Category Archives: Scaffolding

Counting Out Value of Coins

Counting out the total value for a set of coins can be very challenging for students who struggle with money.

Here is a video showing how to use a WORD document table a former colleague and I created to support students in a life skills class. The video shows how this handout is used but does so with a virtual version the can be completed on the computer (see image below). Here is a link to the virtual document.

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Worksheet Websites I Use and Recommend

The following are screen shots of online math worksheet websites I use. The variety and the options in the criteria you select for your worksheets for some of these sites allows for differentiation in the classroom.

 

I will start with my favorite site, Math-Aids.com. This site allows for dynamic selection of criteria for each handout (see 2nd photo below) such as choosing the types of coins in problems for counting out the total value. The coin images are outstanding! It also offers content up to Calculus.

 

 

Super Teacher Worksheets is often used elementary schools. It offers content in science and language arts as well. It requires a $25 annual subscription which I easily find to be worthwhile.

 

 

Common Core Sheets is very useful site if you want to find handouts for specific standards by grade level (see 2nd photo below). It offers multiple versions of each handout.

 

 

 

Dads Worksheets provides a large bank of worksheets – multiple versions of each worksheet.

 

 

Math Worksheets 4 Kids offers multiple versions of each worksheet and content in science and language arts. There are many worksheets that provide unique support in how the work is presented, e.g. the Ratio Slope worksheet shown in the 2nd photo below.

 

Visual Fractions – title speaks for itself.

 

Worksheet Works is my 2nd favorite. It offers options in the criteria you choose, e.g. difficulty level (2nd photo below). They also offer unique types of handouts such as a maze with math problems to solve to find the path (2nd photo).

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Base Ten Using Popsicle Sticks

I use the following method as a entry point for double digit numbers.

The photo below shows 2 packs of Popsicle sticks counted as 10 each, followed by single sticks counted as 1 each. The student counts on from 20, with the use of the scaffolded handout (photo at bottom). The handout focuses only on counting on from 20 and shows a photo of 2 of the bundles of sticks. Similar handouts involve counting on from 10 or from 30 etc.

By engaging in the actual counting, the student learns the 10s by doing. This would be followed by counting on from each 10 without the handout.

The use of Popsicle sticks is useful for 2 reasons. First, a bundle of items like shown below is more concrete than the rods for Base 10 blocks. Second, pulling packs of sticks apart of bundling 10 sticks together is an act that is concrete for students and ties into their prior knowledge regarding the grouping of objects (e,g. pack of gum).

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Addition: Concept and Mechanics

The graphic organizer below is used to show the student the steps for addition. It also addresses the concept of addition (which I have addressed previously) as an act of pulling “together” two parts to form a whole.

The student is prompted to move the first part (set of coins in this case) to the number chart. This can be completed with 1 to 1 correspondence or with subitizing (identifying the number of items without counting). Then, the student is prompted to move the second part while counting on, e.g. 7, 8 etc. (as opposed to starting from the left and counting from the first coin: 1, 2 etc.). The chart scaffolds the counting on and allows the student to see the total as a magnitude.

It is important to first teach the students the “rules of the game”, i.e. how to use the graphic organizer. To do this have the student simply move the first part to the number chart then the second part. The student can also be prompted to state the addition problem (written at the top). When the student is fluent with these steps the counting on can be implemented.

The next step would be to replace the coins with the symbolic representation, numbers.

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Multiplying and Carrying a Tens Digit

Carrying the TENS digit in a multiplication problem is a sticking point for many students. To address this, I use a task analysis approach to zero in on the step of identifying the product for the ONES as a prelude to carrying.

In the example below, 5 and 4 are in the ONES place and the product is 20. The task analysis steps involved:

  • compute the product
  • identify the digits in the product
  • identify the digit in the ONES
  • identify the digit in the TENS
  • Understand that the TENS digit must be carried to the TENS column

By creating a place holder for the product and scaffolding it to differentiate between the TENS and the ONES, the student can visualize the product. This reduces the demand placed on working memory. Once mastery with the place holder is demonstrated, it can be faded (and used as necessary as part of corrective feedback).

NOTE: I started this mini-lesson for a student with ADHD by having him warm up with problems without carrying. Also, extra line below the 60 and 20 are used for multiplying by 2 digit numbers (next in the sequence).

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Sales Price Entry Point

A pseudo- concrete representation of a sales price problem is shown below. This is what I use as an entry point for teaching these problems.

  • The entire shape represents the total price of $80. This is 100%, which in student language is “the whole thing.”

  • The discount rate is 25%. Cut with scissors to lop off the 25% which also lops off $20, which is the actual discount. Explain to the student that this 25% is part of the “whole thing.”

  • What remains is 75% or $60. This is the “new price” which is called the sales price.

IMG_20180526_165232.jpg

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Cutting Up the Math Into Bite-sized Pieces

When I train new math and special education teachers I explain that teaching math should be like feeding a hot dog to a baby in a high chair. Cut up the hot dog into bite-sized pieces. The baby will still consumer the entire hot dog. Same with math. Our students can consume the entire math topic being presented but in smaller chunks.

bite sized pieces

My approach to doing this is through a task analysis. This is very similar to chunking. It is a method to cut up the math into bite-sized pieces just as we would break up a common task for students with special needs.

Image result for task analysis

While waiting for my coffee order at a Burger King I saw on the wall a different version of a task analysis. It was a step by step set of directions using photos on how to pour a soft cream ice-cream cone. I thought it was amazing that Burger King can do such a good job training its employees by breaking the task down yet in education we often fall short in terms of breaking a math topic down.

soft cream icecream cone task analysis

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Simplifying Expressions (Combine Like Terms)

Simplifying expressions (see photo below) is one of the most challenging algebra tasks for many students receiving special education services. A major problem is that it is typically presented as symbol manipulation…addressed in very symbolic form.

combine like terms

My approach is to make math relevant and more concrete. Below is a scaffolded handout I use to help unpack the concept. In the handout I start with items the student intuitively understands, tacos and burritos or tacos and dollar bills. In the top left of this handout the student is asked how many tacos he or she has. 3 tacos eventually is written as 3T. See next photo to see how the handout is completed as NOTES for the students.

simplifying expressions tacos

As I work with the problems below I remind the student that the “T” stands for taco so “3T” stands for 3 tacos. This takes the student back to a more concrete understanding of what the symbols mean.

simplifying expressions tacos completed

To address negatives I use photos of eating a taco or burrito. “-2T” is eating 2 tacos.

So “3T – 2T” means I have 3 tacos and ate 2. I have 1 taco left… 1T. For students who may need an even more concrete representation, use actual tacos or other edible items.

simplifying expressions tacos with negatives

 

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Introduction to Solving Equations

I introduce solving equations by building off of the visual presentation used to introduce equations. The two photos below show an example of handouts I use. Below these two photos I offer an explanation of how I use these handouts.

intro to solving equations

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First I develop an understanding of a balanced equation vis-a-vis an unbalance equation using the seesaw representation.intro to equations balanced vs unbalanced

I then explain that the same number of guys must be removed from both sides to keep the seesaw balanced.

intro to solving equations balance and unbalanced

I then apply the subtraction shown above to show how the box (containing an unknown number of guys) is isolated. I explain that the isolated box represents a solution and that getting the box by itself is called solving.

intro to solving equations adding

I use a scaffolded handout to flesh out the “mathy” steps. This would be followed by a regular worksheet.

solving 1 step equations add scaffolded

I extend the solving method using division when there are multiple boxes. I introduce the division by explaining how dividing a Snickers bar results in 2 equal parts. When the boxes are divided I explain both boxes have the same number of guys.intro to solving equations multiplying

The students are then provided a scaffolded handout followed by a regular worksheet.solving 1 step equations multiply scaffolded

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Graphing Linear Functions

Screenshot 2017-12-22 at 11.52.09 AM

Graphing linear functions and the underlying concept are challenging for many students. The video below shows a scaffolded approach to teaching how to graph. This approach also addresses the concept of the graph as a visual representation of all possible solutions (see photo above). Students often do not realize that the line is actually comprised of an infinite set of points which represent all the solutions. Here is a link to the document used in the video.

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