Lesson objective: Multiply and divide within 100, using strategies such as the relationship between multiplication and division as inverse operations.

This lesson helps to build fluency with multiplying and dividing within 100. Arrays are used here because they are the best model to represent both multiplication and division equations. This work develops students' understanding that the inverse relationship between multiplication and division can be used to multiply within 100.

Students engage in Mathematical Practice 1 (Make sense of problems and persevere in solving them) as they understand they are finding an unknown factor. Using manipulatives to represent doubling and halving, students will want to find as many possibilities through their rearrangement of the arrays. They should persevere to find multiple answers and can be asked, "Are those all the possibilities? How do you know? Are there other options that won't work?"

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they understand that they are finding an unknown factor. They draw pictures or arrays, equal groups, or number lines and write equations to represent the situation. Giving students a multiplication equation to represent the problem can help them start to make sense of how they can find the unknown factor. Doubling and halving factors, breaking apart numbers and sharing into equal groups are strategies that will help them to solve these problems. Be sure to ask if there is a better way to solve the problem if you see students still using additive reasoning to count multiple tally marks or share larger numbers into groups. Using number sense and multiplicative reasoning, they can be more efficient in finding answers to division situations.

**Key vocabulary:**

- array
- double
- equal groups
- equation
- half
- inverse operations
- product
- quotient
- unknown factor

******Special materials needed:**

- base ten blocks to reason with, such as breaking apart numbers
- manipulatives such as square tiles, counters or cubes