Free Resources for Algebra: Expressions and Equations - Middle School Connections

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.

A.1 and A.2 Pre-Assessment

Pre-Assessing for Fundamental Understanding

We are going to start this week by looking at using pre-assessments to assess student understanding of the fundamental building blocks that lead to conceptual understanding in Algebra.

Analyzing Pre-Assessment Responses to look for Understanding of Connected Skills

On our blog this week, we will take a look at analyzing pre-assessment responses to look for understanding of connected skills.

Use Formative Assessments to Group and Regroup

Also on our blog this week, we will talk about using formative assessments to group, regroup (and then regroup again).


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Connected Skill 1: The Order of Operations

Click on the following images to find an example video and free practice resources that can be used to highlight the ‘whY.’

Example Video: Simplify Expressions With the Order of Operations

Click on the image to watch a LearnZillion video on the logic behind the order of operations.

YouCubed Activity- Four 4s

Click on the image to open a description of ‘Four 4s’ on the YouCubed website. As students find expressions to make each number using only Four 4s, teachers can hold class discussions about which expressions are actually equivalent using the order of operations, and how grouping symbols can be used to make any expression equivalent to a given number. Click on the image to the right/below for a PDF recording sheet.

PDF Recording Sheet- Four 4s

Click on the image to open a PDF recording sheet for the Four 4s activity described to the left/above.


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Connected Skill 2: The Distributive Property

Click on the following images to find example videos and manipulatives that highlight the ‘whY.’

Example Video 1: Write Equivalent Expressions Using the Distributive Property of Multiplication Over Addition

Click on the image to watch a LearnZillion video on modeling the distributive property with area models.

Example Video 2: PBS- Use Algebra Tiles to Model the Distributive Property

Click on the image to open a PBS video on using algebra tiles to model the distributive property. Digital or tactile algebra tiles can be used to model any application of the distributive property and of combining like terms.

Free Practice Resource: Open Up Resources- Identify Expressions that use the Distributive Property in Authentic Contexts

Click on the image to open the lesson outline from Open Up Resources. This lesson can be used to help clarify misconceptions about the distributive property when working with unknown values.


Connected Skill 3: Addition and Subtraction of Negative Integers

Click on the following images to find example videos and manipulatives that highlight the ‘whY.’ Additionally, click on the image above to watch our Number Line Football animation on Instagram.

Example Video 1: Add Integers Using Chips

Click on the image to watch a LearnZillion video on adding integers using integer chips.

Example Video 2: Subtract Integers Using a Number Line

Click on the image to open a LearnZilliion video on using a number line to subtract integers.

3) App- Two- Color Counters

Click on the image to open a description of Brainingcamp’s Integer Chip app. Integer chips (either digital or tactile) can be used to help students model addition, subtraction, multiplication, and division of integers. They can be used to supplement traditional practice with integer computation from any textbook or resource.

(We do our best to try to suggest free resources on Y Understand Math. However, we have yet to find a free, user-friendly digital integer chips tool. This is an area we have identified as a need in visual mathematics. For now, we recommend the Brainingcamp suite of manipulative apps. Each app is $2.99 by itself, $59/yr for all 15 manipulatives on one device, or $95/year for all 15 manipulatives on 1 teacher and up to 30 student devices).


Patterns to Make Multiplication Generalizations

Connected Skill 4: Using Patterns to Identify Rules for Multiplication and Division of Negatives

Click on the following images to find example videos and manipulatives that highlight the ‘whY.’

1) Explore Multiplying Integers Using Number Line Models- Desmos

Click on the image to open a Desmos lesson by Andrew Stadel on using number lines to make a generalizations about multiplying positive and negative integers. Slides 11-14 ask students to make generalizations about multiplying two negative integers, and it may be helpful to have students try the pattern activity (#3 in this progression) before working with the concept of “the opposite of.”

2) Example Video: Divide Positive and Negative Integers by Observing Patterns

Click on the image to open a LearnZillion video . This video will introduce the concept of looking at patterns to make generalizations.

3) Use Patterns to Make Generalizations about Multiplying Integers - Desmos

Click on the image to open to a Desmos activity by Greta that helps students look at patterns to discover the rule for multiplying two negative integers.