Week 21 · Comparing fractions and checking work · 3 lessons
2
Dot plot and expanded form checks
Discover Mathematics P3: Term 2, Lessons 81–90
GoalRead a dot plot of measurements, answer questions about it, and find mistakes in expanded form.
New words
dot plot · a graph where each dot stands for one piece of dataabove 34 · greater than 34, so 35, 36 and so on, but not 34expanded form · a number written as the sum of its place values
Explanation
A dot plot shows measurements on a number line. Each dot is one jump, so we count the dots, not the numbers under them. The words matter. Above 34 cm means 35 cm or more, so the dots on 34 are not counted. A number in expanded form is split by place value, and the parts must add back to the number. For 1,846 the parts are 1,000 + 800 + 40 + 6. If someone writes 1,000 + 80 + 40 + 6, the sum is 1,126, not 1,846, so there is a mistake. The 8 is in the hundreds place, so its value is 800, not 80. Always add the parts to check.
Worked examples
Children jumped, and the dot plot shows their jump heights. How many jumps were above 34 cm? Count the dots on 35 and 36: 3 + 1 = 4 jumps. The 2 dots on 34 are not above 34.
Digit
Place
Value
1
thousands
1,000
8
hundreds
800
4
tens
40
6
ones
6
Write 1,846 in expanded form. The 1 is in the thousands place, the 8 in the hundreds, the 4 in the tens and the 6 in the ones: 1,000 + 800 + 40 + 6.
Salma
Correct
Parts
1,000 + 80 + 40 + 6
1,000 + 800 + 40 + 6
Sum
1,126
1,846
Salma writes 1,846 = 1,000 + 80 + 40 + 6. Check by adding: 1,000 + 80 + 40 + 6 = 1,126. This is not 1,846, so her 80 should be 800.
Class activity
Jump contest. Ask 8 people to jump as far as they can from a standing start, and measure each jump in whole centimetres. Make a dot plot with a number line and a title. Write two questions about it, such as how many jumps were more than a certain length, and answer them.
Practice
1
The dot plot shows jumps by another group. How many jumps were 30 cm or more?
On 30, 31 and 32 there are 4 + 1 + 2 = 7 dots, so 7 jumps.
2
Write 3,275 in expanded form.
3,000 + 200 + 70 + 5.
3
Write 5,408 in expanded form.
5,000 + 400 + 8. There are no tens, so there is no part for tens.
4
Mostafa writes 2,517 = 2,000 + 50 + 10 + 7. Find his mistake and write it correctly.
The 5 is in the hundreds place, so it is 500, not 50. The correct form is 2,000 + 500 + 10 + 7.
