Equal Parts of Fractions – Intro

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.

CCSS Coherence Map

Jamboard with Sharing Slides

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.

Introduction to Slope

which-jobSlope is one of the the most important topics in algebra and is often understood by students at a superficial level. I suggest introducing slope first by drawing upon prior knowledge and making the concept relevant (see photo above).  This includes presenting the topic using multiple representations: the original real life situation, rates (see photo above) and tables, visuals,  and hands on cutouts (see photos below).

10-dollars-per-hour-graphA key aspect of slope is that it represents a relationship between 2 variables. Color coding (red for hours, green for pay) can be used to highlight the 2 variables and how they interact –  see photo above and below.5-dollars-per-hour-graph

The photo below can be used either in initial instruction, especially for co-taught classes, or as an intervention for students who needs a more concrete representation of a rate (CRA). The clocks (representing hours) and bills can be left in the table for or cut out.cut-outs-hours-bills

Color Coding and Representation for Integers

adding integers chips and colored pencils

This example involves adding integers which is a major challenge for many students. There are two strategies present in the photo.

Color coding is an effective way to break down a concept into parts. Here red is used for negative numbers and yellow for positive. The numbers are written in red and yellow with colored pencils.

The chips are a concrete representation. Typically integers are only presented in number form and often with a rule similar to the one below. The strategy is to count out the appropriate number of red chips for the negative number and yellow chips for positive number. Each yellow chip cancels a red chip and what remains is the final answer. If there are two negative numbers then there is no canceling and the total number of red chips is computed (same with positive and yellow).

  • + + = +
  • – – = –
  • + – use the bigger number…

Rules are easy to forget or mix up especially when students learn the rules for multiplying integers. Concrete allows students to internalize the concept as opposed to memorize some abstract rule in isolation.