# Day 33 · Fifths and tenths for a useful plan

**Show what is ready and what is still needed.**

Useful purpose: Recognise one-fifth and one-tenth, count their multiples and complete the same whole using its denominator.

## 1 · Find the starting point

Check thirds/quarters with a new short strip. Count equal intervals rather than boundary lines. Offer a ten-part strip with eleven boundary lines so the difference is visible.

## 2 · Prepare

Use an original paper banner with ten equal sections and another with five. Plain spoken section descriptions work equally. Optional Mint card F01 uses dollar value labels only; no real money, spending or imported coin image.

## 3 · Brief worked model

MODEL whole banner has ten equal sections. Four ready sections are 4/10: four one-tenth parts. Six more, 6/10, complete it because 4+6=10. A separate five-section banner with two ready sections needs 3/5 more. We do not add 4/10 and 3/5 as the equal-size parts. In F01, $1=100 cents is the primary fact; our original ten equal 10-cent value labels show 1/10 of that $1 value each, not equal areas of real coins.

## 4 · A different guided try

Try an unrelated five-part path card with one section ready; identify 1/5 and the 4/5 needed. Then use a different ten-part reading-progress model with seven ready; name 7/10 and 3/10 remaining. These fictional counts do not track a child’s real reading.

## 5 · Your own attempt

Choose a banner, game strip or value-label plan. Name the whole, partition into five or ten equal parts, mark a multiple and explain the missing same-denominator part. Describe or direct marking if wanted.

## 6 · Observe what was actually shown

Look for five/ten equal parts, correct unit fraction, numerator as selected parts and completion conserving the whole. Distinguish a 10-cent value from one coin in a mixed collection.

## Specific next teaching

If eleven lines are counted as eleven parts, colour/descriptively name each gap on a different strip. If adding denominators, reassemble five equal parts and keep the whole named. If secure, show the same multiple in an equal-group set.

## Three choices you can switch between

### 1 · Banner progress

**How much is still needed?**

MODEL ten equal panels, three ready. Name 3/10 ready and 7/10 to complete; draw a different own banner only if wanted.

Evidence/observation: Supplied completion; an actual project has its own observations.

Specific next teaching: Try five equal panels with different ready count.

### 2 · A dollar in equal value parts

**What whole do these labels show?**

Use F01 or its full words: ten fictional 10-cent value labels make 100 cents. Name one-tenth, four-tenths and six-tenths of that $1 value. Keep coin count, coin area and total value separate.

Evidence/observation: Original derived value representation from a dated primary fact; not a purchase or broad money outcome.

Specific next teaching: Use a paper strip if the monetary whole distracts; later try five equal 20-cent value parts.

### 3 · Choose a tiny project

**Make a five-part or ten-part plan.**

Choose a fictional display, sequence of equal game spaces or equally valued label set. Name what the whole means, show ready and needed parts, then ask a willing helper to interpret the label without silently repairing it.

Evidence/observation: Own making/communication; willing-reader trial only if it actually occurs.

Specific next teaching: If the reader confuses whole and selected part, revise the title before changing the numbers.

[Short child start](../learner/day-33.md) · [Ordinary cues/full alternatives](../aids/README.md) · [Adult preparation](../teacher/PREPARATION.md)