All concepts combined

Rate questions here come in two parts. A press stamps discs at a steady rate, a courier charges for the first kilogram and then for each further 500 g, a printer gives a free box for every 8 boxes ordered, and two taps fill a tank at different rates. Your child finds one rate or charge first and uses it in a second calculation. The questions apply the Primary 5 outcomes on rate as an amount per unit and on finding a rate, a total or a number of units.

• A rate is an amount for each one unit, such as 140 discs each minute or $1.60 for each badge.
• With two quantities and a rate, the third is found by multiplying or dividing.
• In a charge table, the first block has its own price and every further block, or part of one, costs the same.
• A part of a block is charged as a whole block, so round the number of blocks up.
• When two taps run together, their rates add; when one is closed, only the other rate remains.

For courier A, a 2.4 kg parcel is the first 1 kg and 1400 g more. Two blocks of 500 g cover only 1000 g, so 1400 g needs 3 blocks: $3.20 plus 3 times $1.10 is $6.50. A charge that counts only 2 further blocks has left part of the parcel unpaid.

All eight questions are Intermediate. Two use a steady rate: a press stamping discs, and a press printing handbills before a packing charge. Four use a charge with a first block and further blocks: one parcel's mass found from five, two couriers compared on one parcel, a room booked in 15-minute blocks worked back from its bill, and a printer that adds free boxes. One works out the real cost of one badge when a fifth pack comes free. One reads a line graph of two taps filling a tank. Ask your child to write each rate with its two units, such as litres each minute, before using it in the next step.

Why is part of 500 g charged as a whole block? The table says each further 500 g or part of it, so 100 g over a block still starts a new block. Your child counts the blocks needed and rounds up.

What is an effective price? It is what one item really costs once a free item is counted. Four packs of 5 badges for $40 plus a free pack give 25 badges, so each costs $1.60, not $2.

How do you find one tap's rate from a graph? Read how much the volume rises over a stretch of time while that tap runs, and divide by the minutes. When both taps run, take away the rate of the tap already known.