Subtracting a Negative – Why it Becomes Addition

Here is a link to a Jamboard for presenting the transformation (you click on the negative sign and rotate and slide it).

Here is a link to a video showing how this transformation. This video addresses the underlying concept of the transformation by showing an IOU being cancelled.

Base 10 Blocks on Jamboard for Subtraction

The Jamboard

The Jamboard has images of basic base 10 blocks. The background provides side by side tables for numbers and for blocks. Additional blocks are set aside for regrouping. Here is a FB Reel and a YouTube video showing how to use this artifact.

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

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

Overview

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.

Base 10 blocks are a go to representation for place value. They are also easy to implement for addition or subtraction with place. With a group model, they are useful for multiplication and division. It is harder to model multiplication of multi-digit numbers with regrouping. This post presents a Google Jamboard with base 10 blocks on a scaffolded chart to provide such a model.

Overview

The structure aligns with the group representation of multiplication. The # of items in each group is presented first as this aligns with unit rate and slope problems.

Steps

The steps are listed in each photo in the gallery below. Here is a Youtube and FB Reel video showing the steps.

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

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

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.

Prior Knowledge

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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Fractions

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.

Students who struggle with number sense, such as place value, struggle with subsequent math content. Connecting place value to prior knowledge or an area of interest can be an entry point to making place value accessible. This post shows how a student interest (horses) can be leveraged to present place value in a more accessible fashion.

The student likes horseback riding. This can be useful to make the concept relative (10 horses live in a barn) and engaging. Here is a YouTube video and a FB Reel showing how this works. The key is 10 horses can “enter” the barn and disappear.

The Jamboard has a slide with a Legos version. This allows a nice transition from using actual Legos as the 1×1 blocks can connected to make a 10.

Here is a link to the Jamboard. You have to make a copy to use.

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.

Accessing Jamboard

Make a copy to access the Jamboard

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.

Creation of the Jamboard

Below is a step by step visual guide on how I created a version of the Jamboard seen above. Here is a Facebook Reel version with music only. Here is a YouTube version with music only. Here is a PDF for the slides I show and a YouTube version of me talking about the sldes.

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.