Change-to-More Number Stories

Transcription

1 -to-more Number Stories Objective To guide children as they solve change-to-more number stories. 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 basic addition and subtraction facts to compute extended facts. [Operations and Computation Goal 1] Use simple addition facts. [Operations and Computation Goal 1] Create and solve change-to-more number stories. Use a parts-and-total diagram. Key Activities Children are introduced to the change diagram for recording known and missing information in change-to-more number stories. They then solve change-to-more number stories, displaying the information in change diagrams. Ongoing Assessment: Informing Instruction See page 251. Ongoing Assessment: Recognizing Student Achievement Use journal page 81. Key Vocabulary change-to-more number story change diagram mental arithmetic Materials Math Journal 1, pp My Reference Book, pp transparency of Math Masters, p. 432 (optional) pan balance water two paper towels Finding Distances on a Number Grid Math Journal 1, p. 83 penny or other small object Children practice finding the distance between two numbers on a number grid. Math Boxes 4 1 Math Journal 1, p. 84 Children practice and maintain skills through Math Box problems. Home Link 4 1 Math Masters, pp. 90 and 91 Children practice and maintain skills through Home Link activities. READINESS Using a Scale to Show More (or Less) bath scale objects such as books Children are introduced to the concept of change-to-more by weighing objects on a scale. ENRICHMENT Writing -to-more Stories Math Journal 1, p. 80 Math Masters, p. 419 Children use the Fish Poster to write and solve change-to-more stories. Advance Preparation Decide how you will display a change diagram. Make an overhead transparency of Math Masters, page 432, or draw and erase the diagrams on the board as needed. Teacher s Reference Manual, Grades 1 3 pp. 18, Unit 4 Addition and Subtraction

2 Getting ed Mental Math and Reflexes How much? Have children explain their answers., 50,,, Í, Â 90 Á, 5, 2 Í, 1 Â $2.50, Â 30 Í, Í, Í, Â, Î, Î 37 2 Á, 3, 3 Í, 2 Î $3.07, Í 35 Í,, Â, Î 41 2 Á, 6, 4 Í, 2 Â $4.00 Math Message Which weighs more a dry paper towel or a wet paper towel? Why? Wet; the water adds weight. 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS Interactive whiteboard-ready epresentations are available at to help you teach the lesson. The weight of the paper towel increases, or changes to more, when it absorbs liquid. Do the following demonstration with the class. Fold or wad two paper towels of the same size, and place one on each side of a pan balance. The pans will be in balance. Then soak one of the towels in water, wring it out, and put it back in the empty pan. Ask children to explain how they know which towel is heavier. Sample answer: The wet towel is heavier because that pan is lower. Introducing the Diagram (Math Journal 1, p. 80; My Reference Book, pp ) WHOLE-CLASS DISCUSSION NOTE Everyday Mathematics approaches addition and subtraction by exploring these operations in situations in which they are used. Most instances of addition and subtraction can be categorized as parts-and-total, change, or comparison situations. situations come in two types: change-to-more and change-toless. -to-more is also known as adding to and change-to-less can also be understood as taking from. Parts-and-total situations are also known as putting together or taking apart situations. Children are not expected to categorize number stories in these terms at this time. Later lessons will include practice with all types of situations. Read more about addition and subtraction situations in the Teacher s Reference Manual, pages Algebraic Thinking In a change number story, there is a starting quantity. This quantity is increased (or decreased) so the ending quantity is more (or less) than the starting quantity. The focus in this lesson is on change-to-more number stories, in which the starting quantity is increased. -to-less number stories will be discussed in Lesson 4-4. Have children turn to the Fish Poster on journal page 80. Make up a change-to-more number story based on the Fish Poster. For example: Fish K weighs 35 pounds. It swallows Fish D, which weighs 5 pounds. How much does Fish K weigh now? Draw a blank unit box on the board. Ask: Which label goes in the unit box? pounds Display a change diagram (see Advance Preparation) and discuss it as you fill in the numbers. Ask questions such as the following: What do we want to find out from the story? How much Fish K weighs now Do we know Fish K s weight before it swallowed Fish D? Yes, 35 pounds 4 1 Fish A 1 lb 12 in. Fish Poster Fish E 6 lb 24 in. Fish H 14 lb Fish B 3 lb 14 in. Fish F 8 lb Fish I 15 lb Fish K 35 lb 42 in. Math Journal 1, p. 80 Fish C 4 lb 18 in. Fish L 100 lb 72 in. Fish D 5 lb 24 in. Fish G 10 lb Fish J 24 lb 36 in. Lesson

3 Unit pounds 35 +5? =? = 40 NOTE Children are not expected to draw change diagrams at this time. Situation diagrams are provided to help children organize information to solve number stories. Some children may find other strategies more helpful than situation diagrams. NOTE Encourage children to use the number line or number-grid to assist them in finding their solutions. Write 35 in the box. What change occurred? Fish K gained 5 pounds Is this a change to more or change to less? To more Write +5 in the box. Then write? in the box. Tell children that the question mark represents how much Fish K weighs now. How do we find Fish K s weight after it has swallowed Fish D? Add What is Fish K s final weight? 40 pounds Explain to children that they can write a number model that represents the problem using a question mark for what they want to find out (or what they don t know). Write =? below the diagram. Then, below the open sentence, write a number model for the solution to the problem with 40 substituted for the question mark. NOTE Refrain from erasing the question mark and replacing it with the answer. At this stage, it is important that children see both number models: one with a question mark for the unknown and another with the answer in place of the question mark. Children are not expected to write two number models on journal pages. At this time, children will write a number model to represent the solution. Together with children, make up other change-to-more number stories using the Fish Poster. Emphasize stories for which and are known and is to be found, but include some stories for which or is not known and must be found. For example: Fish J swallowed another fish. Fish J now weighs 29 pounds. How much does the fish weigh that Fish J swallowed? 24 +? = 29; 5 pounds Which fish did Fish J swallow? Fish D A fish that swallowed Fish A now weighs 36 pounds. How much did the fish weigh before it swallowed Fish A?? + 1 = 36; 35 pounds Model children s solutions on the board by doing the following: 4 1 Fishy Stories Use the information on journal page 80 for Problems 1 4. Do the following for each number story: Write the numbers you know in the change diagram. Write? for the number you need to find. Answer the question. Write a number model. 1. Fish J swallows Fish B. How much does Fish J weigh now? Answer: 27 pounds 2. Fish K swallows Fish G. How much does Fish K weigh now? Answer: 45 pounds = = Fish L swallows Fish F. How much does Fish L weigh now? Answer: 108 pounds = ? ? ? Step 1 Fill in a change diagram for each problem. Write in the numbers that are known, and write? for the number that is to be found. Step 2 Describe each solution using children s language and procedures as much as possible. Step 3 Write two number models. Write a number model for the problem using a question mark to represent the unknown quantity. Write a second number model for the solution with the answer in place of the question mark. Math Journal 1, p. 81 Read more about change diagrams with the children on My Reference Book, pages Unit 4 Addition and Subtraction

4 Solving -to-more Number Stories (Math Journal 1, pp. 81 and 82) PARTNER Algebraic Thinking Partners complete the problems on journal pages 81 and 82. Check that children are recording the known information in the correct boxes in the change diagram, writing? for the unknown number, and writing a number model. Encourage children to use mental arithmetic to obtain answers. Ongoing Assessment: Recognizing Student Achievement PROBLEM SOLVING Journal Page 81 Problems 1 3 Use journal page 81, Problems 1 3 to assess children s ability to solve a number story. Children are making adequate progress if they correctly solve the problems using manipulatives. Some children may be able to solve the problems using other strategies including the diagram. 4 1 Try This Fishy Stories continued 4. Fish I swallows another fish. Fish I now weighs 20 pounds. Which fish did Fish I swallow? Answer: Fish D 5. Fish F swallows Fish B. Then Fish K swallows Fish F. How much does Fish K weigh now? Answer: 46 pounds 6. Write a number story that involves three different fish. Answers will vary. Answer: Answers will vary = 20 pounds Math Journal 1, p ? 20 Ongoing Assessment: Informing Instruction Watch for children who are having difficulty filling in the change diagram. They may find it helpful to record the weight of each object above its name in the problem. This may make it easier for children to fill in the change diagram. Bring the class together and have partners share their solution strategies. NOTE Lesson commentaries often suggest that children share solution strategies, and sometimes possible strategies are described. This does not mean, however, that children must be comfortable with every strategy. Have children share their strategies. Children will benefit from hearing strategies that others have used. Assist children in choosing a strategy that will work best for them. If none of the children mentions using the number grid or an open number line to explain their strategy, model a problem using these helpful tools. 2 Ongoing Learning & Practice Finding Distances on a Number Grid (Math Journal 1, p. 83) 4 1 Distances on a Number Grid Use the number grid below. Find the distance from the first number to the second. at the first number and count the number of spaces moved to reach the second number and and and and and and and and and and and and and and and and Use the first problem to demonstrate how children should count moves (jumps) in traveling from one number to another. Many children will find that it is easier to find the distance if they use a penny or another small object to act out the jumps from the starting number to the ending number. Encourage children to find the distance between numbers by moving vertically among the rows counting by 10s and moving horizontally counting by 1s Math Journal 1, p Lesson

5 4 1 Math Boxes 1. Write the fact family., Write the number that is 100 more Write,, or. 2,000 1,000 2,500 3,500 4,321 1,234 5,674 5, Math Journal 1, p What time is it? Circle the best answer. A. 6:30 B. 6:25 C. 6:27 D. 5:30 4. How much money? $20 $20 Á Í $ A baseball is shaped like a sphere. Name something else that is shaped like a sphere. Sample answers: basketball, tennis ball, globe 9 57 Math Boxes 4 1 (Math Journal 1, p. 84) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 4-3. The skill in Problem 6 previews Unit 5 content. Home Link 4 1 (Math Masters, pp. 90 and 91) Home Connection Children solve change-to-more number stories. They fill in a change diagram and write a number model for each problem. Children also solve problems in which they: add and subtract multiples of 10. add a 1-digit number to a multiple of 10. subtract a 1-digit number from a 2-digit number where the answer is a multiple of 10. Home Link Master Name HOME LINK 4 1 Number Stories Home Link Master Name HOME LINK 4 1 Number Stories continued Family Your child has learned about a device called a change diagram shown in the example Note below. Diagrams like this can help your child organize the information in a problem. When the information is organized, it is easier to decide which operation (,,, ) to use to solve the problem. diagrams are used to represent problems in which a starting quantity is increased or decreased. For the number stories on this Home Link, the starting quantity is always increased Please return the second page of this Home Link to school tomorrow. Do the following for each number story on the next page: Write the numbers you know in the change diagram. Write? for the number you need to find. Answer the question. Write a number model. Example: Twenty-five children are riding on a bus. At the next stop, 5 more children get on. How many children are on the bus now? 25 5? The starting number of children has been increased. Answer: There are 30 children on the bus now. Possible number model: Becky ate 11 grapes. Later in the day she ate 7 more grapes. How many grapes did she eat in all? 18 grapes 11 7? A large fish weighs 42 pounds. A small fish weighs 10 pounds. The large fish swallows the small fish. How much does the large fish weigh now? 52 pounds 42 10? Bob has 30 baseball cards. He buys 8 more. How many baseball cards does Bob have now? 38 cards Practice Add or subtract ? Math Masters, p. 90 Math Masters, p Unit 4 Addition and Subtraction

6 3 Differentiation Options READINESS Using a Scale to Show More (or Less) ELL SMALL-GROUP 5 15 Min To provide experience with the concept of change-to-more using a concrete model, have children weigh objects on a scale. Select a few objects (books, for example) and place them on the scale. Observe the weight. Add more objects to the scale. Ask: What changed? Sample answers: The number of books or the weight. How did it change? Sample answers: There are more books; the weight is greater; it changed to more. To support English language learners, emphasize and record measurement and comparison vocabulary. Select a number of objects to start with and take some away (change to less). Try several demonstrations with different objects. Remind children that as the number of objects increases, the weight changes to more. As the number of objects decreases, the weight changes to less. ENRICHMENT Writing -to-more Stories (Math Journal 1, p. 80; Math Masters, p. 419) 5 15 Min Algebraic Thinking To apply their knowledge of solving change-to-more stories, have children write change-to-more stories using the Fish Poster on journal page 80. Encourage children to write stories that involve a missing number in the or boxes. For example: Fish J swallows another fish. Fish J now weighs 27 pounds. Which fish did he swallow? Fish B A fish weighs 13 pounds after eating a fish that weighed 3 pounds. Which fish swallowed the 3-pound fish? Fish G Children then exchange the problems with a partner and solve them. Finally, children choose one problem and explain how they solved the problem. Lesson