Connecting Representations
Move between real-world situations, drawings, and number sentences, explaining how each representation connects to the others (quantitative reasoning)
What a learner can do afterwards
- Write a number sentence (e.g. 14 + 5 = 19) to match a word problem and explain the connection
- Draw a bar model or part-whole diagram to represent a problem, then solve using the diagram
- Translate between a concrete model and a symbolic equation, describing what each number represents
The lesson
A math problem can be told three ways: as a real story, as a picture, and as a number sentence. All three tell the same story. Learning to move between them helps you check your thinking and explain your answer.
Ben has 5 blocks. His sister gives him 4 more blocks. Story: Ben starts with some blocks and gets more. Picture: draw 5 blocks, then 4 more blocks next to them. Number sentence: 5 + 4 = 9. All three show the same 9 blocks.
To check your work, look at each number in your sentence. Can you point to it in the picture? Can you find it in the story? If a number does not match, look again at your picture or your story.
A real story, a picture, and a number sentence can show the same math idea. Check that all three match.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.