Exponents and Basic exponent rules are challenging. The Power Rules add another layer of challenge. This post outlines an instructional approach. The original problem is decomposed and then recomposed to show how the underlying concepts of the Power and Power of a Product Rules.

Overview

The Jamboard is configured in similar fashion as the Jamboard used for the Product and Quotient Rules. The exponential terms and variables are moveable parts. The background is a scaffolded to guide the decomposition. Here is a FB Reel and a YouTube video showing how it works. NOTE: I decompose the expression down to individual X values in lieu of using the Product Rule because I want them to see how many Xs there are. Also, the Product would be relatively new to them, I wanted to reduce the task demand placed on the working memory.

Jamboard Access

Here is a link to the Google Jamboard. To get access, you must make a copy.

The Product and Quotient Rules are challenging largely because there are few ways to present them in an accessible format. This post outlines an approach using manipulatives on a Google Jamboard.

Jamboard

The Jamboard activity involves using moveable variables as manipulatives to provide a hands on approach to learning the rules. The first slide presents the idea of exponents as repeated multiplication. The Product and Quotient Rules use the manipulatives approach to unpack the underlying concepts of the rules. Note: there are set problems followed by blank templates. Here is a FB Reel and a YouTube video showing how this works.

Visuals and manipulatives allow for a multi-sensory approach to presenting math topics. Google Jamboard makes implementation of both relatively easy and is effective.

Current Jamboard

Here is an image of Jamboard used to guide multiplication by a 2-digit factor.

Operations on integers and integers in general is challenging for many students. Negative numbers are abstract. Whole numbers and fractions can be represented with images. The activity presented draws upon student prior knowledge of thumbs up and down in a vote to make negative more accessible.

The following images are from a Jamboard. Here are accompanying videos on FB Reels and Youtube showing how this works. There are 3 sets of images (or chunks) loosely following a CRA appoach and all referring to the same two situations.

Prior Knowlege drawing upon a classroom setting (concrete)

Transition using thumbs (representational)

Introduction of adding integers, using thumbs (more abstract but still supported by

Prior Knowledge

The activity starts with a couple of classroom votes using thumbs up and down.

This is followed by scaffolding to focus on how the voting works through a comparison of the quantity of thumbs up vs down.

Transition

This section introduces thumbs as counters for integers, which is a common instructional strategy (yellow for positive and red for negative). The scaffolding is the same.

The concept of fractions as some number of equal parts begins in 1st grade per the Common Core (image below). There are students who struggle with the idea of equal parts and this could undermine student work in subsequent topics. The activity cited in this post is designed to develop the concept of equal parts.

The following images are from a Jamboard used as an introduction to equal parts activity (see photo at the end for access). The activity is chunked to incrementally present more of the ideas underlying equal parts. The use of the Jamboard can be viewed in a FB Reel and on YouTube.

First, the idea of equal is addressed by presenting a situation in which two students are sharing candy. Partitioning out pieces alludes to the set notation of fractions.

The idea of sharing equal amounts transition to sharing a single candy that can be broken into parts. The candy bar image is actually two images of parts. The a non equal sharing is used to unpack equal parts. This is continued for a circular shape and a triangular-ish shape.

Jamboard with Mathy Slides

There are additional slides to do more “mathy” work with equal parts. First, the students are asked to choose the shape that was cut into equal part (rectangle, circle, triangle). Then the students partition the shapes but with a dotted line as scaffolding.

Each shape can be connected to the food images from above. For example, the student may intuitively understand that a pizza is cut from the crust to the tip. I use pizza fractions to unpack the need for common denominators, which reinforces the significance of the concept of equal equal parts cited previously.

Handout

Here is an image of an accompanying worksheet. It draws upon the images from the Jamboard and follows the same sequence.

Accessing the Jamboard

The image below shows how to make a copy of the Jamboard in order to use it.

Slope is one of the most important topics in algebra but perhaps one of the most challenging topics. One issue is that students often think of the formula as opposed to the idea of slope. The images shown below are for a handout that unpacks the idea or concept of slope.

The images show sections of a handout. Slope is a measurement of a graphed line. It measures steepness and also indicates direction. The handout starts by drawing on prior knowledge of measurements for newborns.

Prior knowledge of steepness and up and downhill are invoked.

How to measure steepness is introduced through a focus on stairwells.

The measurement of the length and height of steps leads into the rise and run of a hill. I use “right” and “up” or “down” which focus on direction. The terms “rise” and “run” can be addressed subsequent to the introduction. This part of the handout is scaffolded to reduce task demand and focus on the concept.

Finally, the students are provided a line and apply the ratio procedure. Note: the slopes are not the same as in the prior section.

Jamboard

An accompanying Jamboard will eventually be shared in this space.

The images below are from a handout to introduce elapsed time. This a revised version of another handout I created. The sequence in chunked to incrementally present additional elements. A number line is used to model, first on Jamboard then on a handout, then clocks are introduced. The first problem has an exact hour on the second clock to make it more simple but to still include minutes.

The clocks were created on math-aids.com, which has a page to allow you to choose times to be represented on clocks. They create clocks with color coded hands, which I follow with highlighters on the handouts and Jamboard.

First, the identify the the upcoming whole hour and marks the hands with highlighters or colored pens or pencils.

Determine the number of minutes to the hour.

Identify the whole hour preceding the second time and marks accordingly.

Determine the number of minutes from the whole hour to the second time.

Use the green marks used to identify the whole hours and determine how many hours passed.

I did not create a spot to write the answer to cut back on visuals.

The first page provides an introduction to the use of the number line without having to process the clocks.

Mark the whole hours.

Determine the number of minutes preceding and following the whole hours.

Determine the number of hours that passed.

A Jamboard is used to model the first 4 problems to engage the students kinesthetically and to unpack the concept. The students can do a Jamboard slide then work on the matching problem on the handout. (See photo at bottom for access.)

On the handout, I addressed the minutes of both clocks before determining hours. The Jamboard person can be used to flesh out the concept of time passing as the person walks. As a result, I suggest determining the hours before the minutes on the second clock as the person walks the entire way. When you return to the handout, you can reference the person walking the last 10 minutes and even show the students the Jamboard again when you do those minutes before determining hours.

The post shows a lesson to introduce factoring out a GCF. The handout is chunked to incrementally add task demands. A Jamboard is used as a complement to flesh out the concept of a factoring by allowing engaging the student kinesthetically, with scaffolding as guidance. (See image at bottom for how to make a copy to access it.)

The sequence starts with a review of factoring and distributive property. The boxes are a preview of the scaffolding for the full factoring to be presented in subsequent chunks.

The Jamboard slides aligned with the first chunk has students pull apart the variables with exponents to help them understand the meaning of the exponents during factoring. For example, there are two Xs overlaid on the x squared. Similarly, there are two 5s, one overlaying the other to allow them to be distributed.

The next chunk in the lesson is factoring out with the terms written with the multiplication symbol written in between. The problems are aligned with the distributive problems to help with the concept of “reverse distribution.” The same problems are presented again in box form as the boxes will be used to support the full factoring. Using the same problems helps the students understand how the boxes work. The Jamboard reinforces the distribution by allowing the movement of the 5s out of the binomial, including with the box method.

The last chunk combines the factoring of individual terms and the factoring out. This is conducted with the box methods for support, and then the boxes are faded. The scaffolding starts by writing the expression with parentheses because that step is easy to overlook when explaining it to students and can be confusing for students.

Here is what the final version looks like.

Note: the handout has blank templates for copying and pasting if you want to create your own handout.

Make a copy of the Jamboard in order to access it.

Below are images from a Google Jamboard for a hands on introduction to ratios. (See image at the bottom for how to make a copy in order to use it.) The images are from Clever Cat Creations and provide a visual representation. The moveable items engage the students kinesthetically. It also helps unpack the concept of ratio as a comparison of two quantities as the students count out the quantities and represent them as numbers in a ratio. The scaffolding guides the process.

First, students move the terms to make a connection between the statement and the ratio.

Then the objects are counted and moved.

Then the ratio is written.

The quantities can be flipped to show an alternative ratio.

There is a blank to create your own and another with shapes.

You have to make a copy in order to move the pieces.

Below are images from a Jamboard and a handout that scaffold cross multiplying to solve a proportion. (See image at bottom to make a copy of the Jamboard.) This is an entry point, with a focus on how to write the ensuing equation. Solving would be a prerequisite skill so it is not addressed (but obviously would follow). This allows for less task demand placed on the students and for more time spent on the new steps.

The arrows and shading scaffold the cross multiplication step. Students move the terms from the proportion to the equation. This allows for kinesthetic engagement and helps students see how the equations are formed. The scaffolding for the equation guides students to writing the equation, which I have found a challenging step for some students. The equation is written first as factors to reinforce the idea of multiplication, then the students simplify for the second equation.

The handout draws upon the Jamboard and uses the same scaffolding. The template is blank to allow for use with other handouts. The students can copy problems from another handout and follow the scaffold to get to the equation. The steps and equation can be transferred over to the handout.