Frames and Arrows Having Two Rules

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1 Frames and Arrows Having Two s Objective To guide children as they solve Frames-and-Arrows problems having two rules. 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 Use dollars-and-cents notation. [Number and Numeration Goal 2] Calculate values of coin and bill combinations. [Operations and Computation Goal 2] Identify and use rules for a function involving addition and subtraction of coins. [Patterns, Functions, and Algebra Goal 1] Key Activities Children make up and solve Frames-and- Arrows problems about coins and use coins to solve Frames-and-Arrows problems having two rules. Ongoing Assessment: Informing Instruction See page Practicing Complements of 100 by Playing Dollar Rummy Math Journal 1, p. 71 Math Masters, pp. 454 and 455 scissors Children find as many different combinations of $00 as possible. Math Boxes 3 6 Math Journal 1, p. 72 Children practice and maintain skills through Math Box problems. Home Link 3 6 Math Masters, p. 78 Children practice and maintain skills through Home Link activities. READINESS Counting Up and Back on a Number Line Math Masters, p. 79 Children find the rules for skip counts on a number line. ENRICHMENT Solving Frames-and-Arrows Puzzles Math Masters, p. 80 and crayons Children explore two-rule Frames-and-Arrows diagrams. Ongoing Assessment: Recognizing Student Achievement Use Math Masters, page 43 [Patterns, Functions, and Algebra Goal 1] Materials Math Journal 1, pp. 69 and 70 Home Link 3 5 Math Masters, pp and 431 transparencies of Math Masters, pp and 431 (optional) per child: 5 quarters, 5 dimes, 5 nickels, and 5 pennies Advance Preparation For the Math Message, make one copy of Math Masters, page 75 for every two children. Cut the copies apart and place them near the Math Message. For Part 1, make overhead transparencies of Math Masters, pages and 431, or draw a two-rule Frames-and-Arrows diagram on the board. Teacher s Reference Manual, Grades 1 3 pp. 205, 206 Lesson

2 Getting Started Mental Math and Reflexes Pose comparison number stories, which practice -9 and -8 subtraction facts or +9 and +8 addition facts, depending on which number model a child uses; for example, = 12 or 12-4 = 8. Have children share strategies. Suggestions: Damian is 6 years old. Maya is 9 years older. How old is Maya? 15 years old Jenna has $4. Martina has $12. How many more dollars does Jenna need in order to have the same amount of money as Martina? $8 Jackson has 14 sports magazines in his collection. Luis has 9. How many more magazines does Luis need in order to have the same number of magazines as Jackson? 5 magazines Math Message Here is a Frames-and-Arrows problem that uses nickels: Take a blank Frames-and-Arrows diagram from Math Masters, page 75. Make up a problem that uses nickels, dimes, or quarters. Hand in your problem. Home Link 3 5 Follow-Up Have small groups of children compare their bar graphs by asking questions like the following: What is the greatest number of pockets shown by any graph? The least number? Use all of your group s graphs. What is the total number of people who had zero pockets? 1 pocket? (Continue with other numbers.) 1 Teaching the Lesson Math Message Follow-Up (Math Masters, p. 75) WHOLE-CLASS 3 6 Frames-and-Arrows Diagrams Algebraic Thinking Choose two of the children s Frames-and- Arrows problems. Review filling in frames and finding a missing rule. Share solution strategies with the class on an overhead transparency of Math Masters, page 75 or on the board. Make sure everyone understands these one-rule Frames-and-Arrows diagrams. Solving Frames-and-Arrows Diagrams Having Two s (Math Masters, pp. 76, 77, and 431) PROBLEM SOLVING WHOLE-CLASS 3 6 Frames-and-Arrows Diagrams Math Masters, p. 75 Algebraic Thinking Display the example on Math Masters, page 76. Ask what is different about this Frames-and-Arrows diagram from Frames-and-Arrows diagrams that children have seen before. Sample answer: There are two kinds of arrows, one dashed and one solid. Explain that the two kinds of arrows stand for two different rules. Have children act out the example with you. Start with a dime as indicated in the first frame, add a nickel (solid-arrow rule) to get the result shown in the second frame, add a dime (dashed-arrow rule) to get the result shown in the third frame, and so on. 214 Unit 3 Place Value, Money, and

3 Adjusting the Activity Have children write the appropriate rule above each arrow to help them navigate filling in the frames. For example, write +10 and -5 above the arrows in Problem 1 on Math Masters, page Two- Frames and Arrows Example: A U D I T O R 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 Repeat the procedure with the other problems on Math Masters, pages 76 and 77. Use the Frames-and-Arrows blank diagrams on Math Masters, page 431 to make up more problems as necessary. Subtract 5 2. Subtract Adjusting the Activity In Problems 4 and 5, children find one of the rules and complete the frames. To find the rule, children should use coins to act out the pattern. Children can then fill in the empty frames. Focus on Problems 1 3. With additional practice on journal pages and in Math Boxes throughout the year, children will be better prepa for Problems like 4 and 5. A U D I T O R 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 76 Math Masters, p Two- Frames and Arrows cont. Teaching Aid Master Two- Frames and Arrows Subtract 10 Math Masters, p Math Masters, p. 431 Lesson

4 Date 3 6 Fill in the frames. Use coins to help you. Two- Frames and Arrows Solving Frames-and- Arrows Problems (Math Journal 1, pp. 69 and 70) PROBLEM SOLVING 2. Subtract Algebraic Thinking Children solve Frames-and-Arrows problems and use coins to help them. Encourage children to check each problem after they have completed it by applying the rules to the completed frames. For example, to check Problem 2, children begin with their answer of 10. The solid-arrow rule is. The second frame is 20. Does = 20? Yes, so the answer is correct. 3. Add Math Journal 1, p. 69 $15 $10 85 Ongoing Assessment: Informing Instruction Watch for children who do not have a strategy for completing Frames-and- Arrows problems where the first frame is blank. Suggest that the children write the rule above the arrows. Use either a number grid or a number line to demonstrate how to count up and back. Creating Frames-and- Arrows Problems (Math Masters, p. 431) Algebraic Thinking Children create and solve their own two-rule Frames-and-Arrows problems. Encourage children to vary the operations and numbers they use for the rules. You may want to have children trade papers with a partner to solve each other s problems. Children should check each other s work. Date 3 6 Two- Frames and Arrows continued 4. Fill in the frames. Use coins to help you. Subtract Ongoing Assessment: Recognizing Student Achievement Math Masters Page 431 Use Math Masters, page 431 to assess children s ability to create number patterns and rules in Frames-and-Arrows problems. Children are making adequate progress if they can make up a problem and complete it accurately. Some children may be able to include more difficult numbers for the rules. [Patterns, Functions, and Algebra Goal 1] Fill in the frames and find the missing rules. Use coins to help you. 5. Add Add $00 $05 $15 $20 $45 $35 $30 Math Journal 1, p Unit 3 Place Value, Money, and

5 2 Ongoing Learning & Practice Practicing Complements of 100 by Playing Dollar Rummy (Math Journal 1, p. 65; Math Masters, pp. 454 and 455) PARTNER Explain the rules of Dollar Rummy on journal page 65. Using game cards cut from Math Masters, page 454, have children find as many different combinations of $00 as they can. For another version, use cards cut from Math Masters, page 455. Math Boxes 3 6 (Math Journal 1, p. 72) Mixed Practice Math Boxes in this lesson are pai with Math Boxes in Lesson 3-8. The skills in Problems 5 and 6 preview Unit 4 content. Date 3 6 Dollar Rummy Materials Dollar Rummy cards (Math Masters, p. 454) scissors to cut out cards cards from Math Masters, p. 455 (optional) Players 2 Skill Find complements of 100 Object of the Game To have more $00 pairs Directions Deal 2 Dollar Rummy cards to each player. 2. Put the rest of the deck facedown between the players. 3. Take turns. When it s your turn, take the top card from the deck. Lay it faceup on the table. 4. Look for two cards that add up to $00. Use any cards that are in your hand or faceup on the table. 5. If you find two cards that add up to $00, lay these two cards facedown in front of you. 6. When you can t find any more cards that add up to $00, it is the other player s turn. 7. The game ends when all of the cards have been used or when neither player can make a $00 pair. 8. The winner is the player with more $00 pairs. EM3cuG2MJ1_U03_53-79.indd 71 Math Journal 1, p /18/10 11:46 AM Home Link 3 6 (Math Masters, p. 78) Home Connection Children use coins to solve Framesand-Arrows problems that have two rules. Date Home Link Master 3 6 Math Boxes Write the amount. Fill in the circle next to the best answer. Â Â Î Í Í 56 A How many children have cats? 15 children How many children have fish? 5 children B 55 C 30 D I had 17 tulips. I planted 20 more. How many do I have now? Start Dogs Cats Birds Fish Change Children End ? Answer: Solve = = Unit = = Children s Pets 4. Tomorrow I will get dressed for the day. (Circle one.) tulips 20 Math Journal 1, p Likely Unlikely Impossible 6. Solve = = = = Unit HOME LINK 3 6 Frames-and-Arrows Problems Family Note Frames-and-Arrows diagrams show sequences of numbers numbers that follow one after the other according to a rule. The problems on this Home Link are a variation of the Frames-and-Arrows problems your child brought home in the last unit. In each of the problems below, two different rules are represented by two different arrows Please return this Home Link to school tomorrow. Show someone at home how to solve these Frames-and-Arrows problems. Use coins to help you. 2. Subtract 5 Math Masters, p EM3cuG2MJ1_U03_53-79.indd 72 12/18/10 11:46 AM Lesson

6 3 6 Counting on the Number Line 3 6 Frames-and-Arrows Puzzles Each puzzle has 2 rules. Figure out where to place the rules to solve the problems. Sample answers: Start at 3. Red rule is Add 2. Blue rule is Add Start at Red rule is Add 4. Blue rule is Add 2. Math Masters, p Math Masters, p Start at 19. Red rule is Subtract 4. Blue rule is Subtract Differentiation Options READINESS Counting Up and Back on a Number Line (Math Masters, p. 79) SMALL-GROUP 5 15 Min To explore navigating on a number line, have children find the rules for skip counts on the number line. Introduce the activity by doing several counts with children on the first number line. They should follow along with their fingers and say each stopping point together. Suggestions: Start at 5 and count up by 2s on the number line. Say the stops together. 7, 9, 11, 13, 15, 17, 19 Ask them if they can think of a rule that would mean the same thing as Count up by 2s. Add 2 Write the rule on the board. Start at 20 and count back by 3s on the number line. Say the stops together. 17, 14, 11, 8, 5, 2 Ask them if they can think of a rule that would mean the same thing as Count up by 3s. Subtract 3 Write the rule on the board. Now work on a couple of two-rule problems together, having children use their fingers to follow along on the number line. Tell children that they have been using only one rule, but that now they are going to do counts with two rules. Suggestions: Start at Combine the Add 3 rule and the Add 2 rule. Say the stops together. 4, 6, 9, 11, 14, 16, 19 Have children repeat this two-rule count. This time, have them draw the hops on the number line. Use the crayon when they add 3 (3 hops) and use the crayon when they add 2 (2-hops). Children work with a partner to complete the page. ENRICHMENT Solving Frames-and- Arrows Puzzles (Math Masters, p. 80) SMALL-GROUP 5 15 Min Algebraic Thinking To further explore two-rule Frames-and- Arrows diagrams, have children solve frames-and-arrows puzzles on Math Masters, page 80. The arrows will not always alternate ABAB. Note that the order in which children place the rules will not matter as long as each rule is used the correct number of times. You may want to have children color-code their rules with crayons underline the first rule in and the second rule in for each problem; then draw the appropriate color arrow between the frames. Have children explain their solution strategies. Sample answer: I always take the biggest rule first until I am close to my number. 218 Unit 3 Place Value, Money, and

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