Modeling Comparative Relationships with Tape Diagrams
This Grade 4 Eureka Math skill teaches students to model comparative addition and subtraction word problems using tape diagrams. Each quantity is represented as a bar, with relationships like A is x more than B expressed as A = B + x, and C is y fewer than B expressed as C = B minus y. For example, a red box weighs 450 g, a blue box weighs 120 g more (570 g), and a green box weighs 80 g fewer than blue (490 g); the total is 450 + 570 + 490 = 1,510 g. This visual modeling strategy is taught in Chapter 6 of Eureka Math Grade 4.
Key Concepts
To model comparative relationships, use tape diagrams where each quantity is a bar. If quantity $A$ is $x$ more than quantity $B$, then $A = B + x$. If quantity $C$ is $y$ fewer than quantity $B$, then $C = B y$. The total is the sum of all quantities: $Total = A + B + C + ...$.
Common Questions
How do you draw a tape diagram for a comparative word problem?
Draw a bar for the known quantity. Draw a second bar for the quantity described as more or less: make it longer with an extra section for the more amount, or shorter for the fewer amount.
If the red box weighs 450 g and the blue box weighs 120 g more, how much does blue weigh?
Blue = 450 + 120 = 570 g. Draw a tape for red (450 g) and a tape for blue that is 570 g long, showing the 450 g match plus a 120 g extra section.
If the green box weighs 80 g fewer than the blue box (570 g), how much does green weigh?
Green = 570 minus 80 = 490 g.
How do you find the total weight after modeling with tape diagrams?
Add all individual quantities found from the diagrams: 450 + 570 + 490 = 1,510 g.
What does the tape diagram make visible in a comparison problem?
It makes the relationship between quantities explicit. You can see which bar is longer (more) or shorter (fewer) and identify the extra or missing amount directly from the diagram.