Here is a link to the Intro to Simplifying (no negatives).

Link to the Google Slides used to present the simplifying.

Link to a Youtube video showing how it works.

Link to a Facebook Reel showing how it works.

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# Category: Connections to Prior Knowledge

## Simplifying Algebraic Expressions with Negatives by Eating Tacos and Burritos

## Intro to Subtracting a Negative Integer by Canceling an IOU

## Simplify Rational Monomial Expressions

## This post provides details about a handout for simplifying rational monomial expressions. It incorporates a couple strategies to make the simplification of rational monomial expressions more accessible. The strategies include address prerequisites skills ahead of time, chunking, and scaffolding. This incrementally walks the students through the steps.

### The Pages of the Handout

### Access to Handout

## Intro to Concept of Functions

## Functions are perhaps the most prevalent and important topic covered in secondary math, aside from maybe 1 variable linear equations. The concept of a mathematical function is challenging for many students. This post provides details about a meaning making approach to introducing functions.

### Overview

### Slides of the Jamboard

### Access to Jamboard

## Prerequisite Skills and Current Content

## The effort to provide intervention to fill in gaps is challenging for different reasons. One reason is the effort to balance support for current content while filling in gaps. This post shows an example of how to fill in gaps while working through the current topic.

### Overview

### Example

Handout from mathworksheets4kids
## Introduction to Perimeter and Area

## This post provides a conceptual approach to understanding perimeter and area.

### Overview

### Google Jamboard

### Access to Jamboard.

## Intro to Graphing Linear Functions using Jamboard

## Graphing linear functions may be the most important topic in Algebra 1. While proportional reasoning is a prelude to functions, this is the first formally identified function presented to them. The graphing leads to slope and intercepts, beyond the entry point for graphical representations to functions. This post presents an activity that can serve as the entry point for linear functions.

### Overview

### The Slides

## Fraction Multiplication with Cookies

## Fractions are challenging. Multiplying fractions is really challenging! This post presents a Google Jamboard to introduce students to the concept of multiplication of fractions.

### Overview

### Prior Knowledge

### Fractions

### Access to Jamboard

## Introduction to Division

## My focus is on working with students with special needs. Many struggle with rote memorization, including for multiplication facts. I find that skip counting, with scaffolded support in the learning process, provides them access to multiplication and therefore division. To access division, I use an approach of skip counting to find a missing factor and then connect this to division. This post provides details of a handout using this approach.

### Overview

### Skip Counting

### Factor Tree

### Missing Factor

### Division Problems

### Access to Handout

## Solving Absolute Value Equations Scaffolded

## Absolute value is a challenging for many students. Absolute value equations add an extra layer of challenge. This post presents a scaffolded handout. It starts with an initiation addressing absolute value and then is followed by scaffolded steps for solving that address written and mental steps.

### The Scaffolding

### Initiation

### Blank Templates

### Accessing the Handout

Here is a link to the Intro to Simplifying (no negatives).

Link to the Google Slides used to present the simplifying.

Link to a Youtube video showing how it works.

Link to a Facebook Reel showing how it works.

Link to a YouTube video showing how it works

Link to a Facebook Reel showing how it works.

The handout has 3 pages.

- Page 1 is an initiation with two parts. There is a review of prerequisite skills aligned with the new topic. There is also a preview of the new topic with scaffolding to separate the factors into individual fractions.
- Page 2 provides a Before and Now to draw upon student prior knowledge of simplifying using exponents rules. This is followed by scaffolded steps to separate the expression into individual fractions for each type of term (e.g., Xs). This provides a load reduction for what the student has to focus on.
- Page 3 involves negative and 0 exponents with an additional step to address each.

Here is a link to the handout.

The introduction is presented on a Google Jamboard, to allow for movement in the pairing of inputs and outputs. It starts with analogies pairing of items using a gumball machine and a Coke machine and proceeds incrementally towards the various representations. The functions are contrasted with examples of relationships that are not functions.

- Slides1 and 2 present the gumball and Coke machines. Students can move the items to see how a quarter can result in 2 different color gumballs while the Coke button results in only 1 output.
- In slides 3 and 4, the use of an hourly wage introduces input and output with quantities. Slide 4 shows two different pay amounts for the same number of hours worked. This taps into prior knowledge.
- The sequencing progresses through
- function machines
- equations
- tables
- graphs

- Each includes an example and a non-example.
- The last slide provides a sorting activity.

Here is the link. To access the Jamboard, you need to make a copy.

Various rubrics used to assess teacher instruction includes an effort to build on or connect to prior knowledge. If the student has gaps with prior knowledge, the lesson becomes less accessible for students with the gaps. Previously, I addressed how to support both current content and fill in gaps. The idea is to systematically fill in gaps by addressing prerequisite skills as they arise in new lessons.

The handout out below shows an example of how this can play out. The first page is used as a do now for the content presented on page 2. If you are teaching a student how to solve 1 step equations and are moving into integers, page 1 is a a means of supporting the new content while filling in possible gaps. The first image shows the student will need to evaluate -13 – 3 as part of the solving in the lesson. This can be addressed in the do now, as shown in the 2nd image, page on the right. (Notice all the problems on page 1 are steps to solve on page 2 problems.) This is useful for students with special needs and for differentiation.

Students are prompted to build an rectangular animal pen for some farm animals. The number of fences represents the perimeter. The number of squared segments of grass inside the pen represents the area.

The slides are presented below. This video shows how the manipulatives work.

Here is a link to the Jamboard. Need to make a copy to use it.

The activity is presented on a Google Jamboard, which provides manipulatives. It begins with a relevant context for students, money and being paid for a job. This allows them to engage the function using money. Before using numbers, they engage the work context through images. They are presented the table and then graph representations of the function before getting into the equation. Here is a FB Reel showing the movement of the images.

There are 3 categories of slides. Here is a description of each.

- Table and graph clocks for hours and dollar bill for the money.
- They graph the whole hours first, then fractional hours (1/2 and 1/4) to see that there are points “squeezed in between each other. This leads to the idea of infinite number of points. In turn, this leads to the idea of the line are a visual means to present all the points. The points can be presented as solutions. Hence, the graph presents all the solutions for the function.

- Table and graph with numbers on sticky notes that can be moved from the table to ordered pairs to positions on the coordinate plane.
- The equation, with sticky notes to show numbers substituted in for the variables and then moved to ordered pairs with parentheses.

Here is a link to the Jamboard. You need to make a copy to access it.

The artifact is chunked to incrementally move from multiplication of whole numbers to whole number and fraction to multiplication of fractions. The representation of multiplication as number of objects in a group times number of groups is the structure used throughout. Cookies on a plate is the context used to draw upon prior knowledge and make the idea more concrete.

This serves as an introduction. Each chunk can be followed by practice before moving on to the subsequent chunk.

The Jamboard starts with a representation of multiplication as groups of objects, first with the number of objects in a group and the number of groups. This is presented first as cookies per person to connect to prior knowledge. Then presented per plate as the plate is subsequently used to model the fractions.

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First, whole number times a fraction is presented. This allows for a connection to prior knowledge and introduces fractions in this representation. There are still 6 cookies per group, but now there is only 1/2 a group.

The students can move the cookies onto the plate to see the group of objects. Then they can cut the group in half.

To help make sense of the fractions used in the multiplication of two fractions, the fractional parts of the cookies are presented first.

For multiplication of fractions, the process is the same. There is 1/4 of a cookie in each group, then there is 1/2 a group. As was done previously, 1/2 the group is removed. Conceptually, you can explain to the students that they have 1/4 of a cookie and they split it with a friend.

Here is a link to the Jamboard. You need to make a copy to access it.

This handout focuses on connections to prior knowledge of skip counting and finding a missing factor. The students then make an explicit connection by rewriting division problems as missing factor problems. The handout is linked at the bottom.

If students are struggling with multiplication, they are likely having trouble with skip counting. I start with a warm up on skip counting with the numbers that are easiest for students to skip count. Note: you can start with 2, 5, 10 only if necessary.

I have students solve a missing factor problem using a provided skip counting row. Then they are shown that the problem can be rewritten as a division problem which has the missing factor as the answer. That is, division is another way to write a missing factor problem. You can use factor tree handouts and have students practice rewriting the problem as a division problem. Note: I see that most worksheets are used for prime factorization. Use the first two branches as shown in the image below.

The students are then presented a math sentence only for missing factor. They are to solve for the missing factor. Then they rewrite the math sentence into a division sentence and solve again. I have a separate column to help emphasize that they are lookin to solve a division problem. They have to see the division problem in isolation and then write the quotient.

Finally, the students are presented division problems and rewrite as a missing factor problem. Their mental process can be as follows: “2 times what gives me 10?” and then they skip count by 2s until they reach 10. This can be supported with multiples rows as shown in the factor tree page. A blank page is provided. You can give students a division worksheet and have them copy the problems into the handout.

Here is a link to the handout.

The scaffolding walks students through mental steps to unpack the underlying concepts. The first is a general concept of absolute value. The next two are specific to the problem. At the end, students are prompted to check the solutions to reinforce the concept of two possible values, one being negative and one positive. Note: this is not addressing the case of =0.

The scaffolded handouts are preceded by an initiation. The focus is to unpack the concepts underlying the equation steps. The key is for the students to understand that there are two possible solutions (aside from =0). The handout addresses the reason for two solutions and provides work with the absolute value symbol in this context. Here is a link to a Jamboard that helps unpack the concept of absolute value.

There are 3 practice problems with the template. I use 2 and 6 to help compare the different situations. There is another page with blank templates.

Here is a link to the handout.

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