Expanding with decimals
This is a level 4 number link activity from the Figure It Out series. It is focused on showing an understanding of decimal place value. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Show an understanding of decimal place value.
Expanding with decimals
Achievement objectives
NA4-2: Understand addition and subtraction of fractions, decimals, and integers.
Required materials
- Figure It Out, Link, Number, Book Two, "Expanding with decimals", page 17
- decimal compact numeral cards (see Expanding with decimals CM (.pdf))
- a calculator
See Materials that come with this resource to download:
- Expanding with decimals activity (.pdf)
- Expanding with decimals CM (.pdf)
Activity
This activity builds on the last activity by introducing decimals. Note that the arrows are now on the left side so that the digits can be aligned from the ones place. Note also that the card with the smallest number (which has the most digits) goes on the bottom when a compact numeral is made.
Question 1 challenges students’ perceptions of the relationship between the number of digits and the size of decimal numbers. Many students judge the size of numbers by the number of digits they contain. This will lead to misunderstandings because a one-digit decimal can be larger than a three-digit decimal. Ask the students “What do you look for to judge the size of a decimal number?” A good response would indicate that the first significant digit to the right of the decimal point is a useful place to start (for example, the 2 in 57.23).
Point out to your students that the job of the decimal point is to indicate the position of the ones place. They can then ascertain the value of all other digits. Make sure that the students do not use a column space for the decimal point. If they do, they often lose the relationship between the ones place and the tenths place.
In question 3, the students could approach the comparisons as difference questions initially to find the quantity involved. They could then look at the relationship suggested by the arrow to see if the quantity should be added or subtracted.
1.
Answers will vary. You should have five out of each of the following, in the order listed.
a. 0.5, 0.51, 0.512, 0.514, 0.517, 0.56, 0.562, 0.564, 0.567, 0.58, 0.582, 0.584, 0.587
b. 7.9, 7.91, 7.912, 7.914, 7.917, 7.96, 7.962, 7.964, 7.967, 7.98, 7.982, 7.984, 7.987, 8.01, 8.012, 8.014, 8.017, 8.06, 8.062, 8.064, 8.067, 8.08, 8.082, 8.084, 8.087
c. 3, 3.002, 3.004, 3.007, 3.01, 3.012, 3.014, 3.017, 3.06, 3.062, 3.064, 3.067, 3.08, 3.082, 3.084, 3.087, 3.3, 3.302, 3.304, 3.307, 3.502, 3.504, 3.507, 3.31, 3.312, 3.314, 3.317, 3.36, 3.362, 3.364, 3.367, 3.38, 3.382, 3.384, 3.387, 3.5, 3.51, 3.512, 3.514, 3.517, 3.56, 3.562, 3.564, 3.567, 3.58, 3.582, 3.584, 3.587
2.
a. 7.5 + 3.3 or 7.3 + 3.5
b. 0.567 + 0.312, 0.562 + 0.317, 0.517 + 0.362, or 0.512 + 0.367
c. 8.56 + 7.31, 8.51 + 7.36, 8.36 + 7.51, or 8.31 + 7.56
d. 3.56 + 8.98, 3.58 + 8.96, 3.96 + 8.58, or 3.98 + 8.56
3.
a. + 4.8
b. - 5.45
c. + 0.17
d. - 0.623
e. + 0.62
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