Fact Families Objective To introduce addition/subtraction fact families. www.everydaymathonline.com 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 Write parts-and-total number models. Write addition and subtraction number models using +, -, and =. [Patterns, Functions, and Algebra Goal 2] Generate fact families. [Patterns, Functions, and Algebra Goal 3] Key Activities Children are introduced to addition/ subtraction fact families, using dominoes as a source for number triples. Children generate fact families for number triples. Recognizing Student Achievement Use the Math Message. Informing Instruction See page 1. Key Vocabulary fact family Materials Math Journal 2, p. 113 Home Link 2 Math Masters, pp. 1 18 per child: 2 dominoes slate counters (optional) Practicing with -Collection Boxes Math Journal 2, p. 114 Children practice filling in name-collection boxes. Math Boxes 3 Math Journal 2, p. 1 Children practice and maintain skills through Math Box problems. Home Link 3 Math Masters, p. 1 Children practice and maintain skills through Home Link activities. READINESS Playing Concentration with Number Cards and Dominoes per partnership: number cards 0 (from the Everything Math Deck, if available), 10 dominoes with a total of 0 dots Children practice matching dots on dominoes with numerals. EXTRA PRACTICE Solving Fact Families Math Masters, p. 32 double- dominoes Children practice with fact families. Advance Preparation For Part 1, make one copy of Math Masters, page 1 per two children. Cut the sheets in half and place them near the Math Message. Teacher s Reference Manual, Grades 1 3 pp. 1, 1, 1 18 48 Unit Developing Fact Power
Getting Started Mental Math and Reflexes Tell simple number stories. Children may solve them by using a number line, number grid, tally marks, pictures, counters, or base-10 blocks. Have children share their strategies for each problem. Summarize solutions with an appropriate diagram and number model. Do not force a number story into a particular mold by saying that there is a best diagram for the problem. Suggestions: Mona had 2 when she went to school. She bought milk at lunchtime for. How much money did she have left after buying the milk? 20 Dwayne received helium balloons for his seventh birthday. By the next day, balloons had lost their helium. How many balloons still had helium the next day? balloons Michele read 24 books. Regina read 8 more books than Michele. How many books did Regina read? 32 books Math Message Display Math Masters, page 1. Take a half-sheet of paper and complete the problems. Home Link 2 Follow-Up Ask children to help you list all of the addition facts with sums of 10. Have children share some of the names in their name-collection boxes. Highlight names that are especially creative. 1 Teaching the Lesson Math Message Follow-Up PROBLEM SOLVING WHOLE-CLASS Algebraic Thinking Have children share how they solved the problems on Math Masters, page 1. Solutions to Problem 2 may include: Counting up to 11, starting at (8,, 10, 11, while counting on fingers). Using a guess-and-check approach: I will try 2. + 2 is, so 2 is not enough. + 3 is 10. 3 is not enough, so I will try 4. + 4 is 11, so there are 4 missing dots. Solving an unknown addend problem: Solve 11 = by finding the number that makes 11 when added to, as in 11. For each problem, write three numbers on the board: the number of dots in each half of the domino and the total number of dots. For example, for Problem 1, write 4, 3,. Point out that we can always associate three numbers with any domino. Tell children that they will practice making number models for dominoes by using the three related numbers. Ask them to suggest number models for each problem. Recognizing Student Achievement Math Message Use the Math Message to assess children s ability to find parts and totals. Children are making adequate progress if they are able to answer all 3 problems correctly. 3 Domino Totals 1. Find the total. Draw the missing dots. 2. 3. 11 8 3 Domino Totals 1. Find the total. Draw the missing dots. 2. 3. 11 Math Masters, p. 1 8 Unit domino dots Unit domino dots Lesson 3 4
3 Domino Introducing Addition/ Subtraction Fact Families (Math Masters, pp. 1 and 18) WHOLE-CLASS py g g p Tape the 3 demonstration domino (Math Masters, page 1) to the board (or draw a 3 domino). Then ask: What three numbers go with this domino? 3,, (Write 3,, on the board.) What two number models show how to find the total number of dots? 3 + = ; + 3 = (Write the number models on the board.) What two subtraction number models can you make up that use 3,, and? - 3 = and - = 3 (Write both number models on the board.) Math Masters, p. 1 3,, 3 + = + 3 = - 3 = - = 3 NOTE To encourage further understanding of the +, -, and = symbols, have children fill in missing symbols in number sentences that you write. Adjusting the Activity ELL For subtraction, have children draw a line down the middle of their slates and place counters in each half to model the domino. They can count the total and then remove the counters from one side to generate a subtraction fact. 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 3 Domino Repeat this routine with the 4 demonstration domino (Math Masters, page 18). Focus on the three numbers associated with this domino and the four number models that can be written using these numbers. Explain that the addition and subtraction facts that can be written using the three domino numbers make up a fact family. Fact families show the relationship between addition and subtraction. Distribute two dominoes to each child. Ask children to write on their slates the fact family for each of their dominoes. Facts can be written in horizontal or vertical format. If children have difficulty with the addition turn-around rule, rotate your demonstration domino to model these relationships. You might mention that a subtraction answer can be checked by doing addition. For many first graders, it is helpful to think about 8 - =? as +? = 8. This approach encourages counting up to subtract, a strategy that also works well with multidigit numbers. This also encourages children to look for the unknown number that makes the number model true. Math Masters, p. 18 0 Unit Developing Fact Power
Have several children share their fact families. In one column, list the dominoes that have four different number models (all dominoes except doubles). In another column, list the dominoes that have only two facts (all doubles). Summarize by stating that except for doubles, a fact family has two addition and two subtraction facts. A fact family for doubles has only one addition and one subtraction fact. Writing Addition/Subtraction Fact Families (Math Journal 2, p. 113) Children write fact families for dominoes. NOTE Generating fact families reinforces the inverse relationship between addition and subtraction. Informing Instruction Math Journal 2, p. 113 Watch for children who assume incorrectly that since the two addition facts are turn-around facts, the two subtraction facts must also be turn-around facts, and therefore write subtraction number models such as - = 4. Remind children to write the largest number first when writing a subtraction problem. 2 Ongoing Learning & Practice Practicing with - Collection Boxes (Math Journal 2, p. 114) Use Math Journal 2, page 114 to provide more practice with name-collection boxes. Math Boxes 3 (Math Journal 2, p. 1) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -1. The skills in Problem 4 preview Unit content. Home Link 3 (Math Masters, p. 1) Home Connection Children generate fact families for dominoes. Math Journal 2, p. 114 Lesson 3 1
3 Math Boxes 1. Write the sums. + 10 = 1 = 8 + = 3 + + = 13 2. Fill in the missing numbers. in Rule +10 out in 13 18 3 out 23 28 8 103 13 3 Differentiation Options READINESS Playing Concentration with Number Cards and Dominoes PARTNER 30 Min 3. Add. + 8 = + = + 4 1 10 + 10 1 Math Journal 2, p. 1 4. Draw lines to match the shapes that look alike. Column A Column B To provide experience writing number sentences, children record number sentences based on domino-card pairs they collect. Players place number cards facedown in 2 rows of cards each. They also arrange the dominoes facedown in 2 rows of dominoes each. Players take turns turning over 1 card and 1 domino. If the numbers on the card and the domino match, the player takes the card-domino pair and continues playing. If they do not match, the player puts them back in their original place after the other player has seen them. The game ends when there are no more cards and dominoes left. Have children record the domino-card pairs they won in the form of a number sentence. For example, if they had a 3 0 domino, they should record 3 + 0 = 3. 3 HOME LINK 3 Fact Families Family Note Home Link Master We have extended our work with facts to subtraction facts by introducing fact families. Your child will generate addition facts and subtraction facts for the numbers pictured on the dominoes below. Note that for each problem, there are two addition facts and two subtraction facts. Please return this Home Link to school tomorrow. Write the 3 numbers for each domino. Use the numbers to write the fact family. EXTRA PRACTICE Solving Fact Families (Math Masters, p. 32) Have children practice finding fact families by choosing dominoes and filling in Math Masters, page 32. 1. 2. Numbers:,, Fact family: Fact family: Numbers:,, Practice 3. Write the missing numbers. Rule 2 32 30 28 2 24 Math Masters, p. 1 2 Unit Developing Fact Power