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Color – Easy to Implement Strategy

When my son was in preschool I asked him who was in his class. He replied, ” Natalie, she’s the yellow heart.” Children learn color before they learn words because it is easier to process.

preschool shapes and colors

This is found in children’s toys with color used to guide use of toys.

keyboard for childrens book

The obvious use of color in real life in traffic lights. The colors represent different concepts with red being used universally in the U.S. as representing stop. Color is used to partition an object into sections, as often seen in maps of areas with different sections. Think of how many highlighters are sold to college students to help them highlight key passages in textbooks.

traffic lightsFenway Park, Boston Red Sox's Ballpark - Ballparks Of Baseball in Miller Park Seating Chart With Seat Numbers Image

The use of color help convey information, especially sections of a whole is an effective and easy to use instructional or support strategy.

The top two images below show my earliest attempts to use color. The student for whom this was used was a 7th grade student with asperger’s who tested in math and reading at a 1st grade level.

In lieu of referring to the “horizontal line” I can refer to the “yellow line” as in “find the yellow 3” for plotting the point (3, -2). Color, as in the aforementioned yellow heart, is much more intuitive for students, especially those with a disability.

coordinate plane

Color was used for the same student to represent positive and negative numbers, first with concrete tokens then with colored numbers on paper.

adding integers chips and colored pencils (2)

More examples are shown below. Color helps a student focus on the different parts of an equation or different parts of a ruler.

linear equationsruler

Color can also help organize a room into different parts. Each color represented different courses I taught, e.g. green was used for algebra 2. The room is more organized because of the sections outlined in color. Consider how this can help a student with ADHD, autism or an executive functioning disorder.

 

classroom

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Color Coding for Calculus

IMG_20160223_081145571

This is an example of color coding (highlighting) to help make a calculus problem accessible. You don’t have to know calculus to see that the yellow sections (left and right of the 0) are going up while the green section is going down. Color coding breaks a whole into parts that are easier to see and understand – works in preschool all through calculus!

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Colorado Numeracy Project

CSDE NP

This blog contains information, links and discussions related to Math PD for the ASD NP.

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.

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Color Coding and Different Representation for Rounding

color coding for rounding adjusted (2)

 

There are two strategies used in this example for rounding.

The number line is a different representation for a rounding situation. In CRA this is the representational or pictorial level. Typically students are taught to round by looking only at the numbers which is purely symbolic.

The color coding helps the students discriminate between the number being rounded and the choices for rounding. As I’ve written previously, color coding helps a student discern different parts of a concept.

 

The handouts are found at Super Teacher Worksheets.

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Color Coding the Coordinate Plane

ordered pair ic

I had a 7th grader who could not plot points. He has asperger’s and tested at a 1st grade level in math. Color coding the coordinate plane worked well for him.

As I have written previously color coding is an effective method to break a concept into smaller parts. Finding 5 on the yellow line is an easier direction to follow than finding 5 on the horizontal or x axis for many students.

The numbers in the ordered pairs are color coordinated with the axes colors. Students learn inductively that the first number in the ordered pair relates to the x or horizontal axis (yellow goes with yellow). Identifying the x-axis can be a subsequent step as the act of plotting the point is the immediate goal. In the photo you can see that the first few problems were color coded but eventually this support was faded and he continued to plot the points correctly.

The handout is found at http://www.superteacherworksheets.com/

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Color Coding a Table

table with shaded columns (2)

Color coding is a form of scaffolding. It can be used to highlight specific parts of a diagram or problem or to help differentiate between different parts. Above is my first attempt at using color coding.

The 8th grade student simply could not interpret the table to answer the question – “explain the trend…”. I originally attempted to draw arrows from number to number to no avail. When I colored the two columns and asked him to tell me about the pink numbers then the yellow numbers he was able to interpret then answer the question.

The working memory for many students can be quite limited. Teachers often include many little details that are easy for us to process but can take much more effort by the student. It’s like a computer that has too many applications running at one time and slows down. Asking a student to look at the pink numbers can be much easier to comprehend than asking him to look at the column for year.

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Plotting Points Introduction

Plotting points is surprisingly challenging for some students. Here is an approach originated by one of my former math teacher candidates in a methods class I taught. This approach uses the analogy of setting up a ladder.

First, determine where to position the ladder, then climb the ladder. (brilliant and not my idea). Plot the point on the ladder, then pull the ladder away. The context includes green grass for the x and yellow for y because the y axis extends to the sun. This is shown on a Google Jamboard with moveable objects (you can make a copy to edit and use on your own).

Next, fade the ladder but keep the color – note the color of the numbers in the ordered pair. 3 is green so move along the grass to the 3. Then yellow 5 so move up 5, towards the sun.

Now, keep the the colored numbers and still refer to the green grass (faded) and sun (faded).

Finally, on a handout students can use highlighters as necessary to replicate the grass and sun numbers. The highlighters can be faded to result in a regular plotting a point problem.

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Introduction to Linear Functions – Buying a Used Car

When our 3rd child was born, we decided to buy a used Honda Odyssey as 3 young kids were not fitting into a sedan. Being the stats geek I am (master’s in statistics at the University of South Carolina – total geek) I collected mileage and price data for all the used Odysseys for sale on dealer sites throughout South Carolina. I then created a the scatterplot shown below. I went to a dealer, showed an agent my graph, and he immediately exclaimed “Where did you get that? We create graphs like that every week!”

It was this experience that led me to the idea of using used car data to introduce linear functions. Shopping for a used car has proven to be a relevant, real life activity the students enjoy.

Here is a link to a comprehensive activity that walks students through various components I use for introducing students to linear function topics.

  • Used car shopping to collect data on 10 used cars of a single make and model.
  • Creating a scatterplot for price vs mileage of the used car of choice.
  • Creating a line of best fit (regression line) to model the data.
  • Creating a linear bi-variate equation (regression equation) to model the data.

The activity is presented on a WORD document (feel free to revise). It shows screenshots to walk student through the Carmax website (subject to Carmax revising their website). The screenshots make it easy for the student to navigate, which increases independence. (NOTE: there is an ample number of Youtube videos on using Google Sheets for this activity.)

The end product looks like this. Note the importance of using 1000s of miles as the slope is more meaningful, -$140.64 per thousand miles, as opposed to 14 cents per mile. I would start with the scatterplot alone to unpack the variables, the relationship between the variables, and the ordered pairs. Then the line and equation can be introduced to show a meaningful use of the line and the equation. The y-intercept has meaning with “0 miles” equating to a new car (I do not explain that new cars have miles already accumulated until we unpack the math).

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