Lesson: Subtraction Strategies- Part of a Whole

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Lesson Objective

SWBAT use subtraction to solve a "part of a whole" word problem

Lesson Plan

Building Number Sense (5 minutes)

Name Collection Box (Use the number from the day of school, write number in top left of box, write different “names” for that number in box; coins, base ten blocks, tallies, pictures, words, etc.)

Mental Math Fluency (5 minutes)

Play around the world (one students stands up behind another student, both are asked a fact, if the standing student gets it right they go to the next student if they get it wrong they sit down, if the sitting student gets it right they stand up and go to the next student if they get it wrong they stay sitting)

Problem of the Day  (7 minutes)

A box has green, yellow, and white balls in it. There are 20 balls altogether. 6 balls are yellow and 3 balls are white, so how many balls are green? Explain your answer using words, pictures, and equations.

T: So how did you solve the word problem?

TS: (Example answer) Well I always draw a picture when I have a word problem so I will draw 6 Y’s for the yellow and 3 W’s for the whites. Now I’m going to count them up. So there is nine of those balls but we need 20 balls altogether. So how am I going to figure out how to get from nine to twenty. We can either count up from 9 to 20 or, since I know subtraction gives me the difference between two numbers I know that 20-9 will tell me how many green balls I need to make my total number of balls 20.

We have just discovered a new way to use subtraction! Subtraction can be used to find a part of a whole.

Mini Lesson               (12 minutes)

Subtraction as  PART OF A WHOLE aka subset

Let’s look at another word problem.

I bought a pizza for Joan, Pablo, and Jaime it had 18 pieces in it. Joan and Pablo ate 10 pieces of the pizza, so how many pieces are left over for Jaime?

T: Well we don’t know the number of slices that Jaime has, but we do know how much is in the whole pizza, how much is that?

S: 18

T: Great so that is how much we have altogether. Now all we need to know is how many of the pieces are taken away from our pizza. How many is that?

S: 10

T: Excellent so we now have how many slices are in the whole pizza, and how many are eaten by Joan and Pablo, so to find out how many are left over for Jaime all we have to do is find the difference between the whole and the pieces taken away. Does anybody know a way to find the difference?

S: Subtraction!

T: Great can someone give me the minuend and tell me how they know it’s the minuend?

S: The minuend is 18 because it is the biggest number and the number we are taking away from.


T: Correct, and what will our subtrahend be and how do you know?

S: The subtrahend will be 10 because that is the number we are taking away.

T: Great, now all we need is our difference, what is 18-10?


TS: Well if we have 18 and we take away a ten (the one in the tens place) what are we left with? An 8. So the difference is 8.

T: Even if we aren’t taking away everything we can still find a part of a whole with subtraction, here’s another problem.

I own ten shirts, but when I went to my drawer I could only find 3 shirts, so how many of my shirts are missing?

T: So how are we going to figure this out?

See if kids can come up with some ideas, below is a scaffolded look but feel free to follow your students’ train of thought

T: Well I know altogether I have ten shirts, but in my drawer is only three. So the ones that are missing those would be the difference between the ten I own and the three in my drawer. Well I know to find the difference between two numbers I can use subtraction so I just take my biggest number, make it my minuend and then make my other number the subtrahend and find the difference, to find out how many shirts I am missing.


So I am missing 7 shirts.


Go through some problems pointing out the “whole” number and the known, missing, lost, etc. number. Then go over how subtracting the two numbers shows us the unknown number, number missing, or number left.

Work Time (Zones, Independent, Group 30 minutes)

Blind Mouse

Set up a box of unifix cubes with 3 different colors. Put students into pairs. Have one student pull out unifix cubes with their eyes closed (we will call this the “player”, and the other the “guide”), the other partner (“guide”) will guide the student to put the unifix cubes into another, empty, box. The player can now open their eyes, but the guide must ensure they do not see the unifix cubes. The guide will then tell the player how many unifix cubes there are in all and how many unifix cubes there are of two colors ex: You drew 10 unifix cubes, 3 are blue and 4 are white, how many reds do you have? Now it is the players job to do the math to figure out how much of the third color they have. The player and guide then switch roles and do the same steps. (To keep game going you can keep score and the player gets a point when they get the correct answer, or you can rotate partners or use different manipulatives in different groups ex: one group can have dimes, nickels, and quarters: you drew 15 coins, 3 are quarters, 2 are dimes, how many nickels did you draw?)

Math Reflection/Share (4 minutes)

(This is a time to share work and discuss critically a problem a student had or explain student work. Also this time can be used to ask a difficult question that takes the concept taught one more level up in bloom’s taxonomy)

Can you name the four types of subtraction and what they all share in common?

The four types of subtraction are take away, comparison, equalizing, and part of a whole. They are all related because they all use subtraction, all involve finding a difference between two numbers, all start with a larger number and turn into a smaller number, etc.

1. What went well?

2. What would you change?

3. What needs explanation?

Though the game took a couple times through to get smooth, the students really benefited from having to create and word their own word problems in a real world situation.

I would have had a student pair play a couple of rounds while the class watched in order to have the class see a firsthand example of two students doing it.

You should be jumping back every once and a while to the other forms of subtraction, all of them should be on one chart on the wall so that students can readily see there are four different kinds of subtractions and see examples of each kind. Now is a good time to review all four and talk about similarities and differences and identify some word problems.

Lesson Resources

Math Unit 2 Day 9   Lesson Plan
Math Unit 2 Day 9 Worksheet   Classwork


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