Pattern-Block Fractions

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1 Pattern-lock Fractions Objective To guide students as they find fractional parts of polygonal regions. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Identify the whole or the ONE. [Number and Numeration Goal ] Find fractional parts of polygonal regions. [Number and Numeration Goal ] Identify equivalent fractions. [Number and Numeration Goal 5] Model fraction addition with pattern blocks. [Operations and Computation Goal 5] Identify a triangle, hexagon, trapezoid, and rhombus. [Geometry Goal ] Key Activities Students use pattern blocks to partition -dimensional shapes, and they name fractional parts of regions. Informing Instruction See page 5. ecognizing Student Achievement Use a Math Log or Exit Slip (Math Masters, page or ). [Number and Numeration Goal ] Materials Math Journal, pp. Study Link 7 Math Masters, p. ; p. or (optional) transparency of Math Masters, p. (optional) pattern blocks straightedge slate overhead pattern blocks (optional) pencil or marker (optional) chart paper (optional) Math oxes 7 Math Journal, p. 7 Students practice and maintain skills through Math ox problems. Study Link 7 Math Masters, p. Students practice and maintain skills through Study Link activities. EADINESS uilding ectangles Math Masters, p.,, and green crayons scissors,, and green colo tiles (optional) Students use colo squares to build different rectangles. ENICHMENT Exploring Tangrams Math Masters, pp. 5 and scissors Students determine values of tangram pieces. ENICHMENT Writing Fraction and Mixed-Number Addition Number Stories Students decompose fractions and mixed numbers to write addition number stories with the same answer. Advance Preparation For Part, each partnership or small group needs at least yellow,,, and green pattern blocks. Teacher s eference Manual, Grades pp., Lesson 7 57

2 Getting Started Mental Math and eflexes Pose fraction-of problems. Suggestions: _ of 0 = 5 _ of = _ 5 of 5 = _ of 0 = 5 5_ of = 0 _ 5 of 5 = _ 7 of = 5 _ of = _ of 0 = 0 or $.0 Math Message _ of the students in Mrs. Lopez s class went to the soccer game. _ of the students in Mr. Williams s class also went to the game. Did the same number of students from each class go to the game? Study Link 7 Follow-Up Have students pose the events they made up in Problem and ask partners to find the probabilities. For Problem, have students describe how their pictions for the experiment compa with the actual results. Teaching the Lesson Math Message Follow-Up DISCUSSION As students share their ideas, help them understand that a fraction that is used to name part of a collection is not meaningful if one does not know what it is a fraction of that is, what the whole collection is. For example, half of each class went to the game, but the classes may have different numbers of students. Tell students that in this lesson they will explore how the values of individual pattern blocks change when the whole changes. 7 Pattern-lock Fractions Use Math Masters, page. For Problems, Shape A is the whole.. Cover Shape A with trapezoid blocks. What fraction of the shape is cove by trapezoid?. Cover Shape A with rhombuses. What fraction of the shape is cove by rhombus? rhombuses?. Cover Shape A with trapezoid and triangles. With a straightedge, draw how your shapes look on the hexagon at the right. Label each part with a fraction. 5. Cover Shape A with rhombuses and triangles. Draw the result on the hexagon below. Label each part with a fraction.. Cover Shape A with triangles. What fraction of the shape is cove by triangle? triangles?,or 5 5 triangles?. Cover Shape A with trapezoid, rhombus, and triangle. Draw the result on the hexagon below. Label each part with a fraction. Shape A: small hexagon Exploring Fractional Parts of egions with Pattern locks Lesson 7- consists of three sets of problems. Each set requires the use of one of the three shapes on Math Masters, page and a set of pattern blocks. Each shape can be completely cove by pattern blocks. In each set of problems, students do the following:. Determine what fraction of the shape is cove by each pattern block.. Cover the shape on the master with pattern blocks, as indicated on the journal page.. ecord a partition of the shape on journal page, 5, or.. Label each fractional part of the shape with a fraction. Math Journal, p. 5 Unit 7 Fractions and Their Uses; Chance and Probability

3 Adjusting the Activity Write each of the pattern-block names on the board or on chart paper in the color that matches the block. For example, write rhombus in and triangle in green. A U D I T O Y K I N E S T H E T I C T A C T I L E V I S U A L Solving Problems about Shape A (Math Journal, p. ; Math Masters, p. ) Have students form partnerships or small groups, and pass out pattern blocks, but work with the whole class on Problems on journal page. Students should use Shape A on Math Masters, page for the problems on this journal page. Ask the questions on page one at a time. Have students solve them using pattern blocks and then record their answers in the journal. Consider using a transparency of the master and overhead pattern blocks as you discuss the problems and answers. ELL 7 Pattern-lock Fractions continued Use Math Masters, page. For Problems 7, Shape is the whole. 7. Cover Shape with trapezoids. What fraction of the shape is cove by trapezoid? trapezoids? trapezoids?. Cover Shape with rhombuses. What fraction of the shape is cove by rhombus? rhombuses? 5 rhombuses?. Cover Shape with triangles. What fraction of the shape is cove by triangle?, triangles? or triangles? 0. Cover Shape with hexagons. What fraction of the shape is cove by hexagon? hexagons?. Cover Shape completely with hexagon, rhombus, triangle, and trapezoid. Draw the result on the figure at the right. Label each part with a fraction.. Cover Shape completely with trapezoid, rhombuses, and 5 triangles. Draw the result on the figure at the right. Label each part with a fraction., or, or 5 Math Journal, p. 5 Shape : double hexagon, or Adjusting the Activity ELL Have students write number models to illustrate how Shape A was cove with pattern blocks in Problems. Problem : _ + _ + _ + _ = Problem 5: _ + _ + _ + _ = Problem : _ + _ + _ = A U D I T O Y K I N E S T H E T I C T A C T I L E V I S U A L Solving Problems about Shape (Math Journal, p. 5; Math Masters, p. ) PATNE efore students begin Problems 7 on journal page 5, have them observe that Shape is not the same size as Shape A; therefore, each pattern block takes on a different fractional value. Discuss solutions. Informing Instruction POLEM SOLVING Watch for students who continue to use the single hexagon as the whole. Emphasize that the whole or the ONE is different than that used for the problems on journal page. Encourage students to circle the whole box with a pencil or marker to remind them of the new whole. 7 Pattern-lock Fractions continued Use Math Masters, page. For Problems, Shape C is the whole. Try This. Cover Shape C with trapezoids. What fraction of the shape is cove by trapezoid?, trapezoids? or trapezoids?. Cover Shape C with rhombuses. What fraction of the shape is cove by rhombus?, rhombuses? or rhombuses? 5. Cover Shape C with triangles. What fraction of the shape is cove by triangle?, triangles? or triangles?, or, or, or. Cover Shape C completely, using one or more trapezoids, rhombuses, triangles, and hexagons. Draw the result on the big hexagon below. Label each part with a fraction. Sample answer: Shape C: big hexagon Math Journal, p. Lesson 7 5

4 7 Math oxes. What fraction of the clock face is shaded?, or. Draw angle LMN that measures 0. L Solving Problems about Shape C (Math Journal, p. ; Math Masters, p. ) PATNE POLEM SOLVING. a. In December, of a foot of snow fell on Wintersville. How many inches of snow fell? inches 5 M N obtuse LMN is an (acute or obtuse) angle.. Divide. Use a paper-and-pencil algorithm., or 0 / Problems on journal page are challenging. ecause it is not possible to completely cover Shape C with hexagon blocks, students must determine the fractional values of other pattern blocks. For example, because two trapezoids make one hexagon and one trapezoid is _ of Shape C, a hexagon is _, or _, of Shape C. b. Tina s daughter will be 5 of a year old next week. How many months old will she be? 0 months 5. Each student eats an average of 7 servings of junk food per week. About how many servings of junk food would a class of students eat in a week? 5 servings Math Journal, p Find the area of the figure. square centimeter Area 7.5 square cm 7 ecognizing Student Achievement Math Log or Exit Slip Use a Math Log or an Exit Slip (Math Masters, page or ) to assess students understanding of the relationship between the whole and its fractional parts. Have students explain why the same pattern blocks take on different fractional values for each of Shapes A,, and C. Students are making adequate progress if they indicate that the shapes represent different wholes. Some students may note the relationship between the size of the shapes and how this relationship affects the fractional values of the pattern blocks. For example, the area of Shape is twice the area of Shape A. Therefore, the fractional value of each pattern block for Shape is half its fractional value for Shape A. The area of Shape C is four times the area of Shape A. It takes trapezoids to cover Shape C and trapezoids to cover Shape A. [Number and Numeration Goal ] Ongoing Learning & Practice Study Link Master Name Math oxes 7 (Math Journal, p. 7) STUDY LINK 7 Dividing Squares Use a straightedge and the dots below to help you divide each of the squares into equal parts. Example: Squares A,, C, and D are each divided in half in a different way. A C D. Square E is divided into fourths. Divide squares F, G, and H into fourths, each in a different way. Sample answers: 5 Mixed Practice Math oxes in this lesson are pai with Math oxes in Lesson 7-. The skill in Problem previews Unit content. Writing/easoning Have students write a response to the following: Explain how you determined the number of months in Problem b. Sample answer: There are months in a year. _ of =, so 5_ of = 0. E F G H. Square I is divided into eighths. Divide squares J, K, and L into eighths, each in a different way.sample answers: Study Link 7 (Math Masters, p. ) I J K L. osa has 5 quarters and 0 nickels. She buys juice from a store for herself and her friends. The juice costs 5 cents per can. She gives the cashier _ of the quarters and _ 5 of the nickels. The cashier does not give her any change. How many cans of juice did she buy? cans Home Connection Students divide squares into fourths and eighths in different ways. Show your work on the back of this paper. Practice = = = = Math Masters, p. 0-_EMCS MM_G_U07_575.indd /5/ :57 AM 50 Unit 7 Fractions and Their Uses; Chance and Probability

5 Differentiation Options 7 Teaching Master Name Fractions of ectangles Use,, and green crayons to color the squares at the bottom of the page. Cut out the squares. If your teacher has colo tiles, use those instead. EADINESS uilding ectangles (Math Masters, p. ) PATNE 5 5 Min To explore the relationship of fractional parts to the whole or the ONE, have students use colo squares or tiles to build different rectangles divided into the same fractional parts. ENICHMENT Exploring Tangrams (Math Masters, pp. 5 and ) 5 0 Min To further explore the concept of fractional parts of polygonal regions, have students determine the values of tangram pieces. Sample answer: Use your colo squares to build the following rectangles in at least two different ways. ecord your work.. _ and _. _, _, _ green. _, _, _ green. Make up a problem of your own. G,, green Answers vary. G G G G G G green green green green green green green green green green Math Masters, p. Sample answers: Math Masters, page 5 Problem 5 Completed tangram puzzle ENICHMENT PATNE Writing Fraction and Mixed-Number Addition Number Stories 5 0 Min To explore decomposing fractions and mixed numbers, have students write addition number stories using the same fraction or mixed number as the sum. For example, students write a number story with the answer _ that involves adding fractions with the same denominator. Stories might look similar to the following: Abby used _ cup of flour in one recipe and _ cup of flour in another. How much flour did she use in all? Supat gave _ of his baseball cards to his brother, _ of the cards to his cousin, and _ of the cards to his friend. What fraction of his baseball cards did Supat give away? Have students share their stories with a partner and have them record summary number models. Sample answers: _ + _ = _ ; _ + _ + _ = _ Encourage partners to write stories that have a different summary number model than the ones that have already been recorded. epeat this activity with different fractions and mixed numbers. Suggestions: 5 0 Name 7 Exploring Tangrams. Cut out the tangram pieces at the top of Math Masters, page, and use all 7 pieces to create the large square at the bottom of the page.. If the large square is the whole, or the ONE, find the value of each of the tangram pieces.. Describe the strategy you used to find the value of the small triangle. Sample answer: I figu out how many small triangles it takes to make each of the other shapes. If I were to use just small triangles to make the large square, it would take small triangles. So, a small triangle has a value of _.. Describe how you can prove that you found the correct value of the small triangle. Sample answer: I could add all the values for each piece needed to make the whole to show that they add up to _, or ( _ + _ + _ + _ + _ + _ + _ ). Try This Teaching Master Small Large Medium Small Parallelogram Square Triangle Triangle Triangle _ 5. Use several tangram pieces to create a polygon for which the small square is worth _. Trace the polygon on the back of this page. Give the value of each tangram piece in the polygon. Math Masters, p. 5 Lesson 7 5

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