Finding missing tens

Multiplication strategies

There are many different strategies to use when solving multiplication and division problems. Let’s explore some of the strategies.

Repeated addition and repeated subtraction

We can use repeated addition to represent and solve a multiplication problem and repeated subtraction to represent and solve a division problem. Perhaps you used this strategy when you filled in the missing values in the multiplication chart.

Repeated addition or subtraction occurs when you add or subtract by the same number. Another name for repeated addition or repeated subtraction is skip counting.

Arrays

We can use arrays to represent and solve multiplication and division problems. Did you draw pictures to help find the missing values in the multiplication chart?

An array is a set that shows equal groups in rows and columns. Arrays help us identify equal groups and solve multiplication and division problems.

Number lines

We can use number lines to represent and solve multiplication and division problems.

We can model repeated jumps, or skips, on a number line to represent and solve multiplication and division problems. The jumps or skips represent the equal groups in the situation.

In this learning activity, we will learn to represent and solve multiplication and division situations.

When to multiply and when to divide

Multiplication and division are both used to represent situations that involve repeated groups of equal size. An important part of problem solving is knowing when to use multiplication and when to use division.

When we read word problems, there are key words to help us decide which operations to use to solve.

Multiplication and division: Opposite operations

Multiplication and division are opposite operations. We call multiplication and division inverse operations.

When we multiply, we know the size of the group and the number of groups. We multiply to find the total.

When we divide, there are two types of questions we can solve:

Equal Grouping: We know the size of the group and the total. We divide to find the number of groups.

OR

Equal Sharing: We know the number of groups and the total. We divide to find the size of the group.

These are multiplication sentences that show numbers that are in the same "fact family". In Math, a "fact family" is a group of math facts (or 'equations') made using the same numbers.

Multiplying and dividing with fractions

When we multiply, we combine equal groups and when we divide we decompose a whole into equal groups. We can multiply and divide whole numbers and fractions.

We can use the same tools and strategies to represent and solve multiplication and division problems involving fractions that we use with whole numbers.

Riley was given 5 halves of a sandwich. How many sandwiches does he have? In your number sentence, circle each instance of $\frac{1}{2}$ + $\frac{1}{2}$ to indicate a whole.

Solution using repeated addition

Let’s use repeated addition to represent and solve the problem.

I know that Jasper has eaten $\frac{1}{4}$ of a sandwich. I know that Riley has eaten 5 times as much. Times is a key word to represent multiplication. I know I have to multiply to solve.

I can use repeated addition to solve. I know I have to add $\frac{1}{2}$ five times.

$\frac{1}{2}$ + $\frac{1}{2}$ + $\frac{1}{2}$ + $\frac{1}{2}$ + $\frac{1}{2}$ + $\frac{1}{2}$ = $\frac{5}{2}$

When I add the $\frac{1}{2}$ s together my answer is $\frac{5}{2}.$  I know this means that there are 5 parts but the whole is 2 parts. That means that there are 2 parts = 1 whole.

Since there are 5 parts, I know Riley ate 2 whole sandwiches and $\frac{1}{2}$ of another sandwich.

Jazmine eats half of a banana everyday for a snack. Jazmine has 3 bananas. How many snacks can Jazmine have?

$3-\frac{1}{2}-\frac{1}{2}-\frac{1}{2}-\frac{1}{2}-\frac{1}{2}-\frac{1}{2}.$

Again circle two halves to show one banana.

Solution using a number line

I know that Jazmine runs $\frac{1}{4}$ km every day. I know that Jazmine is training to run 1 km. I see that Jazmine is running the same amount each day and the question is asking “how many days will it take to run the full 1 km?”

This looks like a division question where I know the size of the group and the total, but I have to find the number of groups. This is an equal grouping division question.

I can solve using a number line. My number line represents $\frac{1}{4}$ groups. How many groups of $\frac{1}{4}$ can make to total 1 whole?

I have jumped 4 times to represent 4 groups of one fourth. I know that it will take 4 days for Jazmine to run 1 km if she runs $\frac{1}{4}$ each day.

Challenge

Solve the following problem using tools and strategies you have learned in this lesson.

Is this solution correct?

Here is one solution. Priva’s class will have more markers at each table because Priva’s class has 24 markers and Mathias’ class has 20 markers. Since 24 is greater than 20, Priva’s class will have more markers at the tables. Is this solution correct? Use a variety of representations to show your thinking.

Reflection

How do you feel about what you have learned in this activity?  Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.

Now, record your ideas about your feelings using a voice recorder, speech-to-text, or writing tool.