets.
                \n\"Envision
                \n3 copies of \\(\\frac{1}{6}\\) is \\(\\frac{3}{6}\\).
                \nSo, Suki plants violets in \\(\\frac{3}{6}\\) of the garden.<\/p>\n

                Convince Me! Make Sense and Persevere How can you check to make sure the work and answer given above make sense?
                \nAnswer:
                \nTotal number of parts garden is divided into is: 6 parts
                \nDaisies are planted in 1 part [ 1\/6 fraction]
                \nRoses are planted in 2 parts [ 2\/6 fraction]
                \nSo Suki plants violets in 3 parts as :
                \n1 + 2 = 3
                \n6 – 3\u00a0 = 3 parts
                \n3\/6 unit fraction.<\/p>\n

                Guided Practice<\/strong><\/p>\n

                Make Sense and Persevere<\/strong> Keira and Matt cut a sandwich into 4 equal parts. They each ate 1 part. Keira is 9 years old. Matt is the same age as Keira. What fraction of the sandwich is not eaten?
                \n\"Envision
                \nQuestion 1.
                \nIs there any missing or extra information? Explain.
                \nAnswer:
                \nMissing information : none
                \nExtra information : the ages of Keira and Matt are given [we don’t need their ages to determine the parts of the sandwich left]<\/p>\n

                Question 2.
                \nWhat do you need to find before you can determine how much of the sandwich is left?
                \nAnswer:
                \nWe don’t need to find the any other information as all the needed information is given in the question<\/p>\n

                Question 3.
                \nSolve the problem. If information you need is missing, make up some reasonable information for the problem.
                \nAnswer:
                \nThe sandwich is divided into 4 equal parts
                \nKeira and Matt each ate one part so total parts eaten : 2 parts
                \nnumber of parts left is : 4- 2 = 2 parts<\/p>\n

                Independent Practice<\/strong><\/p>\n

                Make Sense and Persevere<\/strong> Marni planted a vegetable garden. She put lettuce in 1 part, carrots in 4 parts, and broccoli in the rest of her garden. In what fraction of the garden did Marni plant broccoli?
                \nQuestion 4.
                \nIs there any missing or extra information?
                \nAnswer:
                \nMissing information : the question did not specify the number of the parts Marni’s garden is divided into
                \nExtra information : none<\/p>\n

                Question 5.
                \nSolve the problem. If information you need is missing, make up some reasonable information for the problem.
                \nAnswer:
                \nAdditional information : Marni’s garden is divided into 8 parts. She put lettuce in 1 part, carrots in 4 parts, and broccoli in the rest of her garden. In what fraction of the garden did Marni plant broccoli?
                \nAnswer:
                \nfraction in which broccoli is planted : 3\/8
                \nExplanation:
                \nTotal number of parts Marni’s garden is divided into is 8 parts
                \nlettuce : 1 part
                \ncarrots : 4 parts
                \nbroccoli : 8 – (1 + 4)
                \n.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0: 8 – 5 = 3
                \nfraction in which broccoli is planted : 3\/8<\/p>\n

                Question 6.
                \nCan you use a different number of parts and still solve the problem? Explain.
                \nAnswer:
                \nyes
                \nExplanation :
                \nIf Total number of parts Marni’s garden is divided into is 6 parts
                \nlettuce : 1 part
                \ncarrots : 4 parts
                \nbroccoli : 6 – (1 + 4)
                \n.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0: 6 – 5 = 1
                \nfraction in which broccoli is planted : 1\/8<\/p>\n

                Problem Solving<\/strong><\/p>\n

                Performance Task<\/strong>
                \nSports Day<\/strong>
                \nGreen School divides its school gym into 8 equal parts for a sports day. Basketball is in 2 parts, soccer is in 1 part, and volleyball and tennis are in the rest.
                \n\"Envision
                \nQuestion 7.
                \nMake Sense and Persevere The gym teacher wants to know what fraction of the gym is used for tennis. What missing information do you need to solve the problem?
                \nAnswer:
                \nSchool gym is divides into 8 equal parts.
                \nTennis and Volleyball not clearly mentioned, these two are missing information do you need to solve the problem.<\/p>\n

                In 8 and 9, draw a picture to represent the number of parts in each plan.
                \nQuestion 8.
                \nReasoning What fraction of the gym would be used for tennis if 2 parts were for volleyball?
                \n\"Envision
                \nAnswer: 3 parts
                \n\"\"<\/p>\n

                Explanation:
                \nif 2 parts were used for volleyball , three parts used for tennis<\/p>\n

                Question 9.
                \nReasoning<\/strong> What fraction of the gym would be used for tennis if 3 parts were used for volleyball?
                \nAnswer: 2 PARTS
                \n\"\"
                \nExplanation : if 3 parts were used for volleyball , two parts used for tennis as shown in that above picture<\/p>\n

                Question 10.
                \nConstruct Arguments<\/strong> To have the same fraction for tennis as for basketball, which plan, Exercise 8 or 9, should be used? Justify your answer.
                \nAnswer:
                \nplan 9 should be used
                \nExplanation:
                \nfor tennis and basket ball to be equal we need to have equal number of parts for tennis and basket ball
                \nin question 9 plan tennis and basket ball both are takin a space of 2 parts
                \nwhereas in question 8 plan tennis is taking up more space than that of basket ball
                \nso,
                \nfor tennis and basket ball to be equal we need to have equal number of parts for tennis and basket ball<\/p>\n

                Topic 12 Fluency Practice Activity<\/h3>\n

                Follow the path<\/strong>
                \nShade a path from START to FINISH. Follow the sums and differences where the digit in the hundreds place is greater than the digit in the tens place. You can only move up, down, right, or left.
                \nI can … add and subtract within 1,000.
                \n\"Envision
                \nAnswer :
                \n\"\"<\/p>\n

                Topic 12 Vocabulary Review<\/h3>\n

                Understand Vocabulary<\/strong>
                \nWord List<\/p>\n

                  \n
                • denominator<\/li>\n
                • fraction<\/li>\n
                • line plot<\/li>\n
                • nearest fourth inch<\/li>\n
                • nearest half inch<\/li>\n
                • numerator<\/li>\n
                • unit fraction<\/li>\n<\/ul>\n

                  Question 1.
                  \nCircle each unit fraction.
                  \n\\(\\frac{1}{4}\\)
                  \n\\(\\frac{3}{8}\\)
                  \n\\(\\frac{1}{6}\\)
                  \n\\(\\frac{1}{8}\\)
                  \n\\(\\frac{2}{3}\\)
                  \nAnswer:
                  \n\"\"<\/p>\n

                  Question 2.
                  \nCircle each fraction where 6 is the denominator.
                  \n\\(\\frac{3}{6}\\)
                  \n\\(\\frac{6}{8}\\)
                  \n\\(\\frac{1}{6}\\)
                  \n\\(\\frac{5}{6}\\)
                  \n\\(\\frac{4}{8}\\)
                  \nAnswer:
                  \n\"\"<\/p>\n

                  Question 3.
                  \nCircle each fraction where 4 is the numerator.
                  \n\\(\\frac{2}{4}\\)
                  \n\\(\\frac{4}{8}\\)
                  \n\\(\\frac{1}{4}\\)
                  \n\\(\\frac{3}{4}\\)
                  \n\\(\\frac{4}{6}\\)
                  \nAnswer:
                  \n\"\"<\/p>\n

                  Question 4.
                  \nCircle the lengths that could be measurements to the nearest half inch.
                  \n2\\(\\frac{1}{2}\\) in.
                  \n4 in.
                  \n3\\(\\frac{3}{4}\\) in.
                  \n7\\(\\frac{1}{4}\\) in.
                  \n6 in.
                  \nAnswer:
                  \n\"\"<\/p>\n

                  Question 5.
                  \nCircle the lengths that could be measurements to the nearest fourth inch.
                  \n8\\(\\frac{3}{4}\\) in.
                  \n1\\(\\frac{1}{4}\\) in.
                  \n11 in.
                  \n7\\(\\frac{1}{4}\\) in.
                  \n6 in.
                  \nAnswer:
                  \n\"\"<\/p>\n

                  Write always, sometimes, or never.
                  \nQuestion 6.
                  \nThe numerator in a fraction is _?_ greater than the denominator. _________
                  \nAnswer:
                  \nSome times
                  \nExplanation:
                  \nIn a proper<\/span>\u00a0<\/span>fraction<\/span>,<\/span> the<\/span>\u00a0<\/span>numerator<\/span>\u00a0is<\/span> sometimes more<\/span>\u00a0than the<\/span>\u00a0<\/span>denominator<\/span>.<\/span>
                  \n<\/span>Question 7.
                  \n<\/span>A fraction ? _ has a numerator and denominator. __________
                  \nAnswer:
                  \nAlways
                  \nExplanation:
                  \nA<\/span>\u00a0<\/span>fraction<\/span> represents a part of a whole or any number of equal parts.
                  \n<\/span>For example, one-half, eight-fifths, three-quarters.
                  \n<\/span>Question 8
                  \n<\/span>A line plot_?_ shows measurements of lengths. _________
                  \nAnswer:
                  \nNever
                  \nExplanation:
                  \nA <\/span>Line plot<\/em>\u00a0can be\u00a0<\/span>defined<\/em>\u00a0as a graph that displays data as points or check marks above a number line, showing the frequency of each value.<\/span><\/p>\n

                  \n
                  \n
                  \n
                  \n
                  Use Vocabulary in Writing<\/strong><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

                  Question 9.
                  \nUse at least 2 terms from the Word List to explain how to find the unit fraction of the shape shown below.
                  \n\"Envision
                  \nAnswer:
                  \n1\/6
                  \n<\/span>Explanation:
                  \nA unit fraction is any fraction with 1 as its numerator (top number), and a whole number for the denominator (bottom number).
                  \nIf we divide the hexagon into 6 equal parts
                  \nthen each part will be one part of the six parts
                  \nthat is 1\/6<\/p>\n

                  Topic 12 Reteaching<\/h3>\n

                  Set A pages 437-440<\/strong><\/p>\n

                  This is one way to divide a whole into fourths.
                  \n\"Envision
                  \nBecause each of the 4 parts has the same area, each part is one fourth of the whole.
                  \nYou can write this fraction as \\(\\frac{1}{4}\\)
                  \nA unit fraction represents one of the equal parts \\(\\frac{1}{4}\\) is a unit fraction.<\/p>\n

                  Remember<\/strong> that fractions can name equal parts of a whole.<\/p>\n

                  In 1 and 2, draw lines to divide the shape into the given number of equal parts. Then write the fraction that represents 1 part.
                  \nQuestion 1.
                  \n6 equal parts
                  \n\"Envision
                  \nAnswer:
                  \n\"\"
                  \nExplanation:
                  \ntotal area of the figure : 12
                  \n12 divided into 6 parts is 12 \u00f7 6 = 2<\/p>\n

                  Question 2.
                  \n2 equal parts
                  \n\"Envision
                  \nAnswer:
                  \n\"\"
                  \nExplanation:
                  \ntotal area of the figure : 12
                  \n12 divided into 2 parts is 12 \u00f7 2 = 6<\/p>\n

                  Question 3.
                  \nMartin divides a shape into 3 equal parts. What unit fraction can he write to represent 1 part?
                  \nAnswer:<\/p>\n

                  Set B pages 441-444<\/strong><\/p>\n

                  What fraction of this rectangle is shaded?
                  \n\"Envision
                  \nThe rectangle is divided into 8 equal parts. So, the unit fraction of the rectangle is \\(\\frac{1}{8}\\).
                  \nIn the whole rectangle, there are 8 parts of \\(\\frac{1}{8}\\).
                  \n8 copies of \\(\\frac{1}{8}\\) is \\(\\frac{8}{8}\\)
                  \nFor the shaded part there are 6 parts of \\(\\frac{1}{8}\\).
                  \n\"Envision
                  \n6 copies of \\(\\frac{1}{8}\\) is \\(\\frac{6}{8}\\)
                  \nSo, \\(\\frac{6}{8}\\) of the rectangle is shaded.<\/p>\n

                  Remember<\/strong> that you need to think about how many parts there are in all and how many parts are shaded.<\/p>\n

                  In 1-4, write the unit fraction that represents each part of the whole. Next, write the number of shaded parts. Last, write the fraction of the whole that is shaded.
                  \nQuestion 1.
                  \n\"Envision
                  \nAnswer:
                  \nUnit fraction = 1\/3
                  \nNumber of shaded part is one.
                  \nFraction of whole that is shaded = 1\/3
                  \nQuestion 2.
                  \n\"Envision
                  \nAnswer:
                  \nUnit fraction = 5\/6
                  \nNumber of shaded parts are 5
                  \nFraction of whole that is shaded = 5\/6
                  \nQuestion 3.
                  \n\"Envision
                  \nAnswer:
                  \nUnit fraction = 3\/4
                  \nNumber of shaded parts are 3
                  \nFraction of whole that is shaded = 3\/4<\/p>\n

                  Question 4.
                  \n\"Envision
                  \nAnswer:
                  \nUnit fraction = 2\/4
                  \nNumber of shaded parts are 2
                  \nFraction of whole that is shaded = 2\/4<\/p>\n

                  Set C pages 445-448<\/strong><\/p>\n

                  This shape is \\(\\frac{2}{4}\\) of a piece of fabric Tina used in a quilt. You can draw a picture and write a fraction to represent the whole piece of fabric.
                  \n\"Envision
                  \n\\(\\frac{2}{4}\\) is 2 copies of \\(\\frac{1}{4}\\)
                  \nDivide the piece of fabric into 2 equal parts.
                  \n4 copies of \\(\\frac{1}{4}\\) makes \\(\\frac{4}{4}\\). or 1 whole.<\/p>\n

                  Remember<\/strong> that the denominator shows the total number of equal parts in a whole.<\/p>\n

                  In 1 and 2, draw a picture and write a fraction to represent the whole.
                  \nQuestion 1.
                  \n\"Envision
                  \nAnswer:
                  \n\"\"
                  \n1 = 4\/4<\/p>\n

                  Question 2.
                  \n\"Envision
                  \nAnswer:
                  \n\"\"
                  \n1 = 8\/8<\/p>\n

                  Set D pages 449-452<\/strong><\/p>\n

                  You can show fractions on a number line.
                  \nThe fraction \\(\\frac{5}{6}\\) is labeled. What are the missing fractions?
                  \n\"Envision
                  \nFirst, find the unit fraction. The line is divided into six equal lengths. So, the number line shows sixths.
                  \nEach jump represents \\(\\frac{1}{6}\\). So, the first tick mark is labeled \\(\\frac{1}{6}\\). The second tick mark is labeled \\(\\frac{2}{6}\\), and so on.
                  \nThe missing fractions on the number line are \\(\\frac{1}{6}, \\frac{2}{6}, \\frac{3}{6}\\), and \\(\\frac{4}{6}\\)<\/p>\n

                  Remember<\/strong> to first decide what unit fraction is shown on each number line.<\/p>\n

                  In 1 and 2, write the missing fractions on each number line.
                  \nQuestion 1.
                  \n\"Envision
                  \nAnswer:
                  \n1\/4 and 3\/4<\/p>\n

                  Question 2.
                  \n\"Envision
                  \nAnswer:
                  \n1\/8 , 2\/8 , 4\/8 , 5\/8 , 7\/8<\/p>\n

                  Question 3.
                  \nDivide the number line below into 3 equal parts and mark \\(\\frac{2}{3}\\) on the line.
                  \n\"Envision
                  \nAnswer:
                  \n\"\"<\/p>\n

                  Set E pages 453-456<\/strong><\/p>\n

                  Number lines can have fractions greater than 1.
                  \nThe number line below is divided into thirds.
                  \nThe denominator is 3 because the unit fraction is \\(\\frac{1}{3}\\). The numerator shows how many copies of the unit fraction each point represents.
                  \n\"Envision<\/p>\n

                  Remember<\/strong> that the numerator increases by 1 because each part of the number line is 1 more copy of the unit fraction.<\/p>\n

                  Question 1.
                  \nThe number line has equal lengths marked. Write the missing fractions.
                  \n\"Envision
                  \nAnswer:
                  \n1\/6 , 4\/6 , 5\/6 , 7\/6 , 8\/6<\/p>\n

                  Question 2.
                  \nDivide the number line into fourths. Label each point.
                  \n\"Envision
                  \nAnswer:
                  \n\"\"<\/p>\n

                  Set F pages 457-460<\/strong><\/p>\n

                  You can use a line plot to show data, such as lengths measured to the nearest half inch.
                  \nSteps to make a line plot:<\/p>\n

                    \n
                  • Draw a number line and choose a scale.<\/li>\n
                  • The scale should show data values from the least to the greatest.<\/li>\n
                  • Write a title for the line plot.<\/li>\n
                  • Mark a dot for each value.
                    \n\"Envision<\/li>\n<\/ul>\n

                    Remember<\/strong> to mark a dot for each length. Check your completed line plot against the data in the chart.
                    \n\"Envision
                    \nQuestion 1.
                    \nDraw a line plot to show the data.
                    \nAnswer:
                    \n\"\"<\/p>\n

                    Question 2.
                    \nHow many strings does Carl have in all?
                    \nAnswer:
                    \n10 strings
                    \nExplanation:
                    \n2\u00bd inch strings – 04
                    \n3 inch\u00a0 \u00a0 strings – 03
                    \n3\u00bd inch strings – 02
                    \n4 inch\u00a0 \u00a0 strings – 01<\/p>\n

                    Question 3.
                    \nDraw a line that is the same length as the most common string length.
                    \nAnswer:
                    \nMost common string is 2\u00bd inch
                    \n\"\"<\/p>\n

                    Set G pages 461-464<\/strong><\/p>\n

                    You can measure to different lengths, such as to the nearest fourth inch.
                    \nThe closest fourth-inch mark to the end of the length of the rectangle is the 2\\(\\frac{1}{4}\\)-inch mark.
                    \n\"Envision
                    \nThe lengths can be shown on a line plot.<\/p>\n

                    Remember<\/strong> to think about the scale of the line plot. It needs to include the least and greatest values.<\/p>\n

                    Question 1.
                    \nMeasure and record the lengths of 5 classroom objects to the nearest fourth inch. Use objects that are between 1 and 3 inches long.
                    \nAnswer:
                    \nEraser : 1.5 inches
                    \nPencil :\u00a0 2.7 inches
                    \nPen Cap : 2.3 inches
                    \nChalk : 2.3 inches
                    \nSticker : 1 inch<\/p>\n

                    Question 2.
                    \nDraw a line plot to show your data.
                    \nAnswer:
                    \n\"\"<\/p>\n

                    Set H pages 465-468<\/strong><\/p>\n

                    Think about these questions to help you make sense and persevere in solving problems.
                    \nThinking Habits<\/p>\n

                      \n
                    • What do I need to find?<\/li>\n
                    • What do I know?<\/li>\n
                    • What’s my plan for solving the problem?<\/li>\n
                    • What else can I try if I get stuck?<\/li>\n
                    • How can I check that my solution makes sense?
                      \n\"Envision<\/li>\n<\/ul>\n

                      Remember<\/strong> to make sense of the problem by identifying the quantities. Then use what you know to solve.<\/p>\n

                      Gavin divided his notebook into 8 equal parts. He plans to use 3 parts to take notes for math and 2 parts for reading. He has school from 8:30 A.M. to 3:30 P.M. What fraction of his notebook does he have left?
                      \nQuestion 1.
                      \nIs there any missing or extra information? Explain.
                      \nAnswer:
                      \nGavin divided his book into 8 equal parts
                      \n3 parts are used for math 3\/8
                      \n2 parts are used for reading 2\/8
                      \nThe fraction of notebook he has left is :
                      \n3 + 2 = 5
                      \n8 – 5 = 3
                      \nThe fraction of notebook he has left is 3\/5<\/p>\n

                      Question 2.
                      \nSolve the problem. If information you need is missing, make up some reasonable information for the problem. You can draw a picture to help.
                      \nAnswer:
                      \nThe missing information is:
                      \n3\/8 part of the book was used for science<\/p>\n

                      Topic 12 Assessment Practice<\/h3>\n

                      Question 1.
                      \nWhat fraction of the whole is colored green? What fraction of the whole is colored yellow?
                      \n\"Envision
                      \nAnswer:
                      \n3\/6 fraction of the whole is colored green.
                      \n3\/6 fraction of the whole is colored yellow.<\/p>\n

                      Question 2.
                      \nWrite a fraction to name the equal parts of the whole pizza. How many parts would you need to make two whole pizzas? Explain.
                      \n\"Envision
                      \nAnswer:
                      \nFraction name : 1\/8
                      \nwe need 16 parts to make 2 whole pizzas
                      \nExplanation:
                      \n1 pizza needs 8 parts to make 1 whole so we need 16 parts [8 + 8 = 16] to make 2 wholes<\/p>\n

                      Question 3.
                      \nThis line segment represents \\(\\frac{1}{3}\\) of the distance from Mal’s house to the library. Which represents the whole distance and has an accurate explanation?
                      \n\"Envision
                      \nA. \"Envision The line segment represents \\(\\frac{1}{3}\\) the distance from Mal’s house to the library. So, the whole distance is 3 times as long.
                      \nB. \"Envision The line segment represents \\(\\frac{1}{3}\\) the distance from Mal’s house to the library. So, the whole distance is 2 times as long.
                      \nC. \"Envision The line segment represents \\(\\frac{1}{3}\\) the distance from Mal’s house to the library. So, the whole distance is 4 times as long.
                      \nD. \"Envision The line segment represents the distance from Mal’s house to the library. So, the whole distance is the identical line segment.
                      \nAnswer:
                      \nOption A
                      \nExplanation:
                      \nThe line segment represents 1\/3 the distance from Mal’s house to the library. So, the whole distance is 3 times as long.<\/p>\n

                      Question 4.
                      \nWhich point is at \\(\\frac{3}{6}\\) on the number line?
                      \n\"Envision
                      \nA. Point A
                      \nB. Point B
                      \nC. Point C
                      \nD. Point D
                      \nAnswer:
                      \nPoint B<\/p>\n

                      Question 5.
                      \nWhich of the fractions would be to the right of 1 on a number line? Select all that apply.
                      \n\"Envision
                      \nAnswer:
                      \n5\/4<\/p>\n

                      Question 6.
                      \nA. Draw a picture to show \\(\\frac{2}{4}\\).
                      \nAnswer:
                      \n\"\"<\/p>\n

                      B. Explain how you knew you had shaded the correct amount of your picture.
                      \nAnswer:
                      \nDivide the circle into fourths and then shade 2 of the 4 parts blue<\/p>\n

                      Question 7.
                      \nJeremy put pepperoni on \\(\\frac{1}{2}\\) of a pizza. He put olives on \\(\\frac{1}{3}\\) of the pizza. What fraction of the pizza did NOT have pepperoni? What fraction of the pizza did NOT have olives?
                      \nAnswer:
                      \n1\/2 of the fraction did not have pepperoni.
                      \n2\/3 of the fraction did not have olives.<\/p>\n

                      Question 8.
                      \nOne point on the number line below has been named with the fraction \\(\\frac{2}{4}\\). Write a fraction for each of the other points shown.
                      \n\"Envision
                      \nAnswer:
                      \n\"\"<\/p>\n

                      Question 9.
                      \nExplain how you know \\(\\frac{3}{3}\\) represents a whole.
                      \nAnswer:
                      \nFraction 3\/3 means 3 parts of 3 parts
                      \nDividing 3 with 3 we get 1
                      \nSo the fraction 3\/3 is a whole 1<\/p>\n

                      Question 10.
                      \nJared folded a piece of paper 9 inches by 12 inches into sections as shown below. What fraction of the total area is in each section? Explain.
                      \n\"Envision
                      \nAnswer:
                      \nFraction of total Area is 36
                      \nExplanation:
                      \nArea of total paper = 9 x 12 = 108 sq.inches
                      \nThe paper is divided into 3 equal part
                      \nArea of each part = 108 \u00f7 3 = 36 sq.inches<\/p>\n

                      Question 11.
                      \nHow many \\(\\frac{2}{8}\\)s do you need to get \\(\\frac{8}{8}\\)?
                      \nAnswer:
                      \nFour
                      \nExplanation:
                      \nwe need four 2\/8 fractions to get 8\/8
                      \n2\/8 + 2\/8 + 2\/8 + 2\/8 = 8\/8<\/p>\n

                      Question 12.
                      \nLane’s class is painting a mural with 6 equal parts. They spent 45 minutes painting on each of 2 days. On the first day, the class painted \\(\\frac{1}{6}\\) of the mural. The next day, the class painted another \\(\\frac{1}{6}\\) of the mural. How many \\(\\frac{1}{6}\\) parts did the class paint in the two days?
                      \nA. 1
                      \nB. 2
                      \nC. 3
                      \nD. 4
                      \nAnswer:
                      \nOption B
                      \nExplanation:
                      \nThe class paints 1\/6 part each day in d days the class paints 2\/6 parts
                      \n1\/6 – day 1
                      \n1\/6 – day 2
                      \nBy day 2 no of parts painted are 1\/6 + 1\/6 = 2\/6<\/p>\n

                      Question 13.
                      \nHow many \\(\\frac{1}{8}\\) s do you need to get \\(\\frac{5}{8}\\)? Use the number line below for help.
                      \nA. 1
                      \nB. 3
                      \nC. 5
                      \nD. 8
                      \n\"Envision
                      \nAnswer:
                      \nOption C
                      \nExplanation:
                      \nYou need 5 yards to make 1\/8 as 5\/8<\/p>\n

                      Question 14.
                      \nWhich point represents 6 lengths of \\(\\frac{1}{8}\\) on the number line? Explain.
                      \n\"Envision
                      \nAnswer:
                      \nPoint D<\/p>\n

                      Question 15.
                      \nDivide the circle into 8 equal parts. What fraction does each part represent?
                      \n\"Envision
                      \nAnswer:
                      \n\"\"
                      \nEach part represent1\/8 fraction.<\/p>\n

                      Question 16.
                      \nSeth drew \\(\\frac{2}{4}\\) of a shape below. Draw a picture to show the whole shape and write a fraction to represent the whole.
                      \n\"Envision
                      \nAnswer:
                      \n\"\"
                      \nExplanation:
                      \nOne whole is 4\/4 that means to get 4\/4 we need to have 2 parts of 2\/4
                      \nAs 2\/4 + 2\/4 = 4\/4<\/p>\n

                      Question 17.
                      \nMara believes the point marked on the number line is \\(\\frac{2}{3}\\). Is she correct? Explain.
                      \n\"Envision
                      \nAnswer:
                      \nMara is wrong
                      \nExplanation:
                      \nthe markings of the fractions on the number line are not correct
                      \n[the markings are not even there is a lot of gap between 1\/3 and 3\/3]
                      \n\"\"<\/p>\n

                      Question 18.
                      \nSelect all the sentences that describe this shape.
                      \n\"Envision
                      \nAnswer:
                      \n\"\"<\/p>\n

                      Question 19.
                      \nDivide the number line into equal lengths. Then mark and label the given fraction.
                      \n6 equal lengths; \\(\\frac{5}{6}\\)
                      \n\"Envision
                      \nAnswer:
                      \n\"\"
                      \nExplanation:
                      \nFirst divide the number line into 6 equal parts like in the picture below
                      \n\"\"
                      \nThen mark the 5\/6th point
                      \n\"\"<\/p>\n

                      Question 20.
                      \nTony collects colored strings. The table shows the lengths of some of his strings.
                      \n\"Envision
                      \nA. Measure the lengths of Tony’s red and brown strings shown below to the nearest fourth inch.
                      \n\"Envision
                      \nAnswer:
                      \nRed string\u00a0 \u00a0 \u00a0: 3\u00a0 \u00a0 \u00a0inches
                      \nBrown string : 2\u00be inches<\/p>\n

                      B. Draw a line plot to show the lengths of Tony’s 7 strings to the nearest fourth inch.
                      \nAnswer:
                      \n\"\"<\/p>\n

                      Topic 12 Performance Task<\/h3>\n

                      Art Display
                      \nThree students, Zach, Allie, and Paige, are making an art display.<\/p>\n

                      Use the Paint Colors list and the design at the right to answer Questions 1-4.
                      \nQuestion 1.
                      \nThe display will be divided into 8 equal parts. Paint Colors Draw lines to show one way to do this. Then write the fraction that describes the the total shape that is represented by 1 equal part.
                      \nPaint Colors<\/p>\n

                        \n
                      • Allie is painting the blue parts.<\/li>\n
                      • Paige is painting the red parts.<\/li>\n
                      • Zach is painting the yellow parts.<\/li>\n
                      • \u00a0Each student will paint at least 2 parts.
                        \n\"Envision<\/li>\n<\/ul>\n

                        Answer:
                        \n\"\"
                        \n1\/8 part<\/p>\n

                        Question 2.
                        \nShade the parts blue, yellow, or red to show how many parts each student could paint. Write fractions to show how much of the total display Allie and Paige painted.
                        \nAnswer:<\/p>\n

                        \"\"<\/p>\n

                          \n
                        • Allie is painting the 3 blue parts.\u00a0 \u00a0 \u00a0 3\/8<\/li>\n
                        • Paige is painting the 3 red parts.\u00a0 \u00a0 \u00a0 3\/8<\/li>\n
                        • Zach is painting the 2 yellow parts.<\/li>\n<\/ul>\n

                          Question 3.
                          \nDivide the number line into the number of equal parts of the display. Then mark a dot to show the fraction of the display that Zach painted on the number line.
                          \n\"Envision
                          \nAnswer:
                          \n\"\"<\/p>\n

                          Question 4.
                          \nWhich fraction represents the whole display? Explain. Then mark a dot to show where this fraction is located on the number line above.
                          \nAnswer:
                          \n8\/8 is the whole fraction
                          \n\"\"<\/p>\n

                          Use the Ribbon Lengths diagram on the right and the Number of Ribbons table below to answer Question 5.
                          \n\"Envision<\/p>\n

                          Question 5.
                          \nThe students will use the ribbon lengths at the right in their display
                          \nPart A
                          \nMeasure and record the lengths of each of these ribbons to the nearest fourth inch.
                          \nAnswer:
                          \nRED Ribbon : 3\u00be
                          \nBLUE Ribbon : 3 2\/4\u00a0 [3\u00bd]
                          \nGREEN Ribbon : 3\u00bc<\/p>\n

                          Part B
                          \nThe Number of Ribbons table shows how many of each color ribbon will be used. Draw a line plot to show this data.
                          \n\"Envision
                          \nAnswer:
                          \n\"\"<\/p>\n

                          Question 6.
                          \nIn order to complete the display, the students recorded the number of half-hour sessions they spent working together. The number line below is divided into equal parts. Each part represents half an hour. Write the missing fractions on the number line.
                          \n\"Envision
                          \nAnswer:
                          \n\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

                          Go through the\u00a0enVision Math Common Core Grade 3 Answer Key\u00a0Topic 12 Understand Fractions as Numbers\u00a0regularly and improve your accuracy in solving questions. enVision Math Common Core 3rd Grade Answers Key Topic 12 Understand Fractions as Numbers Essential Question: What are different interpretations of a fraction? Answer: There are five different interpretations of fractions. Explanation: \u00a0Fractions …<\/p>\n","protected":false},"author":1,"featured_media":25594,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/enVision-Math-Common-Core-Grade-3-Answer-Key-Topic-12-Understand-Fractions-as-Numbers.png","_links":{"self":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/8467"}],"collection":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/comments?post=8467"}],"version-history":[{"count":5,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/8467\/revisions"}],"predecessor-version":[{"id":27692,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/8467\/revisions\/27692"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media\/25594"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=8467"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=8467"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=8467"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}