Comparing Quantities: Greater, Less, Equal - First Grade Mathematics
In your everyday life, you often compare amounts: Who has more apple slices? Are there enough pencils for everyone? Is my tower taller or shorter than yours? In mathematics, comparing quantities means examining two groups or numbers to decide which one has more items, which one has fewer items, or if both amounts are exactly the same. In this chapter, you will learn the precise mathematical vocabulary for comparison, use matching strategies to prove your answers, and learn how to compare any two numbers from 0 up to 20.
The Vocabulary of Comparison
Mathematicians use specific words when comparing quantities.
Comparison Terms and Meanings:
GREATER THAN: More items, a bigger quantity, further along the number path.
LESS THAN: Fewer items, a smaller quantity, closer to zero.
EQUAL TO: The exact same quantity, a balanced match.
Greater Than Means More
When one group has a larger count of items than another group, we say the first group is greater than the second group. For example, 8 is greater than 5.
Less Than Means Fewer
When one group has a smaller count of items than another group, we say the first group is less than (or fewer than) the second group. For example, 3 is less than 7.
Equal To Means the Same
When two collections contain the exact same count, they are equal. For example, 6 blocks is equal to 6 blocks. Neither group has more, and neither group has less.
Strategies for Comparing Groups
There are three reliable strategies you can use to compare quantities up to 20.
Strategy 1: One-to-One Matching
Group A: (*) (*) (*) (*) (*) (*) (*) -> 7 stars
| | | |
Group B: [#] [#] [#] [#] -> 4 squares
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Result: 3 stars are left over without a partner!
7 is GREATER THAN 4.
4 is LESS THAN 7.
Strategy 1: Matching Side by Side
Line up the objects from both groups in parallel rows. Match each object in the first row to an object directly underneath it in the second row. Whichever row has leftover items is the greater group. The row that runs out of items first is the lesser group.
Strategy 2: Using the Number Path
Look at a number path from 1 to 20. Numbers that appear further to the right (further away from 0) are greater. Numbers that appear further to the left (closer to 0) are less. Because 14 is to the right of 9 on the number path, 14 is greater than 9.
Strategy 2: The Number Path
| 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16|17|18|19|20|
^ ^
Lesser Greater
Strategy 3: Comparing Tens and Ones
For numbers between 11 and 20, look at how many tens and ones each number has. Compare 16 and 12: Both numbers have 1 ten. But 16 has 6 ones, while 12 has only 2 ones. Since 6 ones is more than 2 ones, 16 is greater than 12. Compare 19 and 20: 19 has 1 ten and 9 ones. 20 has 2 complete tens. Since 2 tens is greater than 1 ten, 20 is greater than 19.
Practice Exercises
Exercise 1: Compare the numbers 6 and 9. Which number is greater, and which number is less? Write two complete comparison sentences using the words "greater than" and "less than."
Exercise 2: You have a group of 15 blue marbles and a group of 15 red marbles. Which comparison word describes the relationship between these two groups?
Exercise 3: Use the number path to compare 11 and 18. Explain how you know which number is greater.
Exercise 4: Box A contains 1 ten and 3 ones. Box B contains 1 ten and 7 ones. Which box has more items, and what number does each box hold?
Solutions and Explanations
Solution to Exercise 1: The number 9 is greater than 6, and the number 6 is less than 9. Sentence one: 9 is greater than 6. Sentence two: 6 is less than 9.
Solution to Exercise 2: The word "equal to" describes the relationship because both groups contain the exact same count of 15 marbles (15 is equal to 15).
Solution to Exercise 3: 18 is greater than 11. On the number path, 18 is further to the right and further from zero than 11.
Solution to Exercise 4: Box B has more items. Box A holds the number 13 (1 ten + 3 ones). Box B holds the number 17 (1 ten + 7 ones). Both boxes have 1 ten, but Box B has 7 ones, which is more than the 3 ones in Box A, so 17 is greater than 13.