Situations and Equations
10 min
Narrative
The purpose of this Warm-up is to elicit the idea that letters can be used to represent an unknown quantity in a tape diagram and an equation, which will be useful when students represent unknown quantities in word problems later in the lesson. While students may notice and wonder many things about these images, the fact that a letter can be used to represent an unknown in the same way as a question mark, line, or box is the important discussion point.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
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 first diagram→4 parts: ?, 8, 8, 8 with total 128
- 2Observe second diagram→4 parts: b, 8, 8, 8 with total 128
- 3Notice the difference→First uses ? for unknown, second uses letter b
- 4Recognize equivalence→Letter b can represent unknown just like ?; both show b + (3×8) = 128
Sample Response
Students may notice:
- The total in each diagram is 128.
- There are 3 parts that have 8. This could be expressed as 3×8.
- There’s a question mark in the large section in one diagram, but a letter in the other.
Students may wonder:
- Why does one have a question mark and one has the letter b?
- What problem could each diagram represent?
Activity Synthesis (Teacher Notes)
- “These diagrams show us that we can use a letter to represent an unknown quantity, the way we have used a question mark, a line, or a box in previous lessons. We will explore this idea further during today’s lesson.”
Standards
- 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>
20 min
15 min
Knowledge Components
All skills for this lesson
Situations and Equations
10 min
Narrative
The purpose of this Warm-up is to elicit the idea that letters can be used to represent an unknown quantity in a tape diagram and an equation, which will be useful when students represent unknown quantities in word problems later in the lesson. While students may notice and wonder many things about these images, the fact that a letter can be used to represent an unknown in the same way as a question mark, line, or box is the important discussion point.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
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 first diagram→4 parts: ?, 8, 8, 8 with total 128
- 2Observe second diagram→4 parts: b, 8, 8, 8 with total 128
- 3Notice the difference→First uses ? for unknown, second uses letter b
- 4Recognize equivalence→Letter b can represent unknown just like ?; both show b + (3×8) = 128
Sample Response
Students may notice:
- The total in each diagram is 128.
- There are 3 parts that have 8. This could be expressed as 3×8.
- There’s a question mark in the large section in one diagram, but a letter in the other.
Students may wonder:
- Why does one have a question mark and one has the letter b?
- What problem could each diagram represent?
Activity Synthesis (Teacher Notes)
- “These diagrams show us that we can use a letter to represent an unknown quantity, the way we have used a question mark, a line, or a box in previous lessons. We will explore this idea further during today’s lesson.”
Standards
- 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>