1. Four-Step Problem Solving Process
First Grade
who?
what?
Details
less
actions?
more

2. Four-Step Process for Problem Solving
Teaches the importance of language within math problems
Provides foundation for algebraic understanding
Provides for differentiated instruction
Developed in Singapore
Visual representation of details and actions which assists children with problem solving
Helps children logically think using visual models to determine their computations
Fosters quantitative reasoning (number sense) when teachers question
Empowers students to think systematically and master more difficult problems
Makes 2 step problems easy to work

3. Four-Step Process for Solving Problems
Step 2-Details and Model Drawing
Step 1-Main Idea
Who
What
Draw One Unit:
A drawing, or model, of the Unifix cube(s)
Read one sentence at a time and adjust the Unifix cubes and the drawing (or model) of the Unifix cubes
Main Idea of Question (What do you want to find out?)
Step 3-Strategy/Solve
Step 4-How
Step 1
Read the problem.
What is the main idea of the question? What do you want to find out?
Write the main idea of the question.
Step 2 is about the details and making a drawing (model drawing).
Who is the problem about?
What is the problem about?
Take out 1 unifix cube for each what (variable). Then, DRAW one unit (a drawing of the Unifix cube) for each what (variable).
Reread the problem one sentence at a time. Adjust the drawing(s), or model(s), as you learn more information.
When the bar is complete, it may help to have the student draw a line around the perimeter of the bar so they understand that it is a unit bar.
Label the drawing.
Step 3: What operation can we use to solve the problem?
Solve the problem.
Step 4: How did you solve the problem?
Solve the Problem
Describe how the problem was solved.

4. Four Step Process Model Drawing Main Idea Details or
Read the problem. What do you want to find out?
Write the main idea from the question.
Details or
Write who the problem is about
Write what the problem is about
Use one Unifix cube to represent each “what” or variable.
Then, draw the Unifix cube to represent one unit.
Reread the problem one sentence at a time.
Adjust the Unifix cubes and the drawing (model) of the Unifix cubes to match the story problem and label.
Put a question mark on the drawing, or model, to show what you are trying to find out.
Model Drawing

5. Four-Step Process Continued
3. Strategy/Solve the Problem
Write the number sentence and solve the problem.
4. How
Describe how the problem was solved.

6. Addition Action: Put Together
When adding, we often use the term “put together” because we use the action of putting things together. This is the only type of action we use when adding.
Action: Put Together

7. Ann has 2 toys. Jeff has 3 toys. How many toys do they have together?
Step 2: Details and Model Drawing
Step 1 Main Idea 2 ]
Toys together?
Ann- toys or A.T. ? 3
Jeff- toys or J.T.
Step 3: Strategy/Solve
Step 4: How
Step 1
Read the problem.
What is the main idea of the question? What do you want to find out?
Write the main idea of the question.
Step 2 is about the details and making a drawing.
Who is the problem about?
What is the problem about?
Let’s take out 1 unifix cube for each what (variable). Now, DRAW one unit (a drawing of the unifix cube) for each what (variable).
Reread the problem one sentence at a time. Label and adjust the drawings (or models) as you go.
Read the first sentence. Ann has 2 toys. Let’s add another unifix cube to show 2 toys.
To represent that, we need to draw another Unifix cube which will make a unit bar. Label the unit bar to show 2. When the bar is complete, it may help to have the student draw a line around the perimeter of the bar so they understand that it is a unit bar.
Read the next sentence. Jeff has 3 toys.
We have 1 unit (Unifix cube). What will we need to do to our Unifix cubes to show Jeff’s toys? (Add two more)
How many more units ( or Unifix cubes) will we need to draw? (2)
Label Jeff’s unit bar to show 3. When the bar is complete, it may help to have the student draw a line around the perimeter of the bar so they understand that it is a unit bar.
Let’s read the next sentence. “How many toys do they have together?”
Think about what the question is asking. What are we looking for?
Are we looking for just Ann’s toys?
Are we looking for just Jeff’s toys?
Are we looking for both of their toys?
Let’s show what we are looking for by linking them together with a brace and placing the ? beside the brace.
Step 3-Strategy/Solve the Problem
What operation could we use to figure out the answer to the question?
What should we do? (Add the numbers together) Why? (To see how many toys they have together)
Solve the problem.
Step 4
What could we write to describe how we solved the problem? 2
+ 3
Add 2 and 3
5 sum

8. ] ? Andy and Henry went to the zoo.
Andy and Henry went to the zoo. Andy saw Henry saw How many animals did the 2 boys see?
Andy saw
Henry saw
How many animals did the 2 boys see?
Details
Main Idea 4 ]
A. T. (Abbreviate for Andy-Turkeys)
H. P. (Abbreviate for Henry-Penguins)
animals 2 boys see? ? 5
Strategy/Solve
How
Step 1
Read the problem.
What is the main idea of the question? What do you want to find out?
Write the main idea of the question.
Step 2 is about the details and making a drawing.
Who is the problem about?
What is the problem about?
Let’s take out 1 unifix cube for each what (variable). Now, DRAW one unit (a drawing of the unifix cube) for each what (variable).
Reread the problem one sentence at a time. Label and adjust the drawings (or models) as you go. . When the bar is complete, it may help to have the student draw a line around the perimeter of the bar so they understand that it is a unit bar.
Step 3-Strategy/Solve the Problem
What operation could we use to figure out the answer to the question?
What should we do? Why?
Solve the problem.
Step 4
What could we write to describe how we solved the problem? 4
+ 5
Put together 4 and 5
9 sum

9. Subtraction Action: Take Away
There are three different actions that we use in subtraction problems. They are:
Take Away
Compare
Missing Part
The first type of action we will look at is take away. In this type of problem items are taken away from the whole group.
Action: Take Away

10. Amy has 4 toys. She gave away 1 toy. How many toys are left?]
Step 2
Step 1 4 X
A.T. (abbreviate for Ann- toys)
Toys left 1 ?
Step 3
Step 4
Step 1
Read the problem.
What is the main idea of the question? What do you want to find out?
Write the main idea of the question.
Step 2 is about the details and making a drawing.
Who is the problem about?
What is the problem about?
Let’s take out 1 unifix cube for each what (variable). Now, DRAW one unit (a drawing of the unifix cube) for each what (variable).
Reread the problem one sentence at a time. Label and adjust the drawings (or models) as you go.
Read the first sentence. Amy has 4 toys. Let’s add enough unifix cubes to show 4 toys.
To represent that, we need to draw more Unifix cubes. How many units (or Unifix cubes) will we need to draw to show 4 toys? Label the unit bar to show 4. When the bar is complete, it may help to have the student draw a line around the perimeter of the bar so they understand that it is a unit bar.
Read the next sentence. She gave away 1 toy.
What will we need to do to our Unifix cubes to show this action in the sentence? (Take one away)
To show Amy giving away 1 toy, let’s mark with an X the toys she gave away.
Let’s read the next sentence. “How many toys are left?”
Think about what the question is asking. What are we looking for?
Let’s put a brace and a ? to show this on the model (or drawing).
Step 3: Strategy/Solve
What is Amy doing? (Giving away one toy)
Is she going to have more toys or fewer toys? (Fewer)
What operation could we do to figure out the answer to the question? (Subtraction)
What should we do? (Take away) Why?
Solve the problem.
Step 4: How
What could we write to describe how we solved the problem? (Subtract 1 from 4 or take one away from 4) 4
- 1
Subtract 1 from 4. 3

11. Action: Compare Subtraction
The second type of subtraction action we will look at is “compare”.
We use this type of action when we are comparing two groups.

12. Steve has 4 toys. Jill has 1 toy
Steve has 4 toys. Jill has 1 toy. How many more toys does Steve have than Jill?
Step 1
Step 2 ] 4
S.T. (Abbreviate for Steve – Toys)
J.T. (Abbreviate for Jill-Toys)
More toys Steve than Jill ? 1
Step 3
Step 4
Step 1
Read the problem.
What is the main idea of the question? What do you want to find out?
Write the main idea of the question.
Step 2 is about the details and making a drawing.
Who is the problem about?
What is the problem about?
Let’s take out 1 unifix cube for each what (variable). Now, DRAW one unit (a drawing of the unifix cube) for each what (variable).
Reread the problem one sentence at a time. Label and adjust the drawings (or models) as you go.
Read the first sentence. Steve has 4 toys. Let’s add Unifix cubes to show 4 toys.
To represent that, we need to draw more Unifix cubes. How many units will we need to show 4 toys? Label the unit bar to show 4. When the bar is complete, it may help to have the student draw a line around the perimeter of the bar so they understand that it is a unit bar.
Read the next sentence. Jill has 1 toy.
What will we need to do to our Unifix cubes to show this sentence? (Nothing, we already have one) Draw one unit to show Jeff’s toys.
Do we need to draw any more Unifix cubes? (No, we already drew one and that is all Jill has.) When the bar is complete, it may help to have the student draw a line around the perimeter of the bar so they understand that it is a unit bar.
Let’s read the next sentence. “How many more toys does Steve have than Jill?”
Think about what the question is asking. What are we looking for?
What is the action in the story? (Compare)
Let’s show that action by drawing a line between Steve’s toys and Jill’s toys.
What part of the model are we looking for? (How many more toys Steve has than Jill)
Let’s put a brace and a ? to show this on the model.
Step 3
What operation could we do to figure out the answer to the question? (subtraction)
What should we do? Why? (compare, to see how many more )
Solve the problem.
Step 4
What could we write to describe how we found the answer? (I compared 1 and 4 or subtract one from four) 4
- 1
Subtract 1 from 4.
3 diff.

13. fewer cones than apples?
Ana has cones. Leo has apples. How many fewer cones are there than apples?
Details
Main Idea 3
A.C.(abbreviate for Ana-cones)
L.A. (abbreviate for Leo-Apples)
fewer cones than apples? ? ] 4
How
Strategy/Solve
Step 1
Read the problem.
What is the main idea of the question? What do you want to find out?
Write the main idea of the question.
Step 2 is about the details and making a drawing.
Who is the problem about?
What is the problem about?
Let’s take out 1 unifix cube for each what (variable). Now, DRAW one unit (a drawing of the unifix cube) for each what (variable).
Reread the problem one sentence at a time. Label and adjust the drawings (or models) as you go.
Read the first sentence. Ana has 3 cones. Let’s add unifix cubes to show 3 cones.
To represent that, we need to draw more Unifix cubes. How many more units (Unifix cubes) do we need to draw to show 3 cones? Label the unit bar to show 3. When the bar is complete, it may help to have the student draw a line around the perimeter of the bar so they understand that it is a unit bar.
Read the next sentence. Leo has 4 apples.
We have 1 unit (Unifix cube). What will we need to do to our Unifix cubes to show Leo’s apples? (Add three more)
How many more units ( or Unifix cubes) will we need to draw? (3)
Label Leo’s unit bar to show 4 .When the bar is complete, it may help to have the student draw a line around the perimeter of the bar so they understand that it is a unit bar.
Let’s read the next sentence. “How many fewer cones are there than apples?”
Think about what the question is asking. What are we looking for?
Let’s show what we are looking for by drawing lines between Ana’s cones and Leo’s apples. Let’s draw a brace around the extra apple that Leo has and place the ? above the brace.
Step 3-Strategy/Solve the Problem
What operation could we use to figure out the answer to the question? subtraction
What should we do? (Compare) Why?
Solve the problem.
Step 4- How
What could we write to describe how we solved the problem? 4
- 3
Subtract 3 from 4 1

14. Subtraction Action: Missing Part
The third type of action we will look at in subtraction is “Missing Part”. We use this action when we are trying to find out how many from the group are unknown or missing.

15. Step 3/Strategy (Solve)
Alex has 5 balls. Three are baseballs. The rest are footballs. How many are footballs?
Step 2/ Details
Step 1/ Main Idea ] 5
A.B. (abbreviate Alex-Balls) B B B F F
footballs ] 3 ?
Step 3/Strategy (Solve)
Step 4/ How
Step 1
Read the problem.
What is the main idea of the question?
Write the main idea of the question.
Step 2 is about the details.
Who is the problem about?
What is the problem about?
Let’s take out 1 Unifix cube for each “what” (variable). Now, DRAW one unit (a drawing of the unifix cube) for each “what” (variable).
Reread the problem one sentence at a time. Label and adjust the drawing (model) as you go.
Read the first sentence. Alex has 5 balls. Let’s use the unifix cubes to show 5 balls.
To represent that, we need to draw more Unifix cubes. How many more Unifix cubes, or units, will we need to draw to show 5 balls? Label the unit bar to show 5. When the bar is complete, it may help to have the student draw a line around the perimeter of the bar so they understand that it is a unit bar.
Read the next sentence. Three are baseballs.
Let’s label part of the model to show 3 baseballs by putting a B (for Baseball) on three of the balls.
Let’s read the next sentence: The rest are footballs. Label the rest of the units (Unifix cubes) with an F for Football.
Let’s read the next sentence. “How many are footballs?”
Think about what the question is asking.
What part of the model, or drawing, are we looking for?
Let’s put a brace and a ? to show this on the model.
Step 3
What operation could we do to figure out the answer to the question? (subtraction)
Why?
Solve the problem and write the answer.
Step 4
What could we write to describe how we solved the problem? (Subtract 3 from 5) 5
- 3
Subtract 3 from 5. 2

16. Tips
Be sure all the drawings of the Unifix cubes (units) for each variable are touching each other so comparisons are clearer.
In the drawing, list the variables in the order they appear in the problem.
Include labels and brackets to help clarify drawings.
Too often, students rush through a problem and answer the wrong question. Placing the question mark beside what you are trying to find helps to prevent that.

17. Extra Information in Word Problems
Sometimes there will be extra information in a word problem. Try to keep students focused on what the question is asking them to find.
If a child understands that the details are usually what is needed to answer the main idea of the question, he will be less likely to include information that is not needed.
However, if the child includes the extra information in the drawing, placing the ? in the model will help them understand what information is needed to answer the question.