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Math Lesson: Fact Families
(multiplication and division) / Grade Level: 3-4
Lesson Summary: The teacher pre-assess students’ knowledge by showing them two related multiplication and division fact family problems and asking students what the two problems have in common. The teacher guides students through using fact family houses to find the related multiplication and division facts. Students work in groups to play a Fact Family Memory game for independent practice. Pairs of advanced learners create their own versions of Fact Family Memory and then switch with another pair and play each other’s games. Struggling learners work in pairs with teacher guidance to manipulate number cards to create fact families.
Lesson Objectives:
The students will know…
· How to identify multiplication and division fact families.
· How to write multiplication and division fact families.
The students will be able to…
· Identify multiplication and division facts within fact families.
· Write multiplication and division fact families.
Learning Styles Targeted:
Visual / Auditory / Kinesthetic/Tactile
Pre-Assessment: Write 4 + 6 = 10, 6 + 4 = 10, 10 – 6 = 4, and 10 – 4 = 6 on the board. Ask students what those four equations represent. Elicit responses until a student says, “fact family.” Tell students that the fact family written on the board is an addition and subtraction fact family, and today they will be learning how to write and recognize multiplication and division fact families.
Whole-Class Instruction
Materials Needed: 1 laminated Fact Family House* per student, 1 dry-erase marker per student, 1 tissue per student, 1 set of pre-cut Memory Game cards* copied onto cardstock per group of students, 1 piece of notebook paper per student, writing utensils
Procedure:
1) Give each student a dry-erase marker, a tissue, and a laminated Fact Family House. Refer back to the example facts used in the pre-assessment. Ask students what three numbers were used in all of the facts. Elicit responses until a student says 4, 6, and 10. Tell students that addition and subtraction fact families use the same three numbers repeatedly but in different orders just like multiplication and division fact families. Tell students that they are going to practice writing number sentences that belong to the same multiplication and division fact family.
2) Draw a house on the board like the one on the students’ papers. Write the numbers 4, 6, and 24 under the rooftop. See the example Fact Family House in supplemental resources, if necessary. Explain to students that each of the facts in this fact family will use those three numbers repeatedly but in different orders.
3) Ask students to think of a multiplication sentence that involves all three numbers. Elicit responses, recording 4 x 6 = 24 or 6 x 4 = 24 beside one of the multiplication symbols on the house. Model for students how to reverse the order of the two factors to find the other multiplication problem. Students should record both problems on their house mats.
4) Tell students that the fact family for 4, 6, and 24 also includes two division facts. Ask students to think of a division sentence that involves all three numbers. Elicit responses, recording 24 ÷ 6 = 4 or 24 ÷ 4 = 6 beside one of the division symbols. Students should do the same. Model for students how to find the other division sentence by reversing the order of the divisor and the quotient. Students should record the final fact in their house as well.
5) Have students erase their Fact Family House mats, and repeat the process of leading them through writing the 3 numbers involved in a fact family, writing the related multiplication and division facts, and discussing the similarities among the facts. Repeat the process until students can independently create a fact family for three given numbers. Some suggested numbers are 8, 5, and 40; 6, 9, and 54; 7, 3, and 21; and 2, 11, and 22.
6) When students understand how to write a fact family for three given numbers, put students into groups of 3-4 and tell them that they are going to play a Fact Family Memory game. Give each group its own set of pre-cut Memory game cards. You may want to copy them onto different colors of cardstock to keep the game pieces from getting mixed together. Have students lay the cards face down on the table or the floor. Explain to students that the player who goes first will turn over two cards and see if those two cards belong in the same fact family. If so, that player gets to keep the fact family match and take another turn. If not, that player must turn the cards face down again and the next player takes his/her turn. Play continues until all matches have been made or time is up. The player that makes the most matches wins the game.
Note: If you want a paper/pencil assessment of students’ understanding of fact families, you may want to give each student a piece of notebook paper and have them record the fact family matches made during the memory game along with the other number sentences within that fact family.
Advanced Learner
Materials Needed: 20 index cards per pair of students, 1 plastic baggie per pair of students, writing utensils, crayons or colored pencils
Procedure:
1) Put advanced students to create their own versions of Fact Family Memory. Give each pair of students 20 blank index cards and a plastic sandwich bag. Model for students how to write a multiplication or division fact on one of the index cards. Ask students for the other facts in the same fact family, and model for them how to create separate index cards for each number sentence.
2) Tell students that they should think of 5 different fact families and make cards for each of those fact families, using a total of 20 index cards. Check for understanding, and allow students to create Memory games in pairs. You may want each pair to color the backs of their index cards with one specific color to keep each group’s game separate from the other groups.
3) When pairs have finished, check their index cards to make sure they are correct. Have students switch games with other pairs and play each other’s games. The student-made Memory games can be used in a math center in the future.
Struggling Learner
Materials Needed: 1 Struggling Learners Number Cards* page per pair of students, 1 pair of scissors per pair of students, 1 individual student whiteboard per pair of students, 1 dry-erase marker per pair of students, 1 tissue per pair of students, Example Board* for teacher reference, 1 copy of the Struggling Learners Recording Sheet* per student, 1 copy of the Struggling Learners Recording Sheet* to project under a document camera, writing utensils
Procedure:
1) Put struggling learners into pairs, and give each pair a copy of the Struggling Learner Number Cards, a pair of scissors, a whiteboard, a dry-erase board, and a tissue. Give each individual student his/her own copy of the recording sheet.
2) On the board, draw a set of blank number sentences like the ones shown on the Example Board in supplemental resources. Student pairs should write the same blank number sentences on their whiteboards. Have students cut out the first set of number cards, the 6, 5, and 30.
3) Students can use those three numbers to create a set of 4 number sentences that make up a fact family. Have students record the three numbers on the recording sheet.
4) Tell students to start with the multiplication facts. Ask students what happens to two whole numbers when you multiply them. Elicit responses until a student says that the numbers get bigger. Tell students the largest of the three numbers, 30, should be the answer to the multiplication problem. Write “30” as the answer to the first blank number sentence on the board. Have pairs place the 30 card as the answer to the first blank number sentence on their whiteboards. Show students that the other two numbers, 5 and 6, are the numbers that are multiplied together to get the largest number. Write in these numbers in the blanks in the first number sentence on the board as students place the 5 and 6 cards in the blanks on their whiteboards. Monitor that students are doing this correctly. When you see that all pairs have placed their cards correctly, ask each student to record this fact on the recording sheet.
5) Tell students that the other multiplication fact is very similar to the first one. Remind students that because 30 is the largest number, it is still the answer to the second multiplication problem. Have students move the 30 card to the second blank number sentence, and write 30 on the board as the answer to the second multiplication fact. Show students that they can switch the order of the 5 and 6 to create a second multiplication problem. Have students record the second multiplication fact on their recording sheets.
6) Tell students that the division facts in this fact family are the exact opposite of the multiplication facts. Tell students that the largest number, 30, is no longer the answer to the problem but is the first number listed in the division problem. Have students move the 30 card to the beginning of the first division sentence. Record 30 as the dividend of the first division problem. Show students that the other two numbers, 5 and 6, represent the divisor and the quotient. Have place their number cards appropriately and then record the number sentence on the recording sheet. Repeat for the other division problem in the fact family.
7) Repeat this process for the remaining sets of number cards. If you feel that some students grasp the concept after some guided practice, you may want them to work with their partner to find the facts in each fact family without teacher guidance. Make sure students are recording the facts for each set of numbers on the recording sheet. While the more independent students are working in pairs, you may want to continue to guide the students who are still struggling.

*see supplemental resources