Subtraction with Renaming Using the Language of Units
#1
Script of 62 - 43
Modeled with number disks
Page 48 Cal. Edition 2A
Page 43 US Edition 2A
Concrete
t. Let’s solve 62 - 43.
Show 62 with your
number disks.
t. How many ones are
there in 62?
s. 2 ones
t. Do we have enough to
subtract 3 ones?
s. No.
t. Let’s change a ten into
ten ones. Do ten
ones equal 1 ten?
s. Yes.
t. How many tens do you
have now?
s. 5 tens
t. How many ones do
you have now?
s. 12 ones
t. Is 5 tens plus 12 ones
equal to 62?
s. Yes.
t. Now can we subtract
our 3 ones?
s. Yes. How many ones are remaining?
s. 9
t. How many tens are remaining after I take away the 4 tens?
s. 2 tens.
t. What is the answer to 62 – 43?
s. 19
t. Great job! 1 ten and 9 ones
Abstract following the concrete.
t. Now let’s record the story of what we did just with numbers. Put away your disks.
s. Students put away disks.
t. If a problem is too challenging for mental math or if we want to check our mental math, most
adults know how to do an algorithm with pencil and paper. It works perfectly.
t. Who remembers what we did first when we were modeling 62 – 43?
s. We modeled 62 with our disks.
t. Excellent. Let’s model 62 with numbers. Who remembers what number were we subtracting?
s. 43.
t. Perfect. First we need to write our numbers vertically so that the tens are with the tens and
the ones are with the ones. The whole amount is 62. We write that above. We are subtracting
43. We write 43 directly below. Show me on your boards how to do that correctly.
t. Excellent. What did we do next?
s. We subtracted the ones by changing a ten into 10 ones.
t. Okay so we got a ten. How many tens did we have after the change?
s. 5 tens.
t. Excellent. We record that by crossing out the 6 tens and changing it to 5 tens. How many
ones did we have?
s. 10 plus 2, 12 ones.
t. Excellent. We record that by crossing out the 2 ones and changing it to 12 ones. Is 5 tens plus
12 equal to 62?
s. Yes.
t. Now can we subtract?
s. Yes.
t. Start with the smallest place value and subtract one place value at a time from the smallest to
the largest.
t. 12 ones minus 3 ones?
s. 9 ones.
t. Record it in the ones place. 5 tens minus 4 tens?
s. 2 tens
t. Record it in the tens place. What is our answer?
s. 19.
t. Excellent! 1 ten and 9 ones. Perfect.
#2
Script of 243 - 18
Modeled with number disks
Page 48 Cal. Edition 2A
Page 44 US Edition 2A
Concrete:
t. Let’s solve 243 - 18.
Show 243 with your number
disks.
How many ones are there in
243?
s. 3 ones
t. Do we have enough to
subtract 8 ones?
s. No.
t. Let’s change a ten into ten
ones. How many tens do
you have now?
s. 3 tens
t. How many ones do you have
s. 13 ones
now?
t. Is 3 tens plus 13 ones equal to 4 tens and 3 ones?
s. Yes.
t. Now can we subtract our 8 ones?
s. Yes. How many ones are remaining?
s. 5 ones
t. How many tens are remaining after taking away the 1 ten?
s. 3 tens.
t. How many hundreds are remaining when I subtract 0 hundreds from 2 hundreds?
s. 2 hundreds.
t. What is the answer to 243 – 18?
s. 225
t. Great job! 2 hundreds, 2 tens and 5 ones
Abstract following the concrete.
t. Now let’s record the story of what we did just with numbers. Put away your disks.
s. Students put away disks.
t. Who remembers what we did first when we were modeling 243 - 18?
s. We modeled 243 with our disks.
t. Excellent. Let’s model 243 with numbers. Who remembers what number were we
subtracting?
s. 18.
t. Perfect. The whole amount is 243. We write that above. We are subtracting 18. We write 18
below 243 in the correct place values. Show me on your boards how to do that.
t. Excellent. What did we do next?
s. We subtracted the ones by changing a ten into 10 ones.
t. Okay so we changed a ten for tens ones. How many tens did we have after the change?
s. 3 tens.
t. Excellent. We record that by crossing out the 4 tens and changing it to 3 tens. How many
ones did we have?
s. 10 plus 3, 13 ones.
t. Excellent. We record that by crossing out the 3 ones and changing it to 13 ones. Is 3 tens plus
12 ones equal to 43?
s. Yes.
t. Now can we subtract?
s. Yes.
t. Start with the smallest place value and subtract one place value at a time from the smallest to
the largest.
t. 13 ones minus 8 ones?
s. 5 ones.
t. Record it in the ones place. 3 tens minus 1 tens?
s. 1 ten. Record it in the tens place. 2 hundreds minus 0 hundreds?
s. 2 hundreds. Record it in the hundreds place
What is our answer?
s. 225.
t. Excellent! 2 hundreds 2 tens and 5 ones. Perfect.
#3
Script of 538 - 293
Modeled with number
disks
Page 50 Cal. Edition 2A
Page 46 US Edition 2A
Concrete:
t. Let’s solve 538 293.Show 538
with your number disks.
How many ones are there in 538?
s. 8 ones
t. Do we have enough to subtract 5 ones?
s. Yes.
t. What is 8 ones minus 5 ones?
s. 3 ones
t. Let’s move on to the next largest place value. How many tens do you see?
s. 3 tens
t. Is that enough to subtract 9 tens?
s. No.
t. Let’s change 1 hundred for 10 tens.
s. Students change.
t. How many hundreds do you have now?
s. 4
t. How many tens do you have now?
s. 13 tens.
t. Subtract your 9 tens. How many tens are remaining?
s. 4 tens.
t. Let’s move on to the next larger place value. How many hundreds do you see?
s. 4
t. Is that enough to subtract 2 hundreds?
s. Yes. 2 hundreds are remaining.
t. Excellent. What is the final answer to 538 – 293?
s. 245
t. Say it in bundles.
s. 2 hundreds 4 tens 5 ones.
Perfect!
Abstract following the concrete.
t. Who remembers what number sentence we just modeled?
s. 538 – 293.
u. Perfect. The whole amount is 538. We write that above. We are subtracting 293. We write
293 below 538 in the correct place values. Show me on your boards how to do that.
t. Excellent. What did we do next?
s. We subtracted the ones easily because there were enough..
t. We did not need to change a ten for 10 ones. What is 8 ones minus 5 ones?
s. 3 ones.
t. What is the next largest place value?
s. The tens.
t. Do we have enough tens to subtract 9 tens?
s. No. We need to change 1 hundred for 10 tens.
t. Excellent. Let’s cross out 1 hundred. How many hundreds are left?
s. 4 hundreds.
t. How many tens do we have in all?
s. 13 tens. 10 from the hundred plus 3 tens already in the tens place.
t. Excellent. What is 13 tens minus 9 tens?
s. 4 tens.
t. What is the next largest place value?
s. The hundreds.
t. What is 4 hundreds minus 2 hundreds?
s. 2 hundreds!
t. What is our final answer of 538 – 293?
s. 245.
t. Say it in bundles for me.
s. 2 hundreds 4 tens 5 ones.
t. Excellent.
#4
Script of 453 - 267
Modeled with number disks
Page 50 Cal. Edition 2A
Page 47 US Edition 2A
Concrete:
t. Let’s solve 453 267.Show 453 with
your number disks.
How many ones are
there in 453?
s. 3 ones
t. Do we have enough to subtract 7 ones?
s. No. We need to change 1 ten for 10 ones.
t. How many tens do you have now after making the change?
s. 4 tens
t. How many ones do you have now after making the change?
s. 13 ones.
t. Is 4 tens and 13 ones equal to 5 tens and 3 ones?
s. yes
t. What is 13 ones minus 7 ones?
s. 6 ones.
t. Let’s move on to the next largest place value. How many tens do you see?
s. 4 tens
t. Is that enough to subtract 6 tens?
s. No.
t. Let’s change 1 hundred for 10 tens.
s. Students change.
t. How many hundreds do you have now?
s. 3
t. How many tens do you have now?
s. 14 tens.
t. Subtract your 6 tens. How many tens are remaining?
s. 8 tens.
t. Let’s move on to the next larger place value. How many hundreds do you see?
s. 3 hundrds
t. Is that enough to subtract 2 hundreds?
s. Yes. 1 hundred is left.
t. Excellent. What is the final answer to 453 – 267?
s. 186
t. Say it in bundles.
s. 1 hundreds 8 tens 6 ones.
t. Perfect! Stretch it out!