Tag Archives: place value

Using $10 and $1 Bills to Represent Regrouping in Addition or Subtraction

Money is intuitive for many students, even when the underlying math is not. For example, I often find that students who do not understand well the concept of Base 10 place value do understand $10 and $1 bills. With this in mind, I created a virtual scaffolded handout that builds on student intuitive understanding of the bills through the use of $10 and $1 bills to represent regrouping. Here is a video showing how I use it.

In the photo below, at the top, a $10 bill was borrowed into the ones column. The reason is that $7 needed to be paid (subtracted) but there were only five $1 bills. In the photo below, bottom, the $10 bill was converted into ten $1 bills. On the left side of the handout, the writing on the numbers shows the “mathy” way to write out the borrowing.

Once the student begins work with only the numbers, the $10s and $1s can be referenced when discussing the TENS and ONES places of the numbers. This will allow the student to make a connection between the numbers and their intuitive, concrete representation of the concept.

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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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Adding ones digits in 2 digit numbers with carrying

A major obstacle in math for many students with special needs is carrying in addition problems. Below is a task analysis approach.

First, I target the step of identifying the ONES and TENS place in the 2 digit sum in the ONES column (below it is 12). In a scaffolded handout I create a box to for the sum with the ONES and TENS separated. At first I give the sum and simply have the student carry the one.

sum of ones given.jpg

Then I have the student find the sum and write it in the box (14 below). Once mastered I have the student write the sum and carry the 1.

sum of ones given

They would have mastered adding single digit numbers before this lesson. I revert back to single digit numbers to allow them to get comfortable with writing the sum off to the side without the scaffolding. (In the example below I modeled this by writing 13.)

sum of ones with color no scaffolding

The last step is to add the TENS digits with the carried 1. I use Base 10 manipulatives to work through all the steps (larger space on the right is for the manipulatives) and have the student write out each step as it is completed with the manipulatives.

sum of ones with carrying with base 10 blocks first

Finally, the student attempts to add without the scaffolding. I continue with color but then fade it.

adding 2 digit numbers with carrying with color no scaffold

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