# Day 34 · Fractions between zero and one

**Make a little trail from zero to one whole.**

Useful purpose: Place unit fractions and multiples on an equal-interval 0–1 number line without counting ticks as parts.

## 1 · Find the starting point

Check what 0 and 1 mean for the chosen whole. Count five equal gaps between six marks; show that marks are boundaries, not separate pieces.

## 2 · Prepare

Use the original MODEL fractions cue or a new paper line. A device can display the SVG, but looking at it is not child software creation. A spoken ordered list with equal-interval description gives the same maths access.

## 3 · Brief worked model

MODEL number line runs from 0 to 1 whole, split into five equal gaps. Labels are 0,1/5,2/5,3/5,4/5,1. The point 3/5 lies at three one-fifth steps from zero. Two more one-fifth steps reach the same whole. A line with uneven gaps cannot show these equal fraction steps accurately, even if its labels look right.

## 4 · A different guided try

Use a new thirds line: 0,1/3,2/3,1. Ask the child to locate 2/3 and explain the missing 1/3. Then offer a quarters line with only endpoints and invite its equal marks. Avoid introducing different-denominator addition as a requirement.

## 5 · Your own attempt

Choose denominator 2,3,4,5 or 10. Make/describe an equal-gap line from 0 to 1, locate a chosen multiple and explain what would reach 1. Use words, tactile-safe paper folding if wanted, typing, signing or an exact adult scribe.

## 6 · Observe what was actually shown

Observe whole/endpoints, equal intervals, interval count, unit label and multiple position. A correct numeral copied onto an uneven line needs further teaching, not automatic N02 clearing.

## Specific next teaching

If ticks and gaps are confused, physically or verbally trace three gaps between four marks in a new line. If secure, connect the same fraction to a set or area while keeping its whole explicit.

## Three choices you can switch between

### 1 · Trail marker

**Where would your marker go?**

MODEL thirds line has equal gaps. Place a marker at 2/3; it is two gaps from 0 and one gap from 1. No timed walking route or body movement needed.

Evidence/observation: Supplied number-line interpretation, not actual travel.

Specific next teaching: Try a different denominator with unlabelled internal marks.

### 2 · Build a clear line

**Help someone find three-fifths.**

Make/describe a five-equal-gap 0–1 line and place 3/5. A helper can draw where directed. Label endpoints and say why six boundary marks do not mean sixths.

Evidence/observation: Own representation; adult operation distinguished.

Specific next teaching: Ask a willing reader to locate a new multiple; record any actual trial and revision.

### 3 · Find the faulty trail

**Could the gaps all be fifths?**

MODEL marks lie at 0,1,2,3,4,10 distance units, with endpoint 10 representing 1 whole. The last gap is much larger. Explain why labelling all gaps 1/5 is invalid and propose equal marks 0,2,4,6,8,10.

Evidence/observation: Supplied geometric reasoning; units are invented diagram distances, not measured centimetres.

Specific next teaching: Return to an equal paper strip before another faulty-line comparison.

[Short child start](../learner/day-34.md) · [Ordinary cues/full alternatives](../aids/README.md) · [Adult preparation](../teacher/PREPARATION.md)