For full lesson outline, see Advantage Math.

Standards:

4.OA.1: Interpret a multiplication equation as a comparison, e.g., interpret 35=5x7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparison as multiplication equations.

4.OA.2: Solve multi step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Objectives:

Math Objectives: I can solve multiplicative comparison problems with unknown group sizes using division, hands-on manipulatives, and bar models.

Language Objectives: I can share my ideas on solving multiplicative comparison equations using division.

Vertical Alignment:

3.OA.1: Interpret products of whole numbers, e.g., interpret 5x7 as the total number of objects in 5 groups of 7 objects each.

4.OA.1: Interpret a multiplication equation as a comparison, e.g., interpret 35=5x7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparison as multiplication equations.

4.OA.2: Solve multi step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

Notes:

1. If unfamiliar with bar models, take some time to read the article titled “Modeling Word Problems,” which is Teacher Resource #1 from Lesson 4.3.

2. This lesson quickly progresses through hands-on manipulatives to pictorial and abstract thinking. Gauge student understanding and divide the lesson into two or more instructional sessions if necessary.

Lesson Outline:

🚀Launch:

The term "times less than" is explained with an example diagram. Students are asked to illustrate or model a comparison word problem.

After the students explore the problem, discuss points a,b,c found in the complete outline in Advantage Math to ensure students understand the commutative property and strategies to solve.

The teacher will also need to teach or record an explanation on how to use bar models in these problems. This is outlined fully in Advantage Math.

🤔Explore:

Have students practice what they have learned about bar models on three different math problems.

💬Discuss:

Have students describe what each part of each of their bar models represent and how they found whatever portion was unknown.

✅Exit Ticket:

Have students create a bar model that corresponds with a word problem, and then use it to solve. Students will also be asked to reflect on their learning.

Additional Resources:

Teacher Resource #1: Article on Errors in Arithmetic Comparisons

Student Resource #1: Thinking Blocks

Differentiation:

Challenge: For students who need a challenge, invite them to create their own word problems that use division as the inverse of multiplication in multiplicative comparison problems.

Struggling: For students who are struggling to use equations to model the problems, allow them to focus on developing the appropriate bar model to match the word problems rather than using only abstract equations .Allow students who are struggling to create bar models to use a manipulative, such as Cuisenaire rods. Require students to sketch and appropriately label their manipulative models to create a pictorial bar model. Invite them to make connections between drawn bar models and concrete objects.