options: Work with radicals and integer exponents.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Understand properties of multiplication and the relationship between multiplication and division.

Interpret the structure of expressions.

Gain familiarity with factors and multiples.

Rewrite rational expressions.

Understand solving equations as a process of reasoning and explain the reasoning.

Use polynomial identities to solve problems.

Add and subtract within 20.

Write and interpret numerical expressions.

Understand the connections between proportional relationships, lines, and linear equations.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Use properties of operations to generate equivalent expressions.

Perform arithmetic operations on polynomials.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Multiply and divide within 100.

Work with equal groups of objects to gain foundations for multiplication.

Understand the relationship between zeros and factors of polynomials.

Use the four operations with whole numbers to solve problems.

Solve equations and inequalities in one variable.

Understand and apply properties of operations and the relationship between addition and subtraction.

Reason about and solve one-variable equations and inequalities.

Solve systems of equations.

Write expressions in equivalent forms to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve equations and inequalities graphically.

Work with addition and subtraction equations.

Represent and solve problems involving multiplication and division.

Generate and analyze patterns.

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

Create equations that describe numbers or relationships
problem_activity: Activity
One purpose of this activity is to practice seeing the total length of a segment as the sum of its pieces, and using the whole side length of a rectangle to express its area. Another is to generate examples of equivalent expressions, and understand why they are equivalent based on an understanding of area and the distributive property.
Monitor for students who write different but equivalent expressions to represent the area of a rectangle. For example,
\(2(t+5+t)\)
,
\(2t+10+2t\)
, and
\(4t+10\)
for figure B.
Student Facing
Complete the table with the length, width, and area of each rectangle.
[IMG]
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "rectangle"}, {"_attributes": {"scope": "col"}, "_value": "length (units)"}, {"_attributes": {"scope": "col"}, "_value": "width (units)"}, {"_attributes": {"scope": "col"}, "_value": "area (square units)"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "A"}, {"span": [{"_attributes": {"class": ["math", "math-repaired"]}, "_value": "\\(a+4\\)"}]}, {}, {}]}, {"td": [{"_value": "B"}, {}, {"_value": "2"}, {}]}, {"td": [{"_value": "C"}, {}, {}, {}]}, {"td": [{"_value": "D"}, {}, {}, {}]}, {"td": [{"_value": "E"}, {}, {}, {}]}]}]}]}
Student Response
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Activity Synthesis
Invite previously-selected students to share different but equivalent expressions for length and area. (Reassure students that it doesn’t matter which side is considered the length or the width.) If any students express confusion over a response, encourage the student who came up with the response to explain. For example, a student might wonder why
\(a+a+a\)
can be expressed as
\(3a\)
.
Display the table from the task statement for all to see, and write any equivalent expressions that are mentioned next to each other. For example, for the area of figure A, you might write
\(5(a+4)\)
,
\((4+a) \boldcdot 5\)
, and
\(5a+20\)
. Show in the figure how you can see
\(5(a+4)\)
(the product of one side and the other whole side) and
\(5a+20\)
(the area of each smaller rectangle, added up). Emphasize that all of these expressions correctly represent the area of the whole figure, and highlight use of the distributive property where it occurs.


correct_option_index: 2