PROBLEM-SOLVING 101 · 01
The Three-Read Method
Understand the story. Connect the quantities. Clarify the question.
When students encounter a word problem, some immediately search for numbers and try to choose an operation. I want them to pause long enough to understand the situation.
In my classroom, we read a problem three times, with a different purpose each time. Students take turns leading, sharing what they notice, and helping classmates make sense of the story.
This is my classroom adaptation of the Three Reads mathematical language routine.
OUR CAT PROBLEM
Four shelves each have six cats. Seven cats move away. How many cats are still on the shelves?
1
FIRST READ
Visualize
“Close your eyes and...”
The class responds: “Visualize!”
Invite a student to read the problem aloud while classmates picture what is happening. Students may keep their eyes open if that helps them attend to the story.
ASK
“What did you picture?”
“What is happening in this story?”
Invite someone to describe the scene, then make a quick sketch. At this point, focus on understanding the situation rather than calculating an answer.
Example: Students picture cats sitting on shelves, with some cats moving away.
2
SECOND READ
Quantities
“What do the numbers mean?”
Invite another student to read and lead. Help students connect each number to the quantity it describes.
In our cat problem, we identify:
shelves
4
cats on each shelf
6
cats moved away
7
There is an important difference between saying “six cats” and saying “six cats on each shelf.” That relationship helps us understand the mathematics.
ASK
“What does each number describe?”
“How are these quantities connected?”
“What changes in the story?”
Record students’ descriptions so they can refer to them as they work.
3
THIRD READ
The Question
“What is the question asking?”
Read the problem together. Ask students to explain what they need to find, using their own words.
For our example:
“We need to find how many cats are still on the shelves after seven move away.”
Clarify what a complete answer will describe. Then invite students to consider how they might represent and solve the problem.
Tip: You can also keep the question covered during the first two readings and reveal it for the third.
From Understanding to Solving
Once students understand the situation, quantities, and question, move into schema instruction and mathematical modeling.
They can represent these relationships with a model and equations:
4 × 6 = 24
24 − 7 = 17
For the cat problem, students might recognize:
EQUAL GROUPS
Four shelves with six cats on each shelf.
A CHANGE
Seven cats move away from the total.
Ask students to explain what each result means. The 24 represents the cats before any move away; the 17 represents the cats remaining.
Return to the story: “Does our answer make sense?”
SEE IT IN MY CLASSROOM
On the Problem of the Day page, students write the story, prepare a model, and lead the three reads for their classmates.
Connections to Mathematical Practice
The following connections describe what students have opportunities to practice when the routine includes explanation and discussion.
MP1
Understanding and Persisting
Students work to understand the situation and identify what they need to find before planning a solution. They return to the story to check their reasoning.
TEACHER PROMPT
“Tell us what is happening before we decide how to solve.”
MP2
Reason abstractly and quantitatively
Students connect numbers to their meanings, represent relationships with symbols, and interpret those symbols in context.
TEACHER PROMPT
“What does the six represent? What does the 24 represent?”
MP6
Communicating Precisely
Students distinguish between quantities such as six cats altogether and six cats on each shelf. They describe the unknown and label their answers clearly.
TEACHER PROMPT
“Can you describe that quantity more precisely?”
Extending Into
MP4
When students move from the readings into drawings, diagrams, or equations, they have an opportunity to model with mathematics.
TEACHER PROMPT
“How does your model show what happened in the story?”