# N22 · Full next teaching

## Previous target

V06B

## Target

Use an estimate without overstating what it decides

## Flexible time

About 8–12 minutes, or shorter visits; unpiloted suggestion.

## Prepare

Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.

## Complete new neutral task

4 pretend display sets cost a made-up $17 each plus one $5 fee. Budget $70. Round both prices up to whole tens for a check. Explain whether that check decides affordability; then calculate exactly.

## Specific criterion

Explain the direction and purpose of rounding, then use an exact total when an estimate cannot settle a close budget question.

## Whole teaching sequence

Read the new brief and ask which quantity is missing. Name units before any calculation. Place the exact unit price below its next whole ten-dollar amount, and the fee below its next ten-dollar amount. Name the resulting total an upper check. When that upper check is above the budget, explicitly keep the decision open and calculate the exact cost.

Build the supplied new example together. Teacher explanation: Upper check 4 × $20 + $10 = $90. It exceeds the budget but cannot alone prove an overrun. Exact cost $73, over by $3. Ask the learner to point to the part of the model that supports each quantity. An upper estimate above the budget does not by itself prove that the exact price is above the budget.

Remove the worked example. Give this changed task privately: The budget changes to the exact total, $73; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate. Offer a different response mode if needed without silently changing the mathematical criterion.

## Supplied joint model

Upper check 4 × $20 + $10 = $90. It exceeds the budget but cannot alone prove an overrun. Exact cost $73, over by $3.

## Equivalent offers

Make/draw using original blank group frames.

Explain/sign/point or dictate reasoning.

Type a private note or use paper; a device is optional.

## Private changed task after removing model

The budget changes to the exact total, $73; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate.

## Staff changed-task possibility

It fits exactly with $0 left. The upper estimate stays $90; it is a check, not the paid total.

## Observe and decide next teaching

Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.