Lesson: Many Ways to Take Away
- Write a subtraction problem on the board (i.e. 7,265-1,999)
- Have a student volunteer to come to board and solve it. Today, we are going to look at some different ways and strategies for doing subtraction.
Teacher Input/Guided Practice:
- Review the basic meanings of subtraction.
Take Away-Give each student a small handful of counters (or candy, if you really want to get their attention). Go to each child and say "You have _________, I am going to take away _________, how many will you have left?" These types of problems ask how many you have left or how many remain.
Compare-Give each student/pair two number lines and some small stickers. You can make number lines with any numbers you would like to work with. For example, with a number line from 1-100 counting by 5s, you could do problems like this: Put a sticker on 87 on one number line, put a sticker on 100 on the other number line. Now find the difference between these two numbers. Show how number lines can be used to compare. These types of problems ask things like how many more or how many less does one group have than another.
Missing Addend-This allows us to use addition to solve subtraction problems. This answers problems like, "Paul needs $6 to go to the movie, he has $4 already. How much does he need to earn?" Switch it to addition by writing $4 + ____ = $6. Put the cards on the board-three subtraction questions and three missing addend number sentences. Have the class match them up.
Mental Math-Benchmark numbers; demonstrate with money Use overhead money or play money for each student to demonstrate the concept of subtraction with benchmark numbers. Give them several scenarios similar to this:
You had $5.00. You spent $3.50 on a comic book. How much do you have left?
Start counting it back in pennies and see how they react. What's wrong? That will take forever! What's a better strategy? Two quarters and one dollar. How did you know and count that? You are used to counting with coin values of nickels, dimes, and quarters. Those are familiar numbers. We can use those same benchmark numbers to help us with subtraction.
Mental math subtraction problems-Do several problems like this together. You can also construct worksheets for them to practice this skill-make sure you have students write how they figured the problem out. This also builds on the mental math addition they did recognizing how many more makes 10, 100, etc. Remind them they have practiced this so they don't think it is a new skill. It helps to have students record the problem while you work it out so they have a visual record of the problem. Use base ten blocks to show each step.
- You had 80 sheep. You sold 57 of them. How many do you have left?
Think Aloud: 3 sheep would get me to 60 (just like pennies-put out 3 cubes). And 20 more sheep (like dimes-put out two ten sticks) would get me to 80. So I have 3 + 20, or 23 sheep left.
- You have 900 cows. Your neighbor has 564 cows. How many more cows do you have?
Think Aloud: 6 more would give me 70-put out 6 cubes, 30 more would give me 600-put out 3 ten sticks. 300 more would give me 900-put out three hundreds squares. Add up (teach them to start with the hundreds place in mental addition because then they end up with expanded form). 300 + 30 + 6 and you get 336, so you have 336 more cows than your neighbor.
Actually writing the problems in expanded form might be helpful for some students.
Go back to the sheep problem. How would you write it in expanded form?
If you subtract 0 - 7 you will get a negative 7, which doesn't work very well in counting sheep, even though it will be very useful later in math. Put out eight ten sticks and then exchange one ten stick for ten one cubes. Can we rename 80 as 70 + 10? Does 70 + 10 have the same value as 80? Then we are okay. Take away the blocks as you do each subtraction.
Larger numbers can get a little tricky. Talk about whether they should use this strategy or the mental math strategy, which would be a better choice?
You have to regroup so you have enough in the tens and ones columns. Model with base ten blocks again. Tell students to take one of the hundreds-that leaves 800 and split that hundred into tens and ones so you could do the problem. The easiest way is 90 + 10-nine ten sticks and ten ones cubes. Take away the blocks for each place as you do the subtraction. This leaves a problem like this:
Do several problems having them choose which strategy is best. Show overhead of sample problems that work with each strategy.
Compensation Strategy-Use the following demonstration to introduce this strategy:
Invite two students with a noticeable height difference to come to the front of the classroom. Measure the difference in their height. Have them both stand on equal size chairs. Explain that while both of their heights were changed to make them taller, because the exact same thing was done to both, there was no change in the difference between their heights.
The same concept applies to numbers. I can make a math problem easier by changing both numbers to make them easier to subtract.
Think: I can make 593 an even 600 by adding 7. If I do that, I must add 7 to 256, which would give me 263. Write your new problem
Think: 7 more would give me 70, 30 more would give me 300, and 300 more would give me 600. So 300 + 30 + 7, or 337, is my answer.
Do the standard algorithm to prove that you get the same answer.
Compensation also works if your students are struggling with subtracting with zeros and cannot yet do it mentally.
- Distribute and explain subtraction worksheet to students.
- Allow time for students complete Subtraction Independent Practice Sheet
- Distribute index cards. Tell students to solve the Exit Question on the index card. Exit Question: Solve 2,546 - 396.
- Explain what strategy you used to solve this problem.
|Subtraction with Zero worksheet||
|Lesson Plan with Sample Problems||