The pattern
An average is a total
Turn the average back into a total before doing anything with it.
An average cannot be added, subtracted or split, but the total behind it can. So the first move is always to turn the average back into that total, by multiplying it by how many there were. Only at the end does dividing turn a total back into an average.
How to spot it
The word 'average' appears alongside a group being split into two parts, or two separate journeys or trips being combined into one overall figure.
Common mistake
Children average two averages directly, such as averaging two speeds or two group averages, without weighting by how many, or how long, each part actually covers.
23 worked solutions
Standard
- A bakery's week — average daily sales A bakery recorded its sales over 5 days: $42, $48, $55, $51 and $44. What was the average daily sales amount over the 5 days?
- A cyclist's five checkpoints — average speed A cyclist's speed was recorded at 5 checkpoints along a race: 18 km/h, 22 km/h, 26 km/h, 24 km/h and 20 km/h. What was the average…
- Average height — a class of 40 pupils In a class of 40 students, the average height is 142 cm. 15 of the students have an average height of 138 cm. What is the average …
- Books read — a bar graph of five children A bar graph shows the number of books read by five children. Emma read 12, Lucas read 8, Mia read 15, Noah read 10, and Olivia rea…
- Courier parcels — the average mass A courier weighed 5 parcels before delivery. Their masses were 12 kg, 15 kg, 19 kg, 17 kg and 12 kg. What was the average mass of …
- Egg trays — the average over four days A bar graph shows the number of egg trays sold by a bakery over four days. The bakery sold 18 trays on Monday, 22 trays on Tuesday…
- Five market stalls — the average donation A bar graph shows the amount donated by five market stalls to a charity drive. Stall A donated $12.50, Stall B donated $8.50, Stal…
- Four cousins — the mean age The mean age of four cousins is 12 years. Three of the cousins are 9, 13, and 15 years old. Find the age of the fourth cousin.
- Four numbers — the missing one The mean of four numbers is 18. Three of the numbers are 15, 20, and 22. Find the fourth number.
- Four parcels — the mean mass The mean mass of four parcels is 24 kg. Three of the parcels have masses of 19 kg, 26 kg, and 30 kg. Find the mass of the fourth p…
- Line graph — average of five temperature readings A line graph shows the temperature at 8 am, 10 am, 12 pm, 2 pm, and 4 pm as 24 C, 27 C, 31 C, 29 C, and 26 C respectively. What is…
- Parcels — total 120 kg, average 12 kg Some parcels have a total mass of 120 kg and an average mass of 12 kg. How many parcels are there?
- Parcels — total 150 kg, average 15 kg Some parcels have a total mass of 150 kg and an average mass of 15 kg. How many parcels are there?
- Savings — the mean of four pupils The mean amount of money saved by four pupils in a week is $18.50. Three of them saved $15, $20.50, and $22.50. How much did the f…
- Seashells — the average of five friends A bar graph shows the number of seashells collected by five friends at the beach. Ben collected 14, Zoe collected 9, Ravi collecte…
- Shop sales — a sixth day pulls the average down A shop recorded sales of $420, $380, $510, $490, and $450 over five days. What is the average daily sale? On the sixth day, the av…
- Test scores — a sixth student joins the group The average score of 5 students is 72. A sixth student joins and the new average becomes 74. What is the sixth student's score?
Challenging
- Ahmad's walk to school and back Ahmad walks from home to school at 5 km/h and returns at 4 km/h. If the school is 2 km away, what is his average speed for the who…
- Priya's ride to the library — average speed Priya cycles from her house to the library at 12 km/h and cycles back home at 8 km/h. The library is 24 km away. What is her avera…
- Rowing upstream and back — average speed A rowing boat travels 15 km upstream at 6 km/h, then rows the same 15 km back downstream at 10 km/h. What is the boat's average sp…
- Tammy — three boxes of apples Tammy has 3 boxes of apples. Box A is 550 g heavier than Box B and 770 g heavier than Box C. The average mass of the 3 boxes is 21…
- The delivery van — average speed there and back A delivery van drives from the depot to a warehouse at 60 km/h, then drives back to the depot at 40 km/h. The warehouse is 120 km …
Very challenging
All the problem patterns → · the revision list
The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.