Assessment Management

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1 Facts Using Doubles Objective To provide opportunities for children to explore and practice doubles-plus-1 and doubles-plus-2 facts, as well as review strategies for solving other addition facts. 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 Develop and practice strategies for addition that use doubles facts. [Operations and Computation Goal 1] Use a variety of addition fact strategies for solving multi-addend addition problems. [Operations and Computation Goals 1 and 2] Key Activities Children identify and practice strategies that use doubles facts. They also practice adding 3 or more addends and discussing the strategies they use. Ongoing Assessment: Recognizing Student Achievement Use Mental Math and Reflexes. [Operations and Computation Goal 4] Key Vocabulary doubles-plus-1 fact doubles-plus-2 fact Materials Math Journal 1, p. 98 Home Link 5 9 counters of two colors or types 3 or 4 dice Advance Preparation Guessing the Grab clear plastic bag pattern blocks paper bag (optional) Children describe the probability of grabbing a given shape from a clear bag containing different shapes. Math Boxes 5 10 Math Journal 1, p. 99 Children practice and maintain skills through Math Box problems. Home Link 5 10 Math Masters, p. 149 Children practice and maintain skills through Home Link activities. READINESS Exploring Doubles number cards 0 10 (from Math Journal 1, Activity Sheet 1; or the Everything Math Deck, if available) counters Children practice with doubles facts using counters. EXTRA PRACTICE Playing Domino Top-It dominoes Children practice comparing quantities and finding sums. Teacher s Reference Manual, Grades 1 3 pp Unit 5 Place Value, Number Stories, and Basic Facts

2 Getting Started Mental Math and Reflexes Tell simple number stories. Children use any strategy to solve them and then share their solution strategies. Summarize solutions with an appropriate diagram and number model. (Remember not to force the solution to a number story into a particular mold.) If children are able to do so, ask them to complete the diagrams and/or suggest a number model. Children should not be expected to do either at this time. Number story suggestions: Malcolm has 7 basketballs and 7 baseballs. How many balls does Malcolm have in all? 14 balls; = 14 Henrietta had 15. She gave the cashier 5 for an eraser. How much money does Henrietta have left? 10 ; 15-5 = 10 Raymond and Eli collect baseball cards. Raymond has 19 cards. Eli has fewer cards than Raymond. The difference between the number of cards that Raymond has and the number of cards Eli has is 10. How many cards does Eli have in all? 9 cards; 19 9 = 10 Math Message Write 5 doubles facts that you are sure about. Home Link 5 9 Follow-Up Briefly go over the answers. Ongoing Assessment: Recognizing Student Achievement Mental Math and Reflexes Use Mental Math and Reflexes to assess children s ability to solve simple number stories. Children are making adequate progress if they are able to correctly answer the first problem. Some children might answer all three problems with relative ease. [Operations and Computation Goal 4] 1 Teaching the Lesson Math Message Follow-Up DISCUSSION Ask children to name the doubles facts they know. List doubles facts in a column on one side of the board until you have listed all of the facts from = 2 through = 20. Leave enough space between each doubles fact to write an additional fact later in the activity. Ask: What do all doubles facts have in common? Sample answers: Both addends are the same; the sums are all even. Tell them that today they will learn how to use doubles facts to solve other facts. Introducing Doubles-Plus-1 Facts Without erasing the doubles facts you listed on the board for the Math Message Follow-Up, focus children s attention on = 10. Have children use one color or type of counters to show two columns of 5 counters each. Represent this on the board with a drawing labeled = = 10 Lesson

3 5 + 5 = = 11 NOTE Knowledge of doubles facts is important, as this lesson focuses on strategies that assume quick recall of these facts. Daily practice of the doubles facts will help reinforce this skill. NOTE Be sure to add Doubles-Plus-1 and Doubles-Plus-2 strategies to your Fact Strategy Wall. Have children add one counter of a different color or type to the top of one column. Represent this on the board by drawing a counter of a different color on top of the right column. Ask: How is this like = 10? How is it different from = 10? Sample answer: It still has two sets of 5 counters, but it has 1 extra counter in one of the columns. Below the drawing, write the number model = 10. Ask: Is this number model true or false? false Erase the 10. How could you use doubles to solve this problem? You can add = 10 and then add one more to make 11. Write 11 to the right of the equals sign. Ask: Is this number model true or false? true Explain that this is called a doubles-plus-1 fact. Repeat this activity with several other doubles-plus-1 facts. Then ask children to look at the list of doubles facts on the board and name some doubles-plus-1 facts that could be solved using the doubles facts. Insert these doubles-plus-1 facts next to the doubles facts in your list of facts. Point to various facts and ask how children could use doubles facts to find the sums. Once children seem to grasp the strategy, ask them to describe the strategy to put on the Fact Strategy Wall. For example, for the fact 3 + 4, children might say: You know that = 6. Since 4 is one more than 3, then is one more than So to solve 3 + 4, you can think of the problem this way: = 6 and = 7 so = 7. Introducing Doubles-Plus-2 Facts Begin again with the doubles fact = 10 written on the board and represented by two columns of 5 counters of the same color or type. Have children make two columns of 5 counters. Have children add two counters of a different color or type to one column. Draw two different counters at the top of one of your columns. Change the number model to = 10. Ask: Is this number model true or false? false Erase the 10. Ask: How can we use the doubles fact = 10 to solve this problem? Since = 10 and there are 2 extra counters, add 2 to 10. Since = 12, then = 12. Explain that this is called a doubles-plus-2 fact. Write 12 to the right of the equals sign. Ask: Is this number model true or false? true 404 Unit 5 Place Value, Number Stories, and Basic Facts

4 Ask: Can anyone think of another doubles fact that can be used to solve this problem? This will likely be a difficult question for children to answer. Guide children by moving one of the counters from the taller column to the shorter column. Again ask: Can anyone think of another doubles fact that can be used to solve this problem? Children should now be able to see that = = 12. Have children use counters to practice using both methods to solve a variety of doubles-plus-2 facts. Some children will find that one method is easier for them than the other. Practicing Using Doubles to Add (Math Journal 1, p. 98) INDEPENDENT In Problems 1 3, children solve problems that could be solved using the doubles-plus-1 strategy. In Problems 5 7, they solve problems that could be solved using the doubles-plus-2 strategies. Take care, however, not to force a particular strategy for a problem. Your most efficient strategy for solving a particular problem may not be the most efficient strategy for every child. Demonstrating a variety of strategies and allowing children to share and discuss their own strategies with the class will allow children to internalize the strategies that are most efficient for them over time. Problems 4 and 8 will give insight into what strategies children are using most comfortably. Date LESSON 5 10 Using Doubles Facts Add. Use doubles facts to help you = = = 7 4. Explain how you solved Answers vary = = = Explain how you solved Answers vary. Math Journal 1, p _EMCS_S_G1_MJ1_U05_ indd 98 Student Page 3/10/11 12:33 PM Doing a Dice-Roll Activity Ask a child to roll the dice and say aloud the numbers shown. Write the numbers on the board as an addition number model with an answer box for the sum. Have another child describe one strategy for adding the numbers. Show the order in which the child adds the numbers by connecting pairs of numbers and writing their sum. Write the sum of the numbers in the answer box. Refer to the Fact Strategy Wall as strategies arise (doubles, doubles-plus-1, doubles-plus-2, making ten, +10, etc.). Write the number model again and ask other children to add in a different order while you note the steps, the strategies used, and the sum. You may wish to use this activity as an ongoing routine to practice fact strategies. As your class becomes more comfortable, try these variations: roll additional dice, roll again when a 1 appears on a die, or include one or more polyhedral die (8 20 sides). Have partnerships or individuals roll dice and record their work on slates or on paper = Lesson

5 2 Ongoing Learning & Practice Guessing the Grab Display a large, clear plastic bag containing 3 orange squares and 5 green triangles. Explain that you are going to close your eyes, reach into the bag, and grab a shape. Ask them which shape they think you will likely grab. Allow them to explain their reasoning. Then grab and remove a shape. Children continue to make predictions about what shape you will remove. Continue to remove shapes from the bag until the bag is empty. Refill the bag with different shapes. Repeat the activity. After doing this activity several times, discuss children s observations. For example: The shape with the greatest quantity is likely to be grabbed. The shape with the least quantity is unlikely to be grabbed. As you remove shapes from the original bag, the likelihood of which shape you grab will change. Adjusting the Activity When children start to see patterns in probability, do this activity with a brown paper bag. Show children what shapes and how many of each shape are in the bag. Then ask them which shape they think you are most likely to remove. Continue the activity as described. 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 Links to the Future Guessing the Grab gives children the opportunity to use the most basic language of probability. They will be exposed to this language throughout the year. Explaining the most basic language of probability is a Grade 2 Goal. 406 Unit 5 Place Value, Number Stories, and Basic Facts

6 Math Boxes 5 10 (Math Journal 1, p. 99) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson The skills in Problem 4 preview Unit 6 content. Home Link 5 10 (Math Masters, p. 149) INDEPENDENT Home Connection Children find the sums of near-doubles addition facts and solve base-10 block riddles. 3 Differentiation Options READINESS Exploring Doubles (Math Journal 1, Activity Sheet 1) PARTNER 5 15 Min To explore doubles using a concrete model, have children model doubles facts using counters. Children mix up number cards and place them in a deck facedown. One child selects a number card and uses that number of counters to make a row. The other child uses the same number of counters to make a row beside the first row. Children each write the doubles fact represented by the counters on a sheet of paper. They draw a picture to go with their doubles fact. Children repeat this activity as time allows. Date LESSON 5 10 Math Boxes 1. Draw and solve. Jade has 5 pennies. Max has 9 pennies. Who has fewer pennies? Jade How many fewer pennies? 4 fewer pennies Sample answer: 3. Record the temperature. F F Math Journal 1, p _EMCS_S_G1_MJ1_U05_ indd 99 Student Page 2. Add = = Count up by 5s. 25,,,,,,, NOTE Remember to reserve time every day to complete the number-line, attendance, calendar, weather, and temperature routines. Name Home Link Master Date 2/17/11 12:41 PM HOME LINK 5 10 Using Doubles Facts Family Note Today children used doubles facts to solve other addition facts. For example, if children know that = 10, then they can use that to solve by solving and adding 1 more. So = 11. We call these doubles-plus-1 facts. Children also learned doubles-plus-2 facts, such as By adding 1 to the larger addend and subtracting 1 from the smaller addend, children can use = 14 to solve = 14. Doubles-plus-2 facts can also be solved by doubling the smaller number and adding 2 more. Review doubles-plus-1 and doubles-plus-2 facts with your child. Please return this Home Link to school tomorrow. Write the sums. Tell someone at home how you can use doubles facts to solve the problems = = = Practice Solve the riddles and 4 = and 7 = 47 Math Masters, p _EMCS_B_MM_G1_U05_ indd 149 3/11/11 11:18 AM Lesson

7 PARTNER EXTRA PRACTICE Playing Domino Top-It Min Children determine sums and compare quantities by playing Domino Top-It. Directions 1. Children place the dominoes facedown on the table. 2. Each child chooses a domino and compares the total number of dots to the total number on his or her partner s domino. 3. The child with the larger total takes both dominoes. Ties are settled by another draw. 4. The game ends when time is up or when all of the dominoes have been drawn. Planning Ahead Provide time for children to work on the number scrolls that they began in Lesson Unit 5 Place Value, Number Stories, and Basic Facts

8 Name Date HOME LINK 5 10 Using Doubles Facts Family Note Today children used doubles facts to solve other addition facts. For example, if children know that = 10, then they can use that to solve by solving and adding 1 more. So = 11. We call these doubles-plus-1 facts. Children also learned doubles-plus-2 facts, such as By adding 1 to the larger addend and subtracting 1 from the smaller addend, children can use = 14 to solve = 14. Doubles-plus-2 facts can also be solved by doubling the smaller number and adding 2 more. Review doubles-plus-1 and doubles-plus-2 facts with your child. Please return this Home Link to school tomorrow. Write the sums. Tell someone at home how you can use doubles facts to solve the problems = 2. = = Copyright Wright Group/McGraw-Hill Practice Solve the riddles and 4 = 9. 4 and 7 = 149

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