Diagrams and Equations for Word Problems
10 min
Narrative
The purpose of this Warm-up is to elicit the idea that diagrams can represent many operations, which will be useful when students connect diagrams to situations and equations in a later activity. While students may notice and wonder many things about these images, what operations the diagrams could represent is the important discussion point.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Solution Steps (4)
- 1Observe Diagram A→Rectangle split into 2 parts: 142 and 20. Represents 142+20=?
- 2Observe Diagram B→Rectangle split into 4 equal parts of 5. Represents 4×5=?
- 3Observe Diagram C→Rectangle split into 5 parts: 142 and four 5s. Represents 142+(4×5)=?
- 4Notice the pattern→Diagram C combines addition and multiplication in one diagram
Sample Response
Students may notice:
- The diagrams show a lot of the same numbers.
- The first diagram shows a 20 and the others show four 5s.
- The total is missing in each diagram.
- The first diagram shows addition.
- The second diagram shows multiplication.
- The total is different in the second diagram.
Students may wonder:
- What is the total in each diagram?
- What operation does the last diagram show?
- Does the last diagram show multiplication and addition?
Activity Synthesis (Teacher Notes)
- “You’ve seen the first two types of diagrams before, when you represented addition situations and multiplication situations. We are going to make sense of the last type of diagram in today's lesson.”
- “What operations do you think could be represented in the last diagram?” (It could be multiplication and addition. Like you multiply 4 times 5 and add it to 142.)
- Consider asking:
- “Could the last diagram represent addition and multiplication?”
Standards
Building Toward
- 3.OA.8·Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
- 3.OA.D.8·Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.<span>This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).</span>
15 min
20 min
Knowledge Components
All skills for this lesson
Role Legend
Target
Essential
Supporting
Foundational
All lesson KCs
4 skills
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Diagrams and Equations for Word Problems
10 min
Narrative
The purpose of this Warm-up is to elicit the idea that diagrams can represent many operations, which will be useful when students connect diagrams to situations and equations in a later activity. While students may notice and wonder many things about these images, what operations the diagrams could represent is the important discussion point.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Solution Steps (4)
- 1Observe Diagram A→Rectangle split into 2 parts: 142 and 20. Represents 142+20=?
- 2Observe Diagram B→Rectangle split into 4 equal parts of 5. Represents 4×5=?
- 3Observe Diagram C→Rectangle split into 5 parts: 142 and four 5s. Represents 142+(4×5)=?
- 4Notice the pattern→Diagram C combines addition and multiplication in one diagram
Sample Response
Students may notice:
- The diagrams show a lot of the same numbers.
- The first diagram shows a 20 and the others show four 5s.
- The total is missing in each diagram.
- The first diagram shows addition.
- The second diagram shows multiplication.
- The total is different in the second diagram.
Students may wonder:
- What is the total in each diagram?
- What operation does the last diagram show?
- Does the last diagram show multiplication and addition?
Activity Synthesis (Teacher Notes)
- “You’ve seen the first two types of diagrams before, when you represented addition situations and multiplication situations. We are going to make sense of the last type of diagram in today's lesson.”
- “What operations do you think could be represented in the last diagram?” (It could be multiplication and addition. Like you multiply 4 times 5 and add it to 142.)
- Consider asking:
- “Could the last diagram represent addition and multiplication?”
Standards
Building Toward
- 3.OA.8·Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
- 3.OA.D.8·Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.<span>This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).</span>