Understanding Comparisons in Mathematics
Comparing helps students develop number sense by encouraging them to think about the size, amount, or value of numbers. When students compare, they begin to understand relationships like greater than, less than, or equal to. This foundational skill is essential for making sense of numbers, solving problems, and working with mathematical concepts like place value, measurement, and fractions.
Key Ideas for Teaching Comparisons
Using Visuals and Hands-On Activities to Teach Comparison
Students understand comparing best when they can see it in action. Using tools like number lines, counters, or objects, teachers can show how to look at two groups or numbers and figure out which is bigger, smaller, or if they are equal. For example, students can use Unifix cubes to build towers representing two numbers and compare their heights. This visual and tactile approach helps students grasp the concept of comparison in a meaningful way.
It’s also important to teach students the language of comparison, such as “greater than,” “less than,” and “equal to.” Giving students opportunities to describe their comparisons using these terms helps build their mathematical vocabulary. For example:
Comparing with Counters: Provide students with two piles of counters. Ask them to count the counters in each pile and compare the amounts. Encourage students to organize the counters inside ten-frames or line them up side by side to visualize the difference. Students can use vocabulary like “greater than,” “less than,” or “equal to” to describe their findings.
Comparing with Connecting Cubes: Give students a set of connecting cubes and numeral cards. Have them build towers using the numbers on the cards, then compare the heights of the towers to determine which is taller. Students can record their comparisons using symbols like >, <, or =. This activity makes the abstract concept of comparing numbers more concrete by giving students a visual and tactile representation.
Comparing Fractions
Students transfer their understanding of comparing whole numbers to comparing fractions by recognizing that the same principles of “greater than,” “less than,” and “equal to” apply. However, they must consider the size of the parts, not just the numbers themselves. Visual models, like fraction bars or number lines, help students see these relationships and build on their existing knowledge of whole numbers to understand how fractions work.
For example, give students a set of fraction tiles and ask them to compare two fractions, such as ½ and ⅓. Have them lay out the tiles on top of the other to visually see the size of each fraction. Next, ask students to determine which fraction is larger by comparing the tiles.
Comparing Decimal Numbers
Concrete and visual models, such as base ten blocks or base ten grids, are essential for helping young students understand comparing decimal numbers. These models provide a hands-on way for students to see how decimal numbers represent parts of a whole and help students see the relative size of decimals, reinforcing the concept that the position of digits determines their value. These models make abstract concepts more tangible, supporting students in developing a deeper understanding of comparing decimals.
For example, give students a base ten decimal grid with 100 squares representing the whole. Have them shade in a certain number of squares to represent a decimal, like 0.7.
After shading, ask students to compare their grids with a partner’s to see which decimal is larger. One student may shade 70 squares (0.7) and another 65 squares (0.65), helping them see that 0.65 is actually smaller than 0.7. This activity helps students understand decimal size by visually connecting the numbers to models.
Connecting Math Vocabulary to Symbols
Students need to understand the relationship between the concepts of “greater than” and “less than” and the symbols that represent them (“>” and “<“). They learn that the “greater than” symbol (>) opens on the left, while the “less than” symbol (<) opens on the right. While many students are taught to think of the symbols as a mouth, it’s important they also learn to read and write the symbols accurately. Understanding these concepts helps ensure students can correctly compare numbers in both written and visual forms.
