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Number Lines & Fractions: Jumps, Positions & Closest Numbers

Maths · Y4 OC Prep
Year 4 OC
Lesson Guide
Explanation
A number line question always starts the same way as a scale question: work out what one mark is worth. Count the gaps between two neighbouring whole numbers. Four gaps mean quarters, three mean thirds, five mean fifths. Then read any mark by counting from the nearest whole number — the mark one to the right of eight is eight and a quarter, the mark one to the left of two on a thirds line is one and two-thirds. The trap is counting marks instead of gaps, or counting all the way from the left end and losing track.
Your Turn
A number line shows 3 and 4 with five gaps between them. What is the mark just left of 4? Check: fifths, so 3⅘.
Watch Out
Lines can start anywhere. "Part of a number line" from 7 to 9 has no 0 on it — read the labels that are there.
Explanation
The jump question draws part of a number line with an arrow showing one jump and asks where you land after some number of jumps. Read the jump size from the marks — one gap on a quarters line is a quarter — and its direction. Then multiply: eleven jumps of a quarter is eleven quarters, which is two wholes and three quarters, because eleven divided by four is two remainder three. Finally subtract from the start, whole first then fraction: nine minus two is seven, minus three quarters is six and a quarter. The picture does not stretch far enough to count, which is deliberate.
Your Turn
Start at 4, jump ¾ to the right, 6 times. Where do you land? Check: 6 × ¾ = 18 quarters = 4½; 4 + 4½ = 8½.
Watch Out
The arrow may span more than one gap — a jump of ¾ on a quarters line. Count the gaps the arrow covers, not the marks.
Explanation
'Closest to two' asks for the smallest distance from two, whether the number is below or above. Write each distance as a fraction: one and three-quarters is a quarter away, two and a third is a third away, two and a half is a half away. Then compare the fractions. With a one on top, a bigger bottom number means a smaller fraction, so a quarter is less than a third and one and three-quarters is the closest. The trap is choosing a number that starts with a two; the number line shows that the whole-number part is not what matters.
Your Turn
Closest to 5: 4⅘, 5¼, 4⅔ or 5⅓? Check: distances ⅕, ¼, ⅓, ⅓ — ⅕ is smallest, so 4⅘.
Watch Out
Compare ⅔ and ¾ carefully: ⅔ = 8⁄12 and ¾ = 9⁄12, so ⅔ is the smaller distance. Don't guess from the tops alone.
Explanation
Placing a mixed number on a number line is two steps: find the whole number, then count the fraction's marks from it. On a line cut into thirds, one and two-thirds is the second mark after one; on a fifths line, one and four-fifths is the fourth mark after one, which is also the mark just before two. Anchoring on the whole number avoids the slip that comes from counting every mark from zero. Always check the division first — a line that looks like quarters may be thirds or fifths, and the letters are placed to punish the assumption.
Your Turn
A line from 2 to 4 is cut into fifths. How many marks after 3 is 3⅗? Check: 3.
Watch Out
An unlabelled whole number is still a whole number. If 1 is not printed, it is still where the long mark is.
Explanation
The reverse question gives the start, the jump and the target and asks how many jumps. Find the distance, turn it into the small unit so that everything is a whole number, and divide by the jump size in that unit: from two and a quarter to six is fifteen quarters, each jump is three quarters, five jumps. If the division leaves a remainder the jumps never land exactly on the target, and the question will ask instead for the first jump past it — which is the quotient plus one. Everything in this lesson comes back to three tools: the value of a mark, jumps turned into wholes and parts, and distance divided by jump. Quiz and exercises now!
Your Turn
From 1½, jumps of ⅔ to the right. Where are you after 6 jumps? Check: 6 × ⅔ = 4; 1½ + 4 = 5½.
Watch Out
Convert the START as well as the target to the small unit. 2¼ is 9 quarters, not 2 quarters.
📌 Key Points — this lesson in a nutshell
  • On a number line, count the gaps between two whole numbers to find what one mark is worth: 4 gaps → quarters, 3 gaps → thirds.
  • n jumps of ¼ is n quarters. Turn it into wholes and quarters: 11 quarters = 2¾. Then add or subtract from the start.
  • "Closest to 2" means the smallest DISTANCE from 2. 1¾ is ¼ away; 2⅓ is ⅓ away. ¼ < ⅓, so 1¾ wins.
  • Fractions with a 1 on top: the bigger the bottom, the smaller the fraction. ⅕ < ¼ < ⅓ < ½.
Step 1: Introduction
Step 1 of 5
Count the gaps between two whole numbers 789?? 012?? Top line: 4 gaps from 7 to 8 → each mark is ¼. The ?s are 7¼ and 8¾. Bottom line: 3 gaps from 0 to 1 → each mark is ⅓. The ?s are ⅓ and 1⅔. Gaps, not marks: 5 marks from 7 to 8 make 4 gaps. Dividing by 5 gives fifths — wrong. Count from the nearest whole number, not from the left end of the line.
Start at 9, jump ¼ to the left, 11 times 6789one jumpstartafter 11 Step 1: one jump is ¼ (one gap of the quarters line), going LEFT. Step 2: 11 jumps = 11 quarters = 2 wholes and 3 quarters = 2¾. Step 3: 9 − 2¾ = 6¼. 11 ÷ 4 = 2 remainder 3 → 2 wholes and 3 quarters. Same division-with-remainder you already know. 9 − 2 = 7, then 7 − ¾ = 6¼. Subtract the whole, then the fraction. Traps: counting 11 marks on the picture (it doesn't reach); going right instead of left; 9 − 2¾ = 7¼. Check: from 6¼, 3 quarter-jumps right is 7, then 8 more quarters is 9. 3 + 8 = 11 ✓.
Closest to 2: the smallest distance wins 1231¾1½2⅔2⅓2½ Distance from 2: 1½ → ½. 1¾ → ¼. 2⅓ → ⅓. 2½ → ½. 2⅔ → ⅔. Smallest distance: ¼ (1¾) beats ⅓ (2⅓). Closest is 1¾. Why ¼ < ⅓: cut a cake into 4 and each piece is smaller than cutting it into 3. Bigger bottom, smaller piece. Below and above both count — "closest" is about distance, not about being under or over. Trap: picking 2⅓ because "it starts with 2". The number line shows it is further away than 1¾. When distances are hard to compare, put both over 12: ¼ = 3⁄12, ⅓ = 4⁄12.
Which letter marks 1⅔? 012PRQS 3 gaps per whole → thirds. Start at the whole number 1, then count 2 marks to the right. 1⅔ is the second mark after 1 → Q. R is 1⅓ (one mark after 1). P is ⅔. S is ⅓. Reverse question: "what number is at R?" → 1 whole and 1 third → 1⅓. Trap: counting 5 marks from 0 for 1⅔ and slipping by one. Anchor on the whole number and count from there. Trap: assuming quarters because most lines use quarters. Count the gaps every time. Fifths line: 1⅘ is four marks after 1, one mark before 2.
From 2¼, jumps of ¾ — how many to land exactly on 6? 23456¾starttarget Distance to cover: 6 − 2¼ = 3¾ = 15 quarters. Each jump is 3 quarters. 15 ÷ 3 = 5 jumps. Work in the small unit (quarters) so everything is a whole number, then divide. Landing points: 3, 3¾, 4½, 5¼, 6. Five jumps ✓ — list them if you have time. "First time BELOW 3, jumping ¾ left from 7": 7 − 3 = 16 quarters; 16 ÷ 3 = 5 r 1. 5 jumps reach 3¼, still above 3; the 6th jump goes below. A remainder means the jumps don't land exactly — read whether the question wants "exactly" or "first past". Same three tools every time: mark value, jumps → wholes and parts, distance ÷ jump. Quiz and exercises now!
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