## Seeing Structure in Expressions Week 3- Middle School Connections - Adding more building blocks throughout middle school

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.

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.

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.’

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.

Connected Skill 2: The Distributive Property

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

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.

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).

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.”