Seeing Structure in Expressions Week 1- Unpacking the Standards - Common Misunderstandings Related to Vocabulary and Representation

CCSS.MATH.CONTENT.HSA.SSE.A.1.A: Interpret parts of an expression, such as terms, factors, and coefficients. CCSS.MATH.CONTENT.HSA.SSE.A.2: Use the structure of an expression to identify ways to rewrite it.

coefficient image

Misunderstanding 1: What does the coefficient represent?

Click on the following images to find an example video, a manipulative/ visual representation that can be used when practicing with this skill, and a free practice resource that highlights the ‘whY.’

Example Video: Coefficients

Click on the image to watch a LearnZillion video on writing expressions using parentheses.

Visual Model: Open Up Resources- Tape Diagrams

Click on the image to open a PDF from Open Up Resources. The lesson uses tape diagrams to highlight the difference between a coefficient and the sum of a variable and a constant.

Free Practice Resource: Open Up Resources- Complete Tape Diagrams and Equations Lesson

Click on the image to open to the complete Open Up Resources lesson on using tape diagrams to model equations.

(You will need to create a free teacher account on Open Up in order to use this resource.)


algebra tiles to model an equation

Misunderstanding 2: What are ‘like’ terms?

Click on the following images to find an example video, a manipulative/ visual representation that can be used when practicing with this skill, and a free practice resource that highlights the ‘whY.’

Example Video: Using Algebra Tiles to Model Expressions

Click on the image to watch a LearnZillion video on using algebra tiles to model an expression to find the area of a tile floor.

Manipulative: Algebra Tiles on the NCTM website

Click on the image to open the NCTM’s Algebra Tiles resource. Students can use this resource to practice modeling expressions.

Free Practice Resource: Desmos- Polygraph- Introduction to Algebra Tiles

Click on the image to open a Polygraph- Introduction to Algebra Tiles game (created by Jessica Borah).

For more information on ‘Polygraph,’ click on ‘learn more.’ (You will need to create a free teacher account on Desmos in order to use this resource.)


equations

Misunderstanding 3: Expressions vs. Equations

Click on the following images to find an example video, a manipulative/ visual representation that can be used when practicing with this skill, and a free practice resource that highlights the ‘whY.’

Example Video: How Are Variables Used in an Expressions?

Click on the image to watch a LearnZillion video on how variables are used in expressions and the difference between an expression and an equation.

Manipulative: Algebra Tiles on the NCTM website

Click on the image to open the NCTM’s Algebra Tiles resource. Students can use this resource to practice modeling expressions and solving equations.

Free Practice Resource: Open Up Resources- Lesson on Using Diagrams to Model Equivalent Expressions

Click on the image to open to the complete Open Up Resources lesson on using diagrams to model equivalent expressions.

(You will need to create a free teacher account on Open Up in order to use this resource.)


exponents

Misunderstanding 4: Exponents Represent Repeated Multiplication

Click on the following images to find an example video, a manipulative/ visual representation that can be used when practicing with this skill, and a free practice resource that highlights the ‘whY.’

Example Video: Find the Square Root of Perfect Squares

Click on the image to watch a LearnZillion video on finding the square root of perfect squares.

Visual Model: Perfect Squares Number Cube Game

Click on the image to open a PDF of a game we created to help students practice with identifying perfect squares. The rules are similar to the traditional ‘squares’ game.

Free Practice Resource: Open Up Lesson on The Meaning of Exponents

Click on the image to open to an Open Up lesson on ‘the meaning of exponents.’

(You will need to create a free teacher account on Open Up in order to use this resource.)


multiply binomials area models

Misunderstanding 5: Multiplying Binomials

Click on the following images to find an example video, a manipulative/ visual representation that can be used when practicing with this skill, and a free practice resource that highlights the ‘whY.’

Example Video: Use Area Models to Multiply Binomials

Click on the image to open a LearnZillion video on how to use an area model to multiply polynomials.

Algebra Tiles App

Manipulative: Algebra Tiles iPad app by Braincamp

Search “Algebra Tiles” by Braincamp, LLC on your iPad App Store to access the above app. It’s a paid app ($1.99), but it is much more user friendly when multiplying binomials.

If you would like a free tool that can also be used to multiply binomials, use the NCTM Algebra Tiles link above and click on ‘expand.’

Free Practice Resource: Desmos- Area- Multiplying Polynomials

Click on the image to open an Area- Multiplying Polynomials investigation (created by Andrew Stadel).

For more information on the lesson, click on ‘teacher’s guide.’ (You will need to create a free teacher account on Desmos in order to use this resource.)