Place Value Practice (Tenths and Hundredths)
Number Framework domain and stage:
Fractions, ratio and proportion, stages 6 - 7, advanced additive to advanced multiplicative
Number, level 3
Prior knowledge. Students should be able to:
- Work successfully with tenths (see the activity ‘place value activity with tenths’)
- Students should have knowledge of 1/100 = 0.01
During these activities, students will meet:
- Different notational forms for large numbers and decimals
- Writing a decimal involving hundredths in expanded form, and vice versa
- Shading decimal fractions
- Place value in decimals
- Convert improper fractions involving hundredths to both a mixed number and a decimal
- Adding and subtracting a hundredth from a number
- Reading a number line marked in tenths
- Simple multiplication of fractions
In these activities, where numbers greater than 1000 are used, different exercises use different notations to show this. For example, in exercise 5 the notation includes the comma, like 1,234, whereas in exercise 7 a space is used, for example 1 234. In other exercises, the number is written as 1234. These conventions may need to be introduced or explained to students.
Another notational difference worth noting is the use of zero before a decimal point. In exercise 8, when a hundredth is added, the notation involves .01, whereas in exercise 9 it involves 0.01.
This exercise taps into the measure construct of decimals, so may be harder for students to work with than the numbers alone. This is because number lines use a different set of conventions to those used in counting. For example, in this exercise it is important for students to start off by looking at the numbers at each end of the interval, then working out what each major mark, and each minor mark stands for. It is surprising how many students assume that each (major) mark stands for one, with each of the little marks being a tenth, and do not realise that they need to start out by identifying the scale on the interval.
This activity introduces students to multiplication of fractions, but uses the more familiar concepts of ‘lots of’. Introductory problems can be modelled using equipment like decipipes or place value blocks before the exercise is introduced. The final problems involve students writing and marking their own problems, including one word problem. This latter should be collected in for marking, to check that students have developed an understanding of the multiplications, and can recognise an instance in which using this process would be of value. Discussing the word problems may be an important follow-up, especially where some students have demonstrated lack of understanding. Modelling what they have created as a problem with materials would be a useful way of correcting misconceptions about which practical problems utilise this skill.
This exercise looks at multiplication of decimals. Note that the standard algorithm will cause some students grief (for example 0.06 x 5 = 0.3, which does not have two decimal places). Again, this topic should be introduced using equipment like decipipes or place value blocks to build an understanding of the process. Using language like 4 lots of three hundredths equals twelve hundredths (and how do we write this) is useful.