Balance Me! LESSON OVERVIEW BUILDING CONCEPTUAL KNOWLEDGE SETTING THE STAGE. Model how to use a balance with quantities of identical objects.

Transcription

1 Balance Me! LESSON FOCUS Using concrete objects to solve equations with one unknown. COMPANION ANCHORS LESSONS Balance Models for Equations; Writing Number Sentences MATERIALS Excursions student pages Transparencies TR1 TR2 Home Connection pages Various classroom objects to use on the balance, for example, pencil, eraser, blocks, book, box of tissues, box of crayons Snap cubes Balances Scissors add balance equal level missing number not equal LANGUAGE DEVELOPMENT LESSON OVERVIEW number sentence plus same symbol quantity In this lesson, children become familiar with the balance as a model of an equation. The balance is used to model and find missing numbers in addition problems. Children learn to read and solve number sentences with one unknown addend. They also play a game of What s the Other Number? to find sums and missing addends. SETTING THE STAGE Model how to use and read a balance. Place an object, for example, a pencil, on one side of the balance and an eraser on the other side. Ask children if the balance is level or not. Discuss what this tells about the objects. Ask if the two objects weigh the same (equal in weight) or not (not equal in weight). Repeat using different objects, such as two different blocks, a book and a block, or a box of tissues and a box of crayons. Guide children to see that equal quantities (weight) make the balance level. Model how to use a balance with quantities of identical objects. Once children are comfortable with knowing how the balance works and telling if the quantity on one side is equal or not equal to the quantity on the other side, place one snap cube on each side. Explain that the balance can be used for comparing the number of objects if the objects are all the same. Ask if the two snap cubes are equal (yes). Continue by putting three cubes on one side and one on the other, letting children see that the balance is not in equilibrium. Then add two cubes to make the number of cubes on each side the same (3). Discuss with children what they think made the balance level and why it did. Display the transparency of Balance Me! TR1. Choose two boxes of cubes, for example, A and C, and ask children if they are equal in number or not. Have children predict what will happen if the cubes were put on opposite sides of the balance. Then check children s answers by modeling the problem on the balance. Repeat with other pairs of boxes, making sure to include at least one case where the sets are equal. BUILDING CONCEPTUAL KNOWLEDGE Introduce number sentences and symbols as means of representing the actions on a balance. Remind children about how you leveled the balance when there were 3 cubes on one side and 1 on the other. (You added 2 cubes to the side with 1 cube.) Model other unequal sets of cubes on the balance, for example, three cubes on one side and five on the other. Have children suggest what to add to one side to make the balance level (2 cubes). Tell children that if they are using objects that are the same, they can write a number sentence to describe what happens on the balance. Explain that when we write number sentences we use symbols. Write the numeral 2 on the board or overhead 85

2 UNIT C Balance Me! projector. Ask children what this symbol means. They should be able to tell you that it is the number two and it represents a quantity. Write a symbol. Ask children whether they know what this symbol means. If they are unsure, tell them that it means add. When we see it in a number sentence, we often say plus. Write an symbol and ask children what it means. Encourage them to describe it in terms of value or quantity and to tell that it means the quantity on one side of the symbol is the same as the quantity on the other side. Remodel the problem on the balance using an equal label. Write a large symbol on a card, and place it on the fulcrum of the balance. Tell children that the left side of the balance will represent what is on the left side of the equal sign, and the right side of the balance will represent what is on the right side of the equal sign. Write Tell children that this is a number sentence. Read it aloud as you point to the symbols. Then, as you remodel this problem, explain, This sentence represents what we did on the balance. We had three cubes on one side and five cubes on the other. We added two cubes to the three cubes to make five cubes and that made the balance level. Introduce a box as a symbol for an unknown in an equation. Display the transparency of Balance Me! TR2, showing only the first number sentence. Ask, What symbols, other than number symbols, do you see in this number sentence? Point out the plus sign and the equal sign. Ask children what each symbol means. Point out the square and explain that we sometimes use symbols in the place of numbers we don t know. Any symbol can be used. In this number sentence, we are using a square. We want to know what number, represented by the square, is added to 3 so that we have a sum (total) of 6. Continue with the next two number sentences. Point out that the symbol does not always have to be just before the sum. Show them the fourth number sentence, and point out that the sum is on the left side of this number sentence. Name Name Balance Me! BALANCE IT! 5Use a balance scale and snap cubes. Find the missing addends. Then complete each number sentence = School District of Hillsborough County. Copying this page without written permission of Metropolitan Teaching and Learning Company is illegal. 7 = = 4 = +?? + = = 8 8 = ? = 5 = = = = 9 9 = = 7 School District of Hillsborough County. Copying this page without written permission of Metropolitan Teaching and Learning Company is illegal UNIT C Balance Me! one hundred twenty-one 121 UNIT C Balance Me! one hundred twenty-three 123 Page 121 Page

3 UNIT C Balance Me! Use a balance to find missing addends in equations with one unknown. Show the first number sentence on Balance Me! TR2. Point to the symbol. Place 3 snap cubes on the left and 6 on the right of the balance scale so that it matches the number sentence 3 6. Ask, What happened to the balance? (The right side of the balance is heavier, so it dropped below the left.) Ask your class how to make the two sides balanced again. Guide children to see that more cubes should be added to the left side. Refer back to the number sentence. Point to the square. Remind children that the square represents a missing quantity. Tell children that they are going to find the missing number. Add one snap cube at a time to the left side of the balance as you count aloud. Stop when the balance is level. Ask children how many cubes you added to the left side (3). Write 3 on the transparency. Repeat this activity with the other four number sentences. You might ask children to come up and demonstrate how to solve for the unknown number after you have modeled a few. BUILDING SKILLS AND STRATEGIES Children in groups of three find missing addends using a balance. Place children into groups of two or three. Give each group a balance, 20 snap cubes, and a small square of paper. Ask children to write an equal sign on the paper. They should then attach it to the fulcrum of their balance. Have children turn to Balance It! Page 121. Tell children that they will complete this activity in the same way the class solved the problems on the overhead Balance Me! TR2. Tell them to place the quantity on the left side of the equation on the left side of the balance and the quantity on the right side of the equation on the right side of the balance. Then find the missing quantity by using snap cubes to make the balance level. Tell them to write the missing number in the equation. Let children work on the activity as you circulate. PUTTING IT INTO ACTION Demonstrate the game What s the Other Number? Ask two children to help you demonstrate a new game. Have them stand at the board with their backs to each other. Ask them to each write a number between 0 and 10 on the board without looking at the other player s number. You may need to use a smaller range of numbers at first, such as between 0 and 5. 7? Tell the two players that they are to look only at their own number. Explain that you are going to tell them the sum of the 2 numbers. After they hear the sum, they should figure out what number the other player wrote on the board. When they know the other player s number, they should say it aloud. For example, the player on the left would be thinking 7? 9. The player on the right would be thinking 2? 9. Give each player an opportunity to discover the other child s number. You may need to help some players use a strategy such as counting on to find the missing addend. Repeat this activity, giving all children a chance to play. Once children understand the game, a child may fill the teacher role. Groups of three children play What s the Other Number? Once children can play the game, divide them into groups of three. Ask one child in each group to tear out What s the Other Number?, page 123, and have the children cut apart the cards. The cards should be mixed up and placed face down.? 2 87

4 UNIT C Balance Me! Ask one child in each group to draw two cards and say the sum. Then he or she gives the other two children one card each. Each child looks only at his or her card and tries to figure out the other child s number. The child who responds with the correct missing addend draws two cards and says the sum in the next round. HOME CONNECTION Have children take home and complete Home Connection, pages 125 and

5 Name Balance Me! BALANCE IT! 5Use a balance scale and snap cubes. Find the missing addends. Then complete each number sentence. = School District of Hillsborough County. Copying this page without written permission of Metropolitan Teaching and Learning Company is illegal. 7 = 2 + = +? 4 + = 8 +? = 5 = = 6 9 = = 4? + = 8 = = = = 7 UNIT C Balance Me! one hundred twenty-one 121

6 122 one hundred twenty-two

7 Name School District of Hillsborough County. Copying this page without written permission of Metropolitan Teaching and Learning Company is illegal UNIT C Balance Me! one hundred twenty-three 123

8 124 one hundred twenty-four

9 Name HOME CONNECTION: FINDING ADDENDS Dear Parent or Guardian: Your child has been learning about finding missing addends. Addends are the numbers that are added together in an addition sentence. For example, in the addition sentence = 5, the numbers 3 and 2 are the addends. School District of Hillsborough County. Copying this page without written permission of Metropolitan Teaching and Learning Company is illegal. Read the instructions and the problems on the other side of this sheet aloud to your child. Help your child come up with the first addend in each problem. Have him or her use whole numbers. For example, if your child s school day is 6 1 /2 hours, have him or her use 7 hours in the problem. Then have your child complete the page. Have your child share the finished page with you. UNIT C Balance Me! one hundred twenty-five 125

10 HOME CONNECTION: FINDING ADDENDS 5Complete the following questions based on data you collect at home. 1. How many more teeth do you need to lose to have lost 10 teeth? number of teeth you have lost How many more hours would you need to sleep each night if you wanted to sleep 15 hours each night? number of hours you sleep How many more hours would you spend in school each day if the school day were 10 hours long? number of hours in your school day How many more times a day would you need to brush your teeth if you wanted to brush your teeth 5 times each day? number of times you brush your teeth each day one hundred twenty-six UNIT C Balence Me!

11 A B C D E F Unit C Balance Me! TR1

12 Unit C Balance Me! TR2