Tag Archives: regrouping

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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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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Making Sense of Fractions – Regrouping with Mixed Numbers

It is easy to get caught up in the steps and rote memorization when working with fractions. The brain processes information more effectively when the information is meaningful. ADHD makes paying attention to rote memorization of steps even more challenging.

Below is an excerpt of work I completed with a middle school student who has ADHD. This was completed extemporaneously as intervention (you see his initial attempt was incorrect) but can be used as Universal Design in whole class instruction.

Here is a break down of how I helped the student after seeing his mistake in his initial attempt. First, I modeled the first mixed number as pizza pies.

Then I presented the problem in pizza terms. “You have 3 pies and 1 slice and you are going to give me 1 pie and 2 slices. Do you have enough slices?” <wait for response> “You don’t, so what can we do?” <wait for response> “We cut up one of the pies.” I have the student cut the pie into fourths.

I then make the connection with the mixed number and guide the student to taking away 1 pie and writing 4/4. This provides more concrete meaning for writing 1 as 4/4.

In turn, this provides meaning for the new mixed number and meaning for the subtraction of the whole numbers (pies) and the fractions (slices).


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