# 3.4 Relating Multiplication to Division

## Unit Goals

• Students learn about and use the relationship between multiplication and division, place value understanding, and the properties of operations to multiply and divide whole numbers within 100. They also represent and solve two-step word problems using the four operations.

### Section A Goals

• Represent and solve “how many groups?” and “how many in each group?” problems.

### Section B Goals

• Understand division as a missing-factor problem.
• Use properties of operations to develop fluency with single-digit multiplication facts, and their related division facts.

### Section C Goals

• Use properties of operations and place value understanding to develop strategies to multiply within 100 and to multiply one-digit numbers by a multiple of 10.

### Section D Goals

• Use properties of operations, place value understanding, and the relationship between multiplication and division to divide within 100.

### Glossary Entries

• algorithm
A set of steps that works every time as long as the steps are carried out correctly.

• area

The number of square units that cover a flat figure without gaps or overlaps.

• array

An arrangement of objects in rows and columns. Each column must contain the same number of objects as the other columns, and each row must have the same number of objects as the other rows.

• bar graph
A way to show how many in each group or category using the length of rectangles.

• division
Finding the number of groups or finding the size of each group when we share into groups of equal size.

• divisor
The number we are dividing by which can represent the size of the groups or the number of groups.

• equation

A statement that includes an equal sign (=). It tells us that what is on one side of the sign is equal to what is on the other side.

• expanded form

A specific way of writing a number as a sum of hundreds, tens, and ones.

Expanded form writes a number as a sum of the value of each digit. Example: 482 written in expanded form is $$400 + 80 + 2$$ .

• expression

An expression has at least 2 numbers and at least one math operation (such as addition, subtraction, multiplication and division).

• factor
When we multiply two whole numbers to get a product, each of those numbers is a factor of the product.

• key
The part of a picture graph that tells what each picture represents.

• multiplication
The operation that tells you the total number of objects when you have a certain number of equal groups.

• parentheses
Grouping symbols that can be used in expressions or equations, such as: $$(3 \times 5) + (2 \times 5), (24 \div 2) + 5 = 17$$.

• picture graph
A way to show how many in each group or category using pictures of the objects or symbols.

• product
The result of multiplying some numbers.

• quotient
The result in a division equation.

• rounding

A formal way to say which number a given number is closer to. For example, for 182, the number 180 is the closest multiple of ten and 200 is the closest multiple of a hundred. We can round 182 to 180 (if rounding to the nearest ten) or 200 (if rounding to the nearest hundred).

• scaled bar graph
A bar graph marked in multiples of some number other than 1.

• scaled picture graph
A picture graph where each picture represents an amount other than 1.

• square centimeter

A square with side lengths of 1 centimeter.

• square foot

A square with side lengths of 1 foot.

• square inch
A square with side lengths of 1 inch.

• square meter
A square with side lengths of 1 meter.