AchieveMath

Levels

K-5

Instructional Intervention

Teaching Math Skills

to Achieve Common Core Outcomes

SAMPLE This document is for demonstration purposes only

Math Skills

Multiply & Divide within 100 – 3.OA.7

Objective: Multiply and Divide within 100 Pre-Requisite

Current

Growth

Work with equal groups of objects to gain foundations for multiplication

Multiply and divide within 100

Multiply and Divide whole numbers with up to four digits

(3.OA.7)

(2.OA.2, 2.OA.3) AchieveMath: Level 2, Lessons 4, 20-22

(4.NBT.5, 4.NBT.6) AchieveMath: Level 3, Lessons 23-26, 33-38

AchieveMath: Level 4, Lessons 23-38

Review & Pre-Assessment • Underline the digit in the ones place of and determine if the number 20 is odd or even (20, even) • 5 x 2 = (10) • 2 x 2 = (4) • 3 X 6 = (18) • 3 X 1 = (3) • Draw a picture to illustrate the following multiplication problems (pictures will vary) ◊ 4 x 4 = (16) ◊ 7 x 4 = (28)

Instruction EXPLORING PROPERTIES OF MULTIPLICATION: • List the following properties on the board: Associative Property, Commutative Property, Identity Property, Zero Property. Create an example of the first property (i.e. (2x4) x7 = 2x (4x7)). Solve this example for the students. Check both sides of the equation with the students to prove that both sides are equal. Follow this procedure with the remaining properties. (PS.1, PS.2) • Divide the students into pairs. Assign two different properties to each pair. Ask each pair to create two examples for the properties. Have the students write the examples. Allow the students time to work out the problems. Have students share their problems. (PS.2, PS.3) • Provide students with 4-10 examples and ask them to identify the corresponding property. Share all answers. (PS.1, PS.2, PS.3) EXPLORING RELATIONSHIPS BETWEEN MULTIPLICATION AND DIVISION: • Provide students with 3-5 sets of completed multiplication problems within 25. Each set should use the same three numbers (i.e. 2 x 3 = 6, 2 x3 =6, and 6 ÷ 3 = 2, 6 ÷ 2 = 3). Ask students to identify the connection between the problems (Students should be able to say that the numbers are the same in AchieveMath

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Multiply & Divide within 100 – 3.OA.7

Math Skills

each set.) Explain that division is the opposite of multiplication, just as subtraction is the opposite of addition. Knowing the multiplication facts will help with division. (PS.1, PS.2) • Model multiplication for one set of given numbers using counters, or tokens. Show how it works for multiplication and division. Repeat this process with the remaining sets. For each set there should be two division and two multiplication facts. (PS.1, PS.2, PS.4) • Divide students into pairs. Give each pair of students counters or tokens and 3-6 division problems (i.e. 10 ÷ 2 =5) . Instruct student to use the counters to divide a given problem, then write another division problems using the same numbers (10 ÷5 = 2), and also write the two corresponding multiplication problems (5 x 2 = 10, 2 x 5 =10). Allow the students time to work out the problems. Have student share their work (PS.3, PS.4) • Provide student with several more problems to work individually, have the students complete the problems by first dividing them and then writing both division problems and the two corresponding multiplication problems. Take note of the students’ ability to work through this application. Share answers. (PS.1, PS.2, PS.3, PS.4) DIVISION OF WHOLE NUMBERS: • Provide students with 3 to 5 division problems within 50 (i.e. 36 ÷ 9 = (4), 45 ÷ 5 = (9), 50 ÷ 5 = (10)). Show a multiplication flash card with the problem 9 x 4, and ask them what the answer would be. Refer to the provided problem 36 divided by 9, what would the answer be? (4) Explain that just as subtraction is the opposite of addition, division is the opposite of multiplication. Show the 5 x 9 card and use it to solve the provided problem 45 ÷ 5? (9). Follow this procedure for the remaining examples. (PS.1, PS.2) • Give pairs of students 3-5 multiplication flash cards containing single digit numbers. Have the students create two division problems for each multiplication fact (i.e. card: 7 x 6 = (42), 42 ÷ 7 = 6, 42 ÷ 6 = 7). Allow the students time to work out the problems. Share all problems (PS.3, PS.7) • Provide students with 5 to 8 division problems. Have students solve for the quotient in these problems and then write the problems and the answers. Take note of the students’ ability to work through these problems. Share answers. (PS.1, PS.2, PS.3) DIVIDE TWO AND THREE DIGIT NUMBERS WITH NO REMAINDERS: • Write down a division problem with two and three digit numbers, and model the division process with the Base 10 blocks, labeling the divisor, quotient and dividend accordingly. Model the division process for 2 to 3 more examples. (PS. 1, PS.2, PS.4) • Provide pairs of students with 3 to 6 division problems, Base ten blocks, and pencils. Instruct students to divide the blocks into the correct groups, exchanging blocks when necessary, solve for the answer and then write down the division problem Allow the students time to work out the problems. As you circulate among the students, ask the students to describe what they are doing. Assist students when necessary. If students are having difficulty, model the problem for them. Have students share their answers. (PS.3, PS.4)

AchieveMath

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Math Skills

Multiply & Divide within 100 – 3.OA.7

• Provide students with 3 to 6 division problems with two to and three digit number to solve individually. Take note of the students’ ability to work through the examples. Are the students able to correctly divide the groups? Share answers. (PS.1, PS.2, PS.3, PS.4)

Scaffolding Additional Support

Additional Challenge or Rigor

• Allow struggling learners to work with a partner

• Pair students with a struggling learner for peer tutoring

• Provide students with multiplication in division problems using only single digit numbers

• Challenge students to complete similar problems with two and three digit numbers

• Provide additional practice problems

• Have student create their own problems and answer to trade with a classmate

• Allow students to use manipulatives such as: counter or tokens, base ten blocks, and multiplication flash cards when solving problems

• Have student identify and explain a real life application

Evidence of Learning • Students will be able to fluently multiply and divide within 100 • Students will be able to demonstrate the relationship between multiplication and division • Student will know from memory all products of two one-digit numbers • Given a multiplication or division problem, students will be able to apply the property of operations to reach a conclusion • Students will understand and apply the properties of operations: Associative Property, Commutative Property, Identity Property, Zero Property

AchieveMath

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