Exploring Decimals on Measuring Scales
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1 Exploring Decimals on Measuring Scales Overview Skills and Knowledge Being able to read mixed numbers with decimals on a measuring scale is an important numeracy skill. In fact it is one of the most important reasons that many students need to understand decimals. This activity presents an opportunity to explore decimal representations in relation to measuring scales. The activity is a valuable follow up to Exploring Decimals as Tenths Parts 1 and 2. It s progressive stages may need to spread over several sessions. Meaning of decimal place value Representing decimals as tenths on measuring scales Reading decimal measuring scales Preparation and Materials For simple scales in tenths Tape measures with tenths markings (1 per pair or small group of students) (optional) Make several copies of Activity Sheets 1, 2 (1 per pair or small group of students). Or create images that can be projected using an OHT or PPT slide Make another copy of Activity Sheet 1, 2 and on them mark arrows to indicate a series of measurements. For example: On Activity Sheet 1 mark numbers such as 0.2, 0.5, 0.7. On Activity Sheet 2 mark numbers such as, 1.3, 1.5 on the first diagram, 2.7, 2.1 on the second, etc. Then photocopy each prepared sheet (1 per pair or small group of students.) Activity Sheet 3 is a template for creating further Practice Sheets by adding appropriate scale markings and arrows as needed. Photocopy Practice Sheets 1, 2 & 3 (1 per student) For extending to other tenth scales Make copies of Activity Sheets 4 as above, and one copy with arrows marking a series of measurements on the diagrams. For extending to scales in hundredths Make copies of Activity Sheets 5 as above, and one copy with arrows marking a series of measurements on the diagrams. DECIMALS EXPLORING DECIMALS ON MEASURING SCALES Page 1 of 13
2 Suggested Procedure Explain to students that you are now going to explore another way of representing decimals. A way that is important for reading measurements on thermometers and temperature gauges, tape measures, dials on car dash boards and many other measuring instruments. Introducing a decimal scale or number line Distribute tape measures and copies of Activity Sheet 1 (1 between pairs or small groups of students). Ask: How many small divisions are there between numbers on this tape or line? [10 small divisions] So what do you think each space represents? Show me where you think.3 would be on the line. [! =.1 = 0.1]!" Ask students to make a mark or arrow to show 0.3 then repeat for a few more examples, including.1 and.5 Emphasise that.5 = ½ is halfway between the two end markers and is shown by a slightly longer line marking. Reading the scales: 0-1 Distribute the copies of Activity Sheet 1 that you have marked with arrows (1 to each pair or small group of students). Ask students to work together to decide what decimal anfd fraction each mark represents. For example 2 10 =.2 or 0.2 Mixed numbers on the scale Next distribute copies of Activity Sheet 2. DECIMALS EXPLORING DECIMALS ON MEASURING SCALES Page 2 of 13
3 Ensure students realise that this time there are different numbers on the scales and so each diagram represents a different part of the measuring scale. Now put some numbers on the board and ask the pairs of students to decide where each of the numbers would go on the diagrams. For example: If you are also using tape measures, ask the students to find these numbers on the tapes. Reading the scales: numbers greater than 1 Now distribute the copies of Activity Sheet 2 that you have marked with the arrows. Ask the students to write the measurements as mixed numbers in fraction and decimal form. 3.4 = 3!!" 3 4 Practice Sheet 1 is appropriate at this stage. Activity Sheet 3 can be used as a template to create more exercises for students needing further practice, now or as revision activities later on. For more authentic practice, students should also be asked to take measurements using actual tape measures. See Measurement section for ideas. Note: Some learners may need help to start at the zero mark on the tape measure, rather than the actual end of the tape. DECIMALS EXPLORING DECIMALS ON MEASURING SCALES Page 3 of 13
4 Extension - Introducing other scale markings for tenths Activity Sheet 4 is designed to ensure students are also exposed to scales that do not have markings for each 0.1. Instead each of the markings in these scales represents 0.2. Learners need practice to get used to these. As before, use unmarked copies of Activity Sheet 4 and ask students to mark a series of measurements on the appropriate diagrams. Ensure there is a mixture of even and odd decimal parts in the numbers chosen. For example: etc Then distribute the copies you have prepared with the arrow markings, as above. Practice Sheet 2 is an appropriate follow up to this stage in the teaching sequence. As above, the template on Activity Sheet 3 can be used for further practice exercises as needed by your students. Extension - Introducing scale markings for hundredths Distribute copies of Activity Sheet 5. Ask students to look carefully at the scale markings on the first diagram and try to decide what each of the marks represents. The degree of detail needed at this point will depend on students prior experience with hundredths. It may be easier it they have previously looked at the activity Exploring Decimals The students should notice that: as Hundredths. The space between 1.2 and 1.3 represents.1 or!!" That space has been cut into 10 smaller sections When you cut tenths into ten again you get hundredths [Refer to the tenths and hundredths grids form the previous activities as reminders] When thinking in hundredths, 1.2 and 1.3 can be re-written as 1.20 and This makes it easier to see the markings in between as 1.21, 1.22 etc. When the zeros are not written like this on the scale we just have to imagine them. DECIMALS EXPLORING DECIMALS ON MEASURING SCALES Page 4 of 13
5 Using similar procedures as in the sections above, ask students to mark on the diagrams a range of numbers which have two decimal places. Then use a version with arrows marked on it for students to read the measurements. Further practice If your learners are likely to be using measuring tools with this type of calibration for future training, then bringing the real instruments to class for further practice would be very helpful to them. The matching activity Matching Decimal Scales and Pictures will be useful to revise this material and assess students understanding. DECIMALS EXPLORING DECIMALS ON MEASURING SCALES Page 5 of 13
6 Exploring decimals on measuring scales Activity Sheet DECIMALS EXPLORING DECIMALS ON MEASURING SCALES Page 6 of 13
7 Exploring decimals on measuring scales Activity Sheet DECIMALS EXPLORING DECIMALS ON MEASURING SCALES Page 7 of 13
8 Exploring decimals on measuring scales Activity Sheet 3 DECIMALS EXPLORING DECIMALS ON MEASURING SCALES Page 8 of 13
9 Exploring decimals on measuring scales Activity Sheet DECIMALS EXPLORING DECIMALS ON MEASURING SCALES Page 9 of 13
10 Exploring decimals on measuring scales Activity Sheet DECIMALS EXPLORING DECIMALS ON MEASURING SCALES Page 10 of 13
11 Exploring decimals on measuring scales Practice Sheet 1 1. What measurement is marked with the arrows? =!" 0. =!" =!" 0. =!" 2. Mark these numbers on the measuring scale = = =!" 0. =!!" DECIMALS EXPLORING DECIMALS ON MEASURING SCALES Page 11 of 13
12 Exploring decimals on measuring scales Practice Sheet 1 (cont.) 3. What are the measurements marked with arrows on this picture? 4. Mark these numbers on the scales. 3.9 is done as an example DECIMALS EXPLORING DECIMALS ON MEASURING SCALES Page 12 of 13
13 Exploring decimals on measuring scales Practice Sheet 2 1. Patricia had her temperature taken. The thermometer looked like this: What was her temperature? 2. For what temperature is this thermostat set? 3. A comfortable room temperature is 20.8 o C. Show this on the thermometer. 4. A summer temperature was 32.7 o C. Show this on the thermometer. 5. Mark these numbers on this scale: DECIMALS EXPLORING DECIMALS ON MEASURING SCALES Page 13 of 13
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