Fractions on a number line

Activities to try

1. 1

   Build the model before you compute

   Why it works: The diagram generates the operations, so you never have to guess an operation from a keyword; partitioning a bar is division and marking off a segment is subtraction. Checking against an estimate catches off-scale answers, and the same model transfers when a quantity changes (e.g. a 3 kg bag still partitions into four equal parts).

   1. Read a multi-step measurement problem, e.g. 'A 2.5 kg bag of flour is shared equally into 4 tubs, then 150 g is taken from one tub — how much is left in that tub?'
   2. Before writing any equation, draw a bar/strip diagram or number line that shows the quantities and how they relate (the whole 2.5 kg, the 4 equal parts, the 150 g removed)
   3. Convert to a common unit where needed (150 g = 0.15 kg, or 2.5 kg = 2500 g) and note the conversion explicitly
   4. Let the structure of your diagram tell you the operations: splitting the bar into 4 equal parts IS the ÷4 (each part = 2500 g ÷ 4 = 625 g = 0.625 kg), and marking off 150 g from one part IS the subtraction (625 g − 150 g = 475 g = 0.475 kg). Working in grams keeps the numbers whole, because 0.625 kg is in thousandths and Grade 4 decimal work usually stops at hundredths.
   5. Estimate roughly first, then check the computed answer against that estimate and label the unit
2. 2

   Convert units before operating

   Why it works: Operations are only valid between quantities expressed in the same unit; converting first prevents combining unlike units, and time is base-60, not base-10.

   1. Given quantities in mixed units (e.g. 0.75 m, 1.2 m and 0.95 m; or 95 cm alongside 0.75 m), identify that they cannot be combined until expressed in one unit
   2. Use a conversion table within a system (km/m/cm, kg/g, l/ml, hr/min) to rewrite every quantity in a common unit (95 cm → 0.95 m)
   3. Only then add, subtract, multiply or divide, and label the result with the correct unit
   4. Treat time carefully: 1 hr 45 min is NOT 1.45; minutes carry at 60, not 100 (e.g. leaving 09:20 and travelling 1 hr 45 min arrives at 11:05)
3. 3

   Self-monitor and compare strategies

   Why it works: Monitoring your own steps and comparing different valid representations can deepen understanding of why the operations follow from the situation, rather than from a cue word.

   1. At the start, ask yourself 'What is the problem asking?' and restate the goal before choosing a representation
   2. After solving, ask 'Does my answer make sense?' and compare it to your up-front estimate
   3. Solve a problem, then view or discuss an alternative strategy for the same problem (e.g. a bar model vs. a number-line path) and explain how each maps to the same operations
   4. Explore a worked example where each diagram segment is annotated with the quantity it stands for and the operation the structure implies — use this for reference, then build your own on a new problem