Checkpoint: fractions, ratios, percentages, and transfer

Where we are on the map

We close proportional reasoning and check readiness for algebraic language.

Begin with a familiar image

One successful sports attempt can be luck; a stable skill reappears under changed conditions and after time has passed.

Precise meaning

At least 8/10 is a guide. Every answer still needs a model, units, a check, and a route back to the support behind an error.

The lesson’s support signal

meaning → model → calculation → check → explain in your own words

model → calculate → explain → correct error → new setting → delayed recall

Worked example

37% = 37/100, 2:3 = 4:6, and 3/8 = 0.375 look different, yet all express relationships between parts and a unit.

Example with a fading prompt

Change the numbers in the example and repeat the solution without copying its steps. Estimate first, calculate exactly, and check against the original condition.

Recall without a prompt

1. Define the main idea in one sentence.
2. Rebuild the support signal from memory.
3. Solve the example with different numbers and explain why every step is valid.

Find and correct the mistake

A calculator output without units is not a complete solution. State what the number means and why its size is reasonable.

Transfer to a new setting

Apply the same relationship to something you can measure yourself. Name the quantities, units, and the boundary within which the model is valid. Check the answer by a second representation or an inverse operation.

Exercise

Required. Solve all ten tasks and show each method. Revisit topics below 8/10 and repeat a changed version after seven days.

With your own data. Create one everyday example with the same structure and show it in words, a formula, and a check.

Optional. Seven days later, change the numbers and repeat without the support map.

Open perspective

The next block introduces letters as names for quantities and leads to expressions and equations.

Course contents