Problem Solving
How do you use what you have learned to problem solve?
Goal:
Goal:
Practice!
Goal: Apply what you have learned about multiplication and division with arrays to solve a word problem.
Can you make an array to solve two problems? You will need 75 counters and a piece of lined paper or graph paper. You will put counters into rows and columns. Then you will trace them to make an array. Follow the problem-solving steps to find the answer! Click the tabs to see how!
Word Problem Solving Steps
- Read the problem.
- Look for important information.
- Write a math sentence.
- Choose a way to solve.
- Solve and label your answer.
Click on each tab to see how to solve both a multiplication problem and a division problem using an array!
Click to see how to solve the first problem!
Caleb found 9 groups of 8 jewels. How many jewels did he find in total?
Follow each step on your own. Then click the step to check your work.
Step 1: Read the Problem
The first step is to read. Write down the problem. Then read the problem again! It is helpful to read the problem as many times as you need to in order to see all of the important information!
Step 2: Find the Important Information
Read the problem again. Look for the important information. The problem has the information you need. There are numbers, a key word, and a question. The first factor is highlighted in red. The second factor is highlighted in yellow. The key words are circled. The question is underlined.
Caleb found 9 groups of 8 jewels. How many jewels did he find
in total?
9 and 8 are the important numbers. The words “of” and “in total” are the key words. The question is the last sentence in the problem.
Caleb found 9 groups of 8 jewels. How many jewels did he find
in total?
The problem uses words that tell you to multiply. 9 and 8 are the important numbers. You need to fill in the factors of the multiplication sentence.
___ \({ \times }\) ___ = ___
Put the first factor on the first line. Put the second factor on the second line. It will look like this:
9 \({ \times }\) 8 = ___
Caleb found 9 groups of 8 jewels. How many jewels did he find
in total?
9 \({ \times }\) 8 = ___
Now create an array to solve the problem. Look at the first factor to find out how many rows you need. Look at the second factor to find out how many columns, or number of shapes in each row, you need. Use the counters to show the correct rows and columns. Then trace each counter to show the array on your paper. You will make a dot where each counter was!
A 9 by 8 array is correct!
Caleb found 9 groups of 8 jewels. How many jewels did he find
in total?
9 \({ \times }\) 8 = ___
Find the product. You can count all of the dots you made. You can also add each row of dots.
9 \({ \times }\) 8 = 72
There are 9 groups of 8. 9 times 8 equals 72.
The answer needs to have a label word. The number and word will answer the question in the problem! Write them on the line.
Question:
How many jewels did Caleb find?
72 jewels
Caleb found 72 jewels in 9 rooms. He found an equal group of jewels in each room. How many jewels were in each room?
Click the steps to see how to solve the division problem using an array!
Step 1: Read the Problem
The first step is to read. Write down the problem. Then read the problem again! It is helpful to read the problem as many times as you need to in order to see all of the important information!
Step 2: Find the Important Information
Read the problem again. Look for the important information. The problem has the information you need. There are numbers, a key word, and a question. The dividend is highlighted in blue. The divisor is highlighted in red. The key words are circled. The question is underlined.
Caleb found 72 jewels in 9 rooms. He found an equal group of jewels in each room. How many jewels were in each room?
72 and 9 are the important numbers. The words “equal group” are the key words. The question is the last sentence in the problem.
Caleb found 72 jewels in 9 rooms. He found an equal group of jewels in each room. How many jewels were in each room?
The problem uses words that tell you to divide. 72 and 9 are the important numbers. You need to fill in the dividend and divisor of the division sentence.
___ \({ \div }\) ___ = ___
Put the dividend on the first line. Put the divisor on the second line. It will look like this:
72 \({ \div }\) 9 = ___
Caleb found 72 jewels in 9 rooms. He found an equal group of jewels in each room. How many jewels were in each room?
72 \({ \div }\) 9 = ___
Now create an array to solve the problem. Get out the same number of counters as the dividend. Each counter represents a jewel! The number of rows is the same number as the divisor. Set up one column that has the same number of counters as the divisor. Then make another column. Make columns until all of the counters are in the array. Trace the counters to make dots. Each row should have the same number of dots.
A 9 by 8 array is correct!
Caleb found 72 jewels in 9 rooms. He found an equal group of jewels in each room. How many jewels were in each room?
72 \({ \div }\) 9 = ___
Did you notice that the array you used to multiply is the same as the one you are using to divide? Now use it to find the quotient! Count the number of dots in one row.
Find the quotient.
72 \({ \div }\) 9 = 8
There are 8 dots in each row. 72 divided by 9 equals 8.
The answer needs to have a label word. The number and word will answer the question in the problem! Write them on the line.
Question:
How many jewels are in each room?
8 jewels
Try to solve the next two problems on your own.
Read the problem. Then use counters to create an array and solve!
Caleb found 10 groups of 7 jewels. How many jewels did he find in total?
- 70 jewels
- 17 jewels
- 70 gold bars
Use a 10 by 7 array. Count all of the dots or add the rows of 10 to find the number of jewels!
Use a 10 by 7 array. Count all of the dots or add the rows of 10 to find the number of jewels!
Use a 10 by 7 array. Count all of the dots or add the rows of 10 to find the number of jewels!
Read the problem. Then use counters to create an array and solve!
Caleb found 70 jewels in 7 rooms. He found an equal group of jewels in each room. How many jewels were in each room?
- 9 gold bars
- 7 jewels
- 10 jewels
Use a 7 by 10 array. Count the dots in one row to find the number of jewels!
Use a 7 by 10 array. Count the dots in one row to find the number of jewels!
Use a 7 by 10 array. Count the dots in one row to find the number of jewels!
Summary
Questions answered correctly:
Questions answered incorrectly: