How Does It Change?
5 min
Narrative
This Warm-up encourages students to quantify the number of squares in a geometric pattern by looking for and making use of structure (MP7). The thinking involved here prepares students to reason about other patterns that illustrate quadratic relationships.
Launch
Arrange students in groups of 2. Give students a minute of quiet think time, and then ask them to share their thinking with their partner.
Student Task
- Expression A: 6⋅8−2⋅3
- Expression B: 4⋅8+2⋅5
- Expression C: 8+8+8+8+5+5
- Expression D: 5⋅6+3⋅4
- Which expression best matches how you would describe the number of small squares in the figure?
- Select at least one other expression and explain how it represents the number of small squares in the figure.
Sample Response
- Expression A: There are 6 rows with 8 small squares but from this 2 rows of 3 small squares have been removed.
- Expression B: There are 4 rows of 8 small squares and to this 2 rows of 5 small squares are added.
- Expression C: This counts each row, starting from the bottom.
- Expression D: There are 5 columns of 6 small squares and 3 columns of 4 small squares.
Activity Synthesis (Teacher Notes)
Make sure that students see how each expression tells us about a way the squares can be counted or how the area of the figure can be determined. If time permits, ask students if they could generate a different expression that also represents the number of squares in the figure.
Standards
- A-SSE.1·Interpret expressions that represent a quantity in terms of its context
- A-SSE.1·Interpret expressions that represent a quantity in terms of its context
- A-SSE.1·Interpret expressions that represent a quantity in terms of its context
- A-SSE.1·Interpret expressions that represent a quantity in terms of its context
- A-SSE.1·Interpret expressions that represent a quantity in terms of its context
- A-SSE.1·Interpret expressions that represent a quantity in terms of its context
- A-SSE.3·Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- A-SSE.3·Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- A-SSE.3·Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- HSA-SSE.A.1·Interpret expressions that represent a quantity in terms of its context.
- HSA-SSE.B.3·Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
How Does It Change?
5 min
Narrative
This Warm-up encourages students to quantify the number of squares in a geometric pattern by looking for and making use of structure (MP7). The thinking involved here prepares students to reason about other patterns that illustrate quadratic relationships.
Launch
Arrange students in groups of 2. Give students a minute of quiet think time, and then ask them to share their thinking with their partner.
Student Task
- Expression A: 6⋅8−2⋅3
- Expression B: 4⋅8+2⋅5
- Expression C: 8+8+8+8+5+5
- Expression D: 5⋅6+3⋅4
- Which expression best matches how you would describe the number of small squares in the figure?
- Select at least one other expression and explain how it represents the number of small squares in the figure.
Sample Response
- Expression A: There are 6 rows with 8 small squares but from this 2 rows of 3 small squares have been removed.
- Expression B: There are 4 rows of 8 small squares and to this 2 rows of 5 small squares are added.
- Expression C: This counts each row, starting from the bottom.
- Expression D: There are 5 columns of 6 small squares and 3 columns of 4 small squares.
Activity Synthesis (Teacher Notes)
Make sure that students see how each expression tells us about a way the squares can be counted or how the area of the figure can be determined. If time permits, ask students if they could generate a different expression that also represents the number of squares in the figure.
Standards
- A-SSE.1·Interpret expressions that represent a quantity in terms of its context
- A-SSE.1·Interpret expressions that represent a quantity in terms of its context
- A-SSE.1·Interpret expressions that represent a quantity in terms of its context
- A-SSE.1·Interpret expressions that represent a quantity in terms of its context
- A-SSE.1·Interpret expressions that represent a quantity in terms of its context
- A-SSE.1·Interpret expressions that represent a quantity in terms of its context
- A-SSE.3·Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- A-SSE.3·Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- A-SSE.3·Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- HSA-SSE.A.1·Interpret expressions that represent a quantity in terms of its context.
- HSA-SSE.B.3·Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.