Addition and subtraction are not just two kinds of answer buttons. They describe relationships between quantities. Sometimes two parts join to make a whole. Sometimes part of a whole is removed. Sometimes the whole is known and one part is missing. The same equation can be understood from more than one model.
MATH-101 · MODULE 04
Build and Break Apart Numbers
Use part-whole relationships to understand joining, separating, and missing-part situations.
A five-hour foundations course
Build number ideas you can see, say, check, and use.
These lessons are deliberately paced. Start with the welcome dialogue, work through the visible model and guide thinking in each cycle, then use the practice question as a check—not as the lesson itself.
Restoring this module…
Before you begin
Guided conversation
In this module, you will build numbers in several ways: 8 can be 5 and 3, 6 and 2, or 7 and 1. The whole remains 8 even when the parts change. Seeing that structure makes facts easier to remember because each fact is connected to a picture, a story, and a related fact.
You will begin with objects, drawings, frames, and number lines before relying on an equation alone. After a worked example, you will choose a model that fits a short situation, solve it, and check whether your answer makes sense. A wrong choice is useful evidence: it tells us whether the story was read as joining, separating, comparing, or finding a missing part.
See
Identify the whole and its parts
Learning target
Name a total and the quantities that make it.
Teach the idea
A part-whole model keeps the relationship visible. If a row has 8 counters and 5 are red while 3 are blue, the whole is 8 and the two parts are 5 and 3. Parts can be different, but together they must rebuild the whole.
See the model
Model: whole 8 = part 5 + part 3.
Guide thinking
Teacher thinking: “I will label the whole before I choose an operation.”
Connected practice
Name the whole
Five green beads and 4 yellow beads are together. What is the whole?
Learner conversation
Pause and explain
Use one of these prompts to explain the idea in your own words. You can keep a private note if that helps you remember a strategy.
- What is the whole in this situation, and which two parts give you evidence for it?
- Show two different ways to make the same number. What did not change?
- How did the story tell you whether to combine, take away, compare, or find a missing part?