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Use Place Value Money to Add or Subtract
Use Place Value Money to Add or Subtract
Both addition with regrouping and subtraction with regrouping (a.k.a. borrowing) are made easier by introducing the concepts with Place Value Money.
Use a set of place value money whole number manipulatives to introduce regrouping, and provide personal sets for student use as they begin solving regrouping problems.
Download a set of $1s, $10s, $100s, and $1000s. Photocopy two of each page for a complete set for regrouping purposes. (Each page photocopied will have an extra, because when cut apart 18 copies forms a complete set of each denomination.)
Use paper of a different color for each denomination (the $1s, $10s, $100s, and $1000s) to make it easier to sort for place value work.
Understand Addition with Regrouping Using Money Models
Understand Addition with Regrouping Using Money Models
For introductions to regrouping in both addition and subtraction, using place value money models takes what often is vague for children about when and how to do it and builds a solid foundation where it makes sense.
1.Demonstrate showing the t op number in place value money $1s and $10s.
2. Then show the bottom number in place value money $1s, $10s, and $100s.
3. With 13 $1s now showing, an even trade of 10 of those for 1 $10 is required — because you can never write two digits in the same place value.
4. Show the process of counting the remaining $1s and writing down the 3, then carrying one ten. Then add the tens and hundreds place, verifying answer with what the manipulatives show.
Once the process of trading to regroup in addition for the tens place when needed, it likely will be possible for the parent or teacher to discuss how that would work with regrouping for hundreds and later thousands without necessarily needing to demonstrate with trading tens for hundreds and hundreds for thousands. But the principle may need further reinforcement and the manipulatives are there to use if so.
Ideally each student would have access to their own set of manipulatives to use to illustrate the process for themselves while completing the first few problems.
Understand Subtraction with Regrouping Using Money Models
Understand Subtraction with Regrouping Using Money Models
A very common problem for students as they learn to regroup (also known as borrowing) to subtract is knowing when, what, and why to mark the correct changes in the process of regrouping. Making it concrete and multisensory with place value money makes the process make sense.
Instead of just memorizing the rules, learners understand when and how to do so.
By using and talking through the place value money models as a bill is "borrowed" and then traded "even steven" for ten of the next lower valued bill, the activity becomes multisensory. It's especially necessary to do during early learning opportunities for the new skill.
Let's take a look how it can work with an often difficult pattern.
Show the top number in a subtraction problem with place value money. 2 $1000 bills in the thousands place and 6 $1s in the ones place.
2. Compare the bottom number in the ones place with the top number. Is the bottom bigger than the top? If so, to get enough ones to do so, borrowing and regrouping is required.
3. Since the BOTTOM number in the ones place is BIGGER than the top, then BORROW. The BBB rule is helpful to remember to check and can help stop the tendency to subtract the top from the bottom if it is lower. (Repetition is key to making it stick.)
4. There are no tens ($10s) to borrow from to regroup or "make change" for the ones place. No hundreds ($100s) either. But there are thousands ($1000s). Ask students how many hundreds equal one thousand. Count by hundreds aloud, laying out the bills, and trade one $1000 for ten $100s. Then mark the changes the trade makes in the thousands and hundreds places.
5. Since the goal is to get enough ones, one $100 will need to be traded for $10s. Ask how many 10s equal 100, and count out the $10s by tens to equal 100 and make the trade. That leaves nine $100s. Mark the changes in the hundreds and tens place.
6. Next, make change for one of the $10s in $1s, counting up by ones to equal ten. That leaves one less $10 in the tens place and ten $1s in the ones place. Mark the changes in the tens and ones place.
7. Now the problem is ready to subtract. In the early learning stages, students will benefit from physically removing the quantity being subtracted from the place value money laid out.
"Our brains are hardwired to our senses, things make sense if we can see them." ~ Anonymous
Subtraction with decimal numbers likewise benefits from using place value numbers with tenths (dimes) and hundredths (pennies).
Tip: Students can find the answer to a subtraction problem from counting up from the digit being subtracted. When using fingers, shat it takes to reach top digit is the difference. Likewise making change in sales transactions can best be solved by counting up rather than borrowing (regrouping) to subtract.
Ordering and Comparing Numbers Using Place Value Money
Ordering and Comparing Numbers Using Place Value Money
Using place value money to illustrate each of the numbers involved can help learners understand the value of digits in a variety of situations at the early stages of developing an understanding of the value of digits in various places.
For instance, let's compare some decimal numbers.
Is 94.1 greater than, less than, or equal to 94.09?
Illustrate the numbers with place value money: 9 $10s, 4 $1s, 1 dime for the first one and 9 $10s, 4 $1s and 9 pennies.
So 94.1 > 94.09.
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