Number Line Widget

A number line Berdee draws exactly from a start, an end and a number of equal parts. Students place a point at a number, name a point, fill in blank labels under ticks, split every part of the line into smaller parts, or say how far a point is from 1/2 or 1. Every tick sits at its exact place, so the line can never be drawn unequal by accident.

Berdee grades by value. A point at 6/8 is right for "show 3/4", and a student who names a point 3/4, 6/8 or 9/12 gets the same answer, unless you ask for one form. Use it for Grade 3 and Grade 4 fractions: where fractions live on a line, equivalent fractions as the same point, and fractions past 1.

Select the widget on the canvas and click the floating ⚙ Configure button to set it up. The settings read in the order you decide them: what students do, the lines, what's on the line, what students answer, what they see and hear, then how it's checked.

Set it up

What students do

Each choice says what students do, and is tagged Graded or Not graded.

• Place a point (Graded): students drag a point from above the line onto it, or tap the line where it goes, then tap Check.
• Name a point (Graded): you put a point on the line. Students type its fraction in a fraction box: they tap the top box, tap digits, tap the bottom box, tap digits, then Check.
• Label ticks (Graded): you choose ticks whose labels are blank. Students fill in each one.
• Split each part (Graded): students choose "split each part into 2, 3, 4…" and watch new ticks appear between the old ones. Then they place or name a point on the new ticks and tap Done.
• How far (Graded): students type how far a point is from 1/2 or 1.
• Show (Not graded): a line with points, labels and rings, for a question you ask around it with other widgets. It scores 0 of 0 and never holds a scene back.

The Graded choices turn Scoring on for you, and each arrives with something to answer: a point to place, a point to name, a blank tick, so you can start from there.

The lines

A widget holds up to 4 lines, stacked. For each line:

• From and to: where it starts and ends, as whole numbers or fractions, such as 0 and 1, 0 and 2, or 0 and 10/4. A line can run past 1.
• Equal parts: how many equal spaces the line is cut into. This is the number of spaces between ticks, not the number of ticks: a line in fourths has 4 parts and 5 ticks. Up to 24 on a line students work on, and up to 100 on a Show line.
• Minor ticks: shorter ticks inside each part, such as tenths with hundredths, or twelfths grouped into thirds.
• Labels: Every tick, Ends, Chosen (only the ticks you tap on the line below) or None.
• Write labels as: Fraction writes each label in the line's own parts, so the end of a line in fourths reads 4/4. Lowest terms writes 1, and 1/2 in the middle.

Add a line adds another, copying the last one's ends and parts. With two or more lines, Scale decides how they line up. Lined up puts every line on one scale, so the same number sits in the same place on each: three lines from 0 to 1 in fourths, eighths and twelfths show 3/4, 6/8 and 9/12 at one spot. Each its own gives each line the full width, for two lines with different wholes, such as kilometres over li.

On the line

Under On the line you see your lines exactly as students will. What a tap on a tick does depends on the switch above it:

• Label ticks: tap a tick to show or hide its label. This is how you make a partly labelled line, such as one labelled only at 0 and 1/4 that runs to 10/4, so students work out the unit first.
• Blank ticks (Label ticks): tap a tick to make its label a blank box students fill in. Tap it again to take the box away. A blank tick never shows its label.
• Add points: tap a tick to put a lettered point there. Drag a point, or select it and use the arrow keys, to move it from tick to tick.

As you work, a line under it says whether each point to place lands on a tick, such as "1/3 is not on a tick of this line." Change the point, change the number of parts, or set Snapping to Free (estimate).

Points to place

In Place a point and Split each part, list each point students place: its letter and the number it belongs at, such as 3/4. With more than one line, choose Any line or the line it must go on. Any tick with the same value is right, so on lined-up lines 3/4 can go on the fourths line or at 6/8 on the eighths line.

Snapping decides where a dropped point stays:

• To ticks: it snaps to the nearest tick. Students never have to hit a thin tick exactly.
• To minor ticks: it snaps to the nearest tick, minor ticks included.
• Free (estimate): it stays where it's dropped. How close counts is how near is near enough, as a fraction of a whole such as 1/20. Leave it empty for About right: within 1/20 of the line's length. Each attempt says too low, about right or too high.

The split

In Split each part:

• Splits students can choose: the numbers students can split each part into, from 2 to 10.
• Grade the split: off, the split is a tool and Berdee still records which split each student chose. On, the split is part of the answer: Must land on a tick lists numbers, such as 1/2, that the split must put on a tick. On a line in fifths, splitting each fifth into 2 puts 1/2 at 5/10, so any split that does that is right.

Points students name and How far from

In Name a point and How far, each point on the line has a switch for whether students answer for it. In How far, choose from 1/2 or from 1 for each point. Add points with Add points on the line.

A point students name can't sit on a tick that shows its label: the answer would be showing. The dialog says so. Hide that label (switch the line to Label ticks and tap it) or move the point.

What students see and hear

• Ring these numbers: 0, 1/2 or 1 ringed and named on the line, as benchmarks to measure from.
• Show the number while dragging (Place a point, Split each part): the number shows under the point as it moves. Leave it off when placing the number is the skill. Screen readers hear "tick 6 of 10" while placing, not the number, for the same reason.

How it's checked

Answers decides what a fraction box accepts:

• Any equal fraction: 6/8, 3/4 and 9/12 are all right for the same point.
• This denominator: only the denominator you set, such as twelfths: 9/12 and not 3/4.
• Lowest terms: only 3/4, not 6/8.

With more than one point to name, Each answer uses a different denominator asks for a different fraction for each, like naming the same point a different way on each of three lines. A How far answer never counts: it can share a denominator with the point it measures.

A box with a denominator of 0 is never right.

Scoring

The Scoring section stays where it is in the Configure dialog. Set the points there. Each Check (or Done in Split each part) is one attempt, so a perfect run is one attempt. Dragging a point around before checking, splitting, and tapping digits never count.

More options

• Worked example (Split each part): splits that Show the next split shows one at a time, such as 2 then 3.
• Starts hidden: a point stays hidden until Show a point reveals it.
• End written as: the end's own name, such as 8/8 or 100/100, in place of the usual label.

If ticks students must tap are closer than 44 pixels, the dialog warns you. Students can still drag with snapping or use the arrow keys, but make the widget wider or use fewer parts if they tap.

How a student uses it

1. Place: drag the lettered point onto the line, or tap the line where it goes. It snaps to a tick (or, on an estimate, stays put). Drag it again to move it. With a keyboard, Tab to the point and use the arrow keys; Home and End jump to the ends. Check grades it.
2. Name: tap the top of the fraction box, tap digits on the pad, tap the bottom, tap digits, then Check.
3. Label ticks: tap a blank label to open its fraction box there. Fill it, then move to the next.
4. Split: choose a number in Split each part into. The new ticks appear between the old ones, which stay longer, and the count is spoken: "Each fourth is split into 2. The line has 8 equal parts." Back returns to the last split.
5. After a right answer the point gets a check and its label. After a wrong one the point stays where the student put it with a gentle mark, and the scene's hint plays. Berdee never moves a wrong point for them.

Why "count the spaces"

The most common mistake on a number line is counting the ticks instead of the spaces between them. A line from 0 to 1 cut into fourths has 5 ticks, so a student counting ticks calls the parts fifths, and names the tick at 3/4 "3/5" or "4/5". Another is taking the end of the line as 1: on a line that runs to 2 in tenths of 2, the tick at 9/10 gets named 9/20.

Berdee spots both and names them on the attempt page. Give students a hint that says what to do: use a behavior on On Check with the condition Misconception equals counted_ticks to say "Count the spaces between the ticks, not the ticks." Or show a hint text with a Visibility rule on the same condition, which hides it again once the answer is right. Step-by-step: Place a fraction on a number line.

Example: split the fourths into eighths and place 6/8

1. Add a Number Line from the toolbox and click ⚙ Configure.
2. Under What students do, choose Split each part.
3. Under The lines, keep the line from 0 to 1 with 4 Equal parts, and Labels on Ends.
4. Under Points to place, set point A to 6/8. The line under the live line says "Every point lands on a tick with a split students can choose": splitting each fourth into 2 makes eighths.
5. Under The split, keep Splits students can choose at 2 to 5. Leave Grade the split off: placing 6/8 is the answer, and a split into 4 (sixteenths) puts 6/8 on a tick too, at 12/16.
6. Click Save, and preview the scene. Split each part into 2, drag A to the sixth tick after 0, and tap Done. It's right. Drag it to the 6th tick of the fourths line before splitting, and it can't go there: there is no 6th part.

To ask "is 6/8 the same point as 3/4?", add a second line from 0 to 1 in fourths, set Scale to Lined up, and ring 3/4 with a Show line under it.

Example: a partly labelled line past 1

For "name the point" on a line labelled only at 0 and 1/4 that runs to 10/4:

1. Choose Name a point. Set From and to to 0 and 10/4, and Equal parts to 10.
2. On the live line, switch to Label ticks. Tap the end to hide its label, then tap the first tick after 0 to label it 1/4.
3. Switch to Add points and tap the 9th tick to put point A at 9/4. Turn on Students name point A.
4. Leave Answers on Any equal fraction. A student who assumes the end is 1 names it 9/10, and the attempt page says so.

Grading and what you see

Berdee checks every answer again on the server, using the lesson as it was published. On each student's attempt page you see one line per answer and a small picture of the line with the student's point:

• Placed at 6/8 · asked for 3/4 · same point ✓
• Placed at 4/5 · asked for 3/4 ✗ · then 6/8 ✓
• Named 4/5 · it's 4/4 (counted ticks, not spaces) ✗ · then 4/4 ✓
• Split each fifth into 2 · 10 parts · placed 1/2 at 5/10 ✓

Use it in logic

Number line has three events:

• On Point Placed: when a learner drops or moves a point (Place a point, Split each part).
• On Split: when a learner splits the parts (Split each part).
• On Check: when a learner taps Check, or Done in Split each part.

It reports Placed value, Placed tick, Parts (after a split), Is on a tick, Misconception (counted_ticks, assumed_end_one, between_ticks, numerator_only or wrong_benchmark), Checks, Is correct and Is answered. It has five methods: Start over, Show the next split, Show a point and Hide a point (by letter), and Show every label. See Widget properties and methods and Events, actions and conditions.

Accessibility

• Every point is a 44-pixel handle with a letter or a pin, never just a dot of color, and benchmarks are ringed and named.
• Everything a drag does also works with a tap and with the keyboard.
• Screen readers hear the line described, such as "Number line from 0 to 2, 10 equal parts, labelled at 0 and at tick 5 as 1".
• With reduced motion on, a split appears without animating and a snap doesn't slide.

Related

• Equal Shares: cut a whole into halves and fourths, before fractions move onto a line.
• Number input: a typed number answer. It can't take a fraction: use Name a point here.
• Choose the right widget