What's the Math? Common Core State Standards FOCUS Domain: Operations and Algebraic Thinking Major Cluster: Add and subtract within 20. Objective: Students will use the doubles to add strategy to help find the sum. Standards 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums. Mathematical Practices 1 Make sense of problems and persevere in solving them. 2 Reason abstractly and quantitatively. 6 Attend to precision. 7 Look for and make use of structure. 8 Look for and express regularity in repeated reasoning. COHERENCE Thinking Across Grades Previous Grade K K.OA.5 Now Grade 1 1.OA.6 Linking to Major Topics Connected to the following critical area of focus: 1. Developing understanding of addition, subtraction, and strategies for addition and subtraction within 20. Connected to the following standards: K.OA.2, K.NBT.1, 1.OA.5, 2.OA.2 RIGOR The exercises increase in complexity throughout the lesson. However, individual student thinking may vary during extended processing. Levels of Complexity Level 1 Understand Concepts Exercises 1 11 Level 2 Apply Concepts Exercises 12 20 Level 3 Extend Concepts Exercises 21 22; Write Math What Students Should Understand You can add the same number to itself to create a doubles fact. Next Grade 2 2.OA.2 What Students Should Be Able To Do Students should be able to add the same addends together to make a double fact. 2 + 2 = 4 3 + 3 = 6 Printed by: Leah Duncan Page 1 of 11 Printed on 11/05/2014 7:58 AM
Building on the Essential Question In this lesson, students will build upon the skills and concepts needed to answer the chapter s Essential Question How do I use strategies to add numbers? Common Core Quick Check, Chapter 3, Answer Key, Common Core Quick Check, Chapter 3, Printed by: Leah Duncan Page 2 of 11 Printed on 11/05/2014 7:58 AM
Developing Vocabulary / Get Ready New Vocabulary / Cognate doubles / dobles addends Activity Discuss with students that an addend is a number being added to another number. Attend to Precision Write the vocabulary word doubles on the board and tell students that double means two. Explain that an addition problem that has the exact same two addends is called a doubles fact. In the problem 4 + 6 = 10, which numbers are the addends? 4 and 6 Write 3 + 3 = 6 on the board. Explain that this is a doubles fact. What do you notice about the addends? They are the same number. English Language Learner Instructional Strategy Vocabulary Support: Cognates Write the word doubles and the Spanish cognate, dobles on a cognate chart. Say, When both addends in a number sentence are the same number, it is a doubles fact. Addends are the numbers being added together. Write the number sentence 2 + 2 = 4. Say, Two plus two equals four. This is a doubles fact because both addends are two. Model other addition number sentences, such as 3 + 3 = 6; 5 + 3 = 8. Include doubles facts and non-doubles facts. Have students identify whether or not the number sentence being modeled is a doubles fact using the sentence frame: That is a doubles fact. or That is not a doubles fact. Have students also show thumbs-up/thumbs-down accordingly to support emerging level students. For non-spanish speaking ELLs, refer to the Multilingual eglossary for interactive definitions in 13 languages. Vocabulary Review, Grade 1, Chapter 3 Printed by: Leah Duncan Page 3 of 11 Printed on 11/05/2014 7:58 AM
Launch the Lesson / Investigate & Model Review Problem of the Day Use counters and a ten-frame to show 3 ways to make 10. Then choose one way to make 10 and tell an addition story. Sample answers: 5 and 5 is 10; 4 and 6 is 10; 3 and 7 is 10 make 10. Persevere in Solving Problems Invite students to work with a partner to find all of the ways to Common Core Quick Check Use this activity as a quick review and assessment of the previous lesson. A printable version is available online. Additional review occurs at the end of the chapter. Additional Literature Connection Read a trade book, such as Double the Ducks by Stuart J. Murphy, to prepare students for this lesson. Use the game Circle Up, the graphic novel How Many Legs, and the Real-World Problem Solving reader Double the Number after this lesson. The Teacher Guide provides suggestions for differentiated instruction. Investigate the Math Target: Conceptual Understanding and Applications Materials: Lesson Presentation slides This investigation emphasizes mathematical reasoning and mathematical processing. How can you use doubles to add? Printed by: Leah Duncan Page 4 of 11 Printed on 11/05/2014 7:58 AM
Students investigate ways to model with math. Students come together to discuss their results to look for and make use of structure. Model the Math Target: Procedural Skills and Fluency Materials: connecting cubes, write-on/wipe-off board, dry erase markers Give each student connecting cubes and a write-on/wipe-off board. Ask two boys and two girls to stand. What addition number sentence can you make by adding the boys and girls? 2 + 2 = 4 2 + 2 = 4 Have students identify each of the addends and the sum. At their seats have the students model the doubles fact using connecting cubes and writing the corresponding addition number sentence on their write-on/wipe-off boards. Next have five boys and five girls stand. What addition number sentence can you make by adding the boys and girls? 5 + 5 = 10 Tell the students at their seats to model the doubles fact and write the corresponding addition number sentence. Repeat the same process with several other number combinations with sums up to 20. Have students tell the doubles fact. Problem of the Day, Grade 1, Chapter 3, Lesson 4 Answer Key, Problem of the Day, Grade 1, Chapter 3, Lesson 4 Connecting Cubes Connecting Cubes Investigate the Math, Grade 1, Chapter 3, Lesson 4 Printed by: Leah Duncan Page 5 of 11 Printed on 11/05/2014 7:58 AM
Teach Explore and Explain You will need connecting cube Read the directions at the bottom of the student page. Have students model the problem using connecting cubes. Display a tower of three connected red cubes and a second tower of three connected green cubes. Stack the two towers to make a single tower of six cubes. Tell students to lay their towers flat in the empty space on the student page to represent a building. Have students trace their tower. Two towers of three cubes each have been added together to make a new tower. We are going to use the doubles to add strategy to find the total number of cubes in the new tower. Lead students through the steps needed to write the addition number sentence. The numbers being added together in an addition number sentence are called addends. What do you notice about the addends in this number sentence? Sample answer: They are the same number. When both addends are the same number, it is a doubles fact. Repeated Reasoning Can you make a doubles fact with every number between 0 and 10? Why or why not? Sample answer: Yes because you can have the addends be the same number from 0 to 10. See and Show Guide students through the example at the top of the student page. Read the sentences to the class. Provide each student with 10 connecting cubes. Have them model the example shown using the cubes. Tell students to trace the dashed numbers that represent the doubles fact. Discuss which numbers are the addends and which number is the sum in the addition number sentence. Reason Quantitatively Ask students: What number is the first addend? 5 What number is the second addend? 5 What do we call this fact? This is a doubles fact. Work through Exercise 1 7 as a class. Talk Math: Collaborative Conversation Discuss with students Can you use doubles to make a sum of 7? Sample answer: No, because the addends cannot be the same when the sum is 7. Look for Patterns On the board, write the sums of the doubles facts from 1 to 7. What do you notice about the sums of doubles facts? Sample answer: The sums increase by 2 each time. Can you think of a number that can not be the sum of doubles fact? Accept any odd number as a correct answer. Virtual Manipulatives Doubles (less than 6) Connecting Cubes Printed by: Leah Duncan Page 6 of 11 Printed on 11/05/2014 7:58 AM
Practice & Apply On My Own Based on your observations, you may choose to assign exercises as noted in the levels below: Approaching Level Guide students through the exercises in On My Own. Help them to use manipulatives. On Level Have students complete the exercises independently. Beyond Level Have students complete the exercises independently without manipulatives. Common Error! Students may have a hard time identifying doubles facts. Encourage them to use manipulatives such as counters or connecting cubes to realize equal groups of addends. Problem Solving Make Sense of Problems Exercise 22 Ask: How many bridges would Emad drive over in one week to go to school? How did you figure out the answer? Sample answer: 10 bridges; I knew that he drove over 2 bridges per day and there are five school days in a week. I used counters to count 5 groups of 2. Reason Abstractly Write Math Have students change the numbers in the exercise so that it is a doubles fact. Formative Assessment You will need write-on/wipe-off boards dry erase markers Response Cards On write-on/wipe-off boards, have students write 4 doubles facts with the corresponding sums. Ask students to hold up their boards and show you their doubles facts. Scrambled Egg City: More Doubles, Sums to 12 Fact Dash Printed by: Leah Duncan Page 7 of 11 Printed on 11/05/2014 7:58 AM
Differentiated Instruction Differentiated Instruction TIER 2: Strategic Intervention Hands-On Activity Materials: pile of purple connecting cubes, pile of yellow connecting cubes Have students take a handful of cubes from one pile. Have them count to see how many cubes they have. Have them take the same number of cubes from the other pile. Have students write an addition number sentence to show the doubles fact they made. Have students repeat the activity with other amounts of cubes. TIER 1 Hands-On Activity Materials: 0 5 or 5 10 number cube, cups, write-on/wipe-off boards, dry erase markers Have students roll a number cube and place this number of counters in a cup. Have students place the same number of counters in a second cup. Have students turn over both cups at the same time to show the counters. Have students write the doubles fact they made on a write-on/wipe-off board. Have students repeat the activity a few times. Extend Hands-On Activity Materials: blank tic-tac-toe boards, pencils, set of number cards from 1 to 9, counters Provide students with blank tic-tac-toe boards. Have them write the numbers 2, 4, 6, 8, 10, 12, 14, 16, and 18 in the squares. In turn, have each student draw a card. Students then double this number and place a counter on the sum on their board. The first player to get three in a row, horizontally, vertically, or diagonally wins. Diferentiated English Language Learner Support Number Game Review the word doubles (dobles) written on the Spanish cognate chart. Based on the number of students, make two sets of index cards using numbers 0 10. Randomly distribute the cards. Ask, Who has the same number as you? Find your double. Have students identify their partner. Have pairs take turns coming forward. Use each pair s numbers to demonstrate a doubles fact. Ask, What is the sum of these doubles? Give students a chance to respond, either orally or with a esture. Then say, The sum is 14. Act It Out Printed by: Leah Duncan Page 8 of 11 Printed on 11/05/2014 7:58 AM
Select 2 groups of 2 students. Ask, How many are in your group? 2 What is the number sentence to add these two groups? 2 + 2 = 4 Write the number sentence on the board. Say, Two and two are addends in this number sentence. When addends are the same, they are called doubles. Repeat with 2 groups of 3 students. 3 + 3 = 6 Ask, Are three and three doubles? Yes Continue modeling other doubles with different groups of students. Turn & Talk Have 3 volunteers stand in a line. Students will say a doubles addition sentence and add them together. Student A says, One. Student B says, Plus one. Student C says, Is two! Then student C moves to student A s place and they all move over. The new student A says, Two. The new student B says, Plus two, and so on. After the volunteers have modeled adding doubles through 10 + 10, divide the class into groups of 3 and have them play the game. Scrambled Egg City: More Doubles, Sums to 12 Fact Dash Enrich Worksheet: Doubles Enrich Worksheet: Doubles, Answer Key Reteach Worksheet: Use Doubles to Add Reteach Worksheet: Use Doubles to Add, Answer Key Enrich Worksheet: Doubles Reteach Worksheet: Use Doubles to Add Doubles Number Cards, 0-12 Tic-Tac-Toe Printed by: Leah Duncan Page 9 of 11 Printed on 11/05/2014 7:58 AM
Wrap It Up My Homework Assign homework after succesful completion of the lesson. Students who understand the concepts may skip the Homework Helper section. Problem Solving Make Sense of Problems Exercise 12 Ask: Is this exercise a doubles fact or not? Why or why not? Sample answer: It is a doubles fact because the number of girls and boys is the same. Vocabulary Check Explain to students that signal words, such as add in Exercise 13 and two in Exercise 14, can provide helpful clues to complete each sentence. Formative Assessment Exit Slip Ask students the following question and have them write their answer on a piece of paper or card. What is the doubles fact if one addend is 4? 4 + 4 = 8 My Homework, Chapter 3, Lesson 4 Answer Key, My Homework, Chapter 3, Lesson 4 The Addition Boogie Connecting Cubes Printed by: Leah Duncan Page 10 of 11 Printed on 11/05/2014 7:58 AM
Printed by: Leah Duncan Page 11 of 11 Printed on 11/05/2014 7:58 AM