1. Problem Solving
Created by Mr. Hemmert

2. ARMT Standards
6 – Solve problems, including word problems, that involve addition and subtraction of four digit numbers with and without regrouping.
7 – Solve problems, including word problems, involving the basic operations of multiplication and division on whole numbers through two-digit multipliers and one-digit divisors.

3. Essential Question
How does problem solving in math apply to our everyday lives?

4. Key Words – List all the key words for the different operations.
Addition
Subtraction
Multiplication
Division
Go to the next slide to check your answers.

5. Key Words – List all the key words for the different operations.
Addition
Subtraction
Multiplication
Division
total
combined
how many in all
how many
difference
have left
how many more
how much more
fewer
in all
altogether
times
in each
half
share equally
Go to the next slide to check your answers.

6. Note about Key Words for Multiplication Word Problems
There is a difference between addition key words and multiplication key words.
In multiplication key words, you are finding a total when given equal groups.
Go to the next slide for an example.

7. Multiplication Key Words
Ex: Scott has 25 boxes of markers. Each box has 10 markers in it. How many markers does Scott have in all?
Do we have groups? What are they?
What key word is letting us know that we need to multiply?
Could you add this problem and get the correct answer?

8. Division Key Words
Divide to find a number of equal groups or the number in equal groups.
Key words like “in each”, “half” and “share equally” suggest you should divide.

9. Example of a Division Word Problem
Mary Alice has invited 220 people to her wedding. She has tables that seat 4 people each. How many tables does Mary Alice need?
What are we trying to solve?
How many tables Mary Alice will need to seat 220 people.

10. Example 1 – Solve
Jacob has 96 baseball cards to place in a baseball card album. He can place 6 cards on each page.
How many pages will Jacob need?
If Jacob had 30 pages, how many baseball cards would it take to fill up all 30 pages?

11. Example 1 Steps to Solve
Jacob has 96 baseball cards to place in a baseball card album. He can place 6 cards on each page.
How many pages will Jacob need?
Step 1 – What operation would I use to solve this problem? What do I know? What am I solving?
Step 2 – Solve
Step 3 – Put your answer in sentence form.
Step 1 – I would use division because I am grouping baseball cards.
Step 2 – 96/6 = 16
Step 3 – Jacob will need 16 pages for 96 baseball cards.

12. Example 1 Solved
Jacob has 96 baseball cards to place in a baseball card album. He can place 6 cards on each page.
How many pages will Jacob need?
Step 1 – I would use division because I’m grouping baseball cards.
Step 2 – 96/6 = 16
Step 3 – Jacob will need 16 pages for 96 baseball cards.
Step 1 – I would use division because I am grouping baseball cards.
Step 2 – 96/6 = 16
Step 3 – Jacob will need 16 pages for 96 baseball cards.

13. Example 1b
Jacob has 96 baseball cards to place in a baseball card album. He can place 6 cards on each page.
If Jacob had 30 pages, how many baseball cards would it take to fill up all 30 pages?
Step 1 – What operation would I use to solve this problem? What do I know? What am I solving?
Step 2 – Solve
Step 3 – Put your answer in sentence form.

14. Example 1b
Jacob has 96 baseball cards to place in a baseball card album. He can place 6 cards on each page.
If Jacob had 30 pages, how many baseball cards would it take to fill up all 30 pages?
Step 1 – Well I know that Jacob has 30 pages and that it takes 6 cards to fill up a page. Therefore, to find how many cards he will need to fill all 30 pages, I will multiply.
Step 2 – 30 times 6 = 180
Step 3 – Jacob will need 180 cards to fill 30 pages in his baseball card album.
Step 1 – Well I know that Jacob has 30 pages and that it takes 6 cards to fill up a page. Therefore, to find how many cards he will need to fill all 30 pages, I will multiply.

15. Example 2
Anna had $6.26. She bought a pack of mints for $0.75 and a soft drink for $1.09.
A. How much did the mints and drink cost together?
B. How much did Anna have left after she bought those two items?

16. Step by Step 2a
Anna had $6.26. She bought a pack of mints for $0.75 and a soft drink for $1.09.
A. How much did the mints and drink cost together?
Step 1 – What operation would I use to solve this problem? What do I know? What am I solving?
Step 2 – Solve
Step 3 – Put your answer in sentence form.

17. Step by Step 2a
Anna had $6.26. She bought a pack of mints for $0.75 and a soft drink for $1.09.
A. How much did the mints and drink cost together?
Step 1 – Since I’m finding the total cost of the mints ($.075) and the soft drink ($1.09) I know I have to add.
Step 2 – $ $1.09 = $1.84
Step 3 – The drink and mints cost $1.84.

18. Step by Step 2b
Anna had $6.26. She bought a pack of mints for $0.75 and a soft drink for $1.09.
B. How much did Anna have left after she bought those two items?
Steps:
Step 1 – What operation would I use to solve this problem? What do I know? What am I solving?
Step 2 – Solve
Step 3 – Put your answer in sentence form.

19. Step by Step 2b
Anna had $6.26. She bought a pack of mints for $0.75 and a soft drink for $1.09.
B. How much did Anna have left after she bought those two items?
Steps:
Step 1 – Since I need to find out how much Anna will have left after buying those two items, I must use my answer from part a (how much money she spent: $1.84) and subtract that from how much money she had to begin with ($6.26)
Step 2 – $ $1.84 =
Step 3 – Anna will have $4.42 left after buying these two items.

20. Your Turn
You are going to complete the rest of the problem solving questions on your worksheet. Be sure to follow the problem solving steps I’ve shown you today. You will be allowed to use a calculator to check your work but you must show me all of your work in order to get the full amount of points.