Knowing that 18 is greater than 14 is useful, but a strong mathematician can show why. In this module, you will make comparisons with evidence: matching objects one-to-one, counting when needed, or locating numbers on a number line.
MATH-101 · MODULE 03
Compare, Order, and Travel Number Paths
Use evidence, benchmarks, and number-line position to compare and order numbers.
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
The symbols >, <, and = are labels for a relationship you have already established. You will not begin by memorizing a symbol trick. First you will decide whether one quantity has more, fewer, or the same number of items. Then you will connect that decision to words, symbols, and positions on a number line.
Number paths are useful because every step has meaning. Moving one step to the right adds one; moving one step to the left subtracts one. You will use friendly benchmarks such as 0, 5, 10, and 20, and later tens, to reason instead of recounting everything from the beginning.
Benchmark
Choose a useful benchmark
Learning target
Locate a nearby known number before locating a new one.
Teach the idea
A benchmark is a number you can find quickly and use as an anchor. On a path from 0 to 20, 10 is often especially useful. To locate 13, begin at 10 and move three equal steps right instead of rebuilding the entire count from zero.
See the model
Model: 10 → 11 → 12 → 13. Three rightward steps from 10 reach 13.
Guide thinking
Teacher thinking: “A close benchmark saves work but does not change the meaning of each step.”
Connected practice
Start near the number
Starting at 10, how many rightward steps reach 14?
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 evidence shows which quantity is greater before you use a comparison symbol?
- Which benchmark helps you locate this number, and how many steps away is it?
- Explain why changing the space between objects does not automatically make one set greater.