Subtraction as Comparing (How Many More?) - First Grade Mathematics

Did you know that subtraction has a second personality? In addition to taking items away, subtraction can also be used to compare two separate groups! Imagine you build a tower of 7 blocks and your friend builds a tower of 4 blocks. Nobody is taking any blocks away, but you might want to know: "How many more blocks are in my tower?" or "How many fewer blocks does my friend have?" In this chapter, you will discover how subtraction finds the difference between two quantities, learn how to line up objects to compare them, and master "how many more" questions.

Comparing Two Towers: Finding the Difference

When you compare two collections, you are looking for the gap or extra space between them. In mathematics, that gap is called the difference.

Comparing Two Towers of Blocks:
Tower A (7 Blocks):   [#][#][#][#][#][#][#]
Tower B (4 Blocks):   [#][#][#][#] : : : :
                                   \_____/
                                  The GAP = 3 extra blocks!

Comparison Equation: 7 - 4 = 3

The Matching Line

Look at the two towers side by side. Up to the fourth block, both towers are the exact same height; they match evenly. But Tower A keeps going! It has 3 extra blocks that do not have partners in Tower B. That extra part of 3 is the difference.

Two Ways to Ask the Same Question:

Question 1: "How many MORE blocks does Tower A have than Tower B?" (Answer: 3 more). Question 2: "How many FEWER blocks does Tower B have than Tower A?" (Answer: 3 fewer). Both questions are asking for the exact same difference, and both are solved with the exact same subtraction equation: 7 - 4 = 3!

Why We Use Subtraction to Compare

Even though nothing is being thrown away, subtraction is the mathematical tool used to measure the difference between two numbers.

The Comparison Model:
[ Larger Quantity ]  -  [ Smaller Quantity ]  =  [ Difference ]
         8           -            5            =       3

Subtracting the Matching Part

Think of it this way: when you compare 8 and 5, you remove the part that matches (the 5 items that both groups share). When you take away the matching 5 from the 8, only the unmatched extras (3) remain! That is why subtraction finds the difference.

Practice Exercises

Exercise 1: Maya has 8 colored pencils. Noah has 5 colored pencils. How many more colored pencils does Maya have than Noah? Write the subtraction equation.

Exercise 2: Liam has 3 toy trucks. Emma has 7 toy trucks. How many fewer toy trucks does Liam have than Emma? Write the subtraction equation.

Exercise 3: Explain why a "how many more" question is solved using subtraction instead of addition.

Exercise 4: Red team scored 9 points. Blue team scored 6 points. How many more points did Red team score than Blue team? Draw a matching diagram to show the difference.

Solutions and Explanations

Solution to Exercise 1: Maya has 3 more colored pencils than Noah. The subtraction equation is 8 - 5 = 3.

Solution to Exercise 2: Liam has 4 fewer toy trucks than Emma. The subtraction equation is 7 - 3 = 4.

Solution to Exercise 3: A "how many more" question is asking for the difference or gap between two amounts. To find the difference, you take the larger amount and subtract the part that matches the smaller amount, leaving behind only the extra items.

Solution to Exercise 4: Red team scored 3 more points than Blue team. Matching diagram: Red: () () () () () () () () () (9 points) Blue: () () () () () (*) (6 points) The first 6 points match; Red has 3 extra unmatched points. Equation: 9 - 6 = 3.