The Hundredths Chart Jigsaw

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					                                The Hundredths Chart Jigsaw
                           A visual image of decimal place value
                                             Years 5 to 7
Goal
The goal is for students to develop a visual map of the patterns of two digit decimals that can assist
them in answering questions like:
  Which is larger: 0.37 or 0.4?
  Round off 0.37 to the nearest tenth.
  What is the difference between 0.48 and 0.6?
  What is 0.43 + 0.2?
The first step is to make the jigsaw by printing out a hundredths chart and cutting it up.


Step 1: Constructing the decimal jigsaw.


The students complete a jigsaw that has
been created out of a grid of the numbers
from 0.01 to 1.2 (template provided).


This is a partially completed jigsaw.




Explicit pedagogies:
  This is an introductory activity preliminary to explorations using two digit decimals.
  Do this by yourself.
For students experiencing difficulty:
    Have a sheet with the hundredths sheet on it so that the students can place the pieces onto the
     chart.
  Have a tenths chart jigsaw for them to complete
  Have a hundreds chart jigsaw for them to complete
  Write in some missing numbers on a partially complete grid.
For students who finish quickly:
      What would have made that jigsaw harder for you to do?

Collect the competed jigsaws. Note that this is important as we want the students to practice
visualising the relationship between the numbers on the hundredths chart.
Step 2: Open jigsaw pieces
Once they complete the hundredths chart jigsaw, give the students the worksheet. This is the first
problem.
      I had a jigsaw piece like this but the numbers have rubbed off. I know one of the numbers was 0.49. What might
      be the numbers on the jigsaw piece?




Explicit pedagogies:
  There is more than one possible response.
  Find as many possible answers as you can.
  Record your answers systematically. You can be creative.
For students experiencing difficulty:
  Use a completed hundredths chart and some blank pieces as prompts.
  Have a see-through piece
For students who finish quickly:
    Find all the possible responses.
    Can you show that you have all the possible answers?
    What if it was a different shaped grid in the first place?


Step 3: More open jigsaw pieces
Also on the worksheet:
      I had a jigsaw piece like this but the numbers have rubbed off. I know one of the numbers was 0.61. What might
      be the numbers on the jigsaw piece?




Explicit pedagogies:
  There is more than one possible response.
  Find as many possible answers as you can.
  Record your answers systematically. You can be creative.
For students experiencing difficulty:
  Use a completed hundredths chart grid and some blank pieces as prompts.
  Have a see through piece
For students who finish quickly:
    Find all the possible responses.
    Can you show that you have all the possible answers?


Step 4: Design a piece
Also on the worksheet:
       The numbers 0.37 and 0.59 are on the same jigsaw piece. What might the rest of the piece look like?
Explicit pedagogies:
  There is more than one possible response.
  Find as many possible answers as you can.
For students experiencing difficulty:
  Use a completed hundredths chart grid (supplied) and some blank pieces as prompts.
  Have a see through piece
For students who finish quickly:
    Would it be possible to design a grid like this but using fractions and not decimals?


Step 5: What calculations
Ask the students in groups, to discuss how they might use the decimal jigsaw to work out:
                Which is larger: 0.37 or 0.4?
                Round off 0.37 to the nearest tenth.
                What is the difference between 0.48 and 0.6?
                What is 0.43 + 0.2?
                What other questions could you use the decimal jigsaw to answer?
Explicit pedagogies:
  There is more than one ways of doing these.
  Make sure you can explain your method clearly.
For students experiencing difficulty:
  Use a completed hundredths chart grid for students who cannot imagine it.
  Provide a calculator to check answers.
For students who finish quickly:
    If it was a thousandths jigsaw what would it look like? What questions could you use it to
     answer?


Step 6: Conclusion and review
Once most students have finished step 2, review the answers of a few students. They can correct
their own work.
Do this at each of the other steps.
In particular, for step 5, give the students an opportunity to explain their methods.
                               Decimal Jigsaw Worksheet
1. I had a jigsaw piece like this but the numbers have rubbed off. I know one of the numbers was
   0.49. What might be the numbers on the jigsaw piece?




2. I had a jigsaw piece like this but the numbers have rubbed off. I know one of the numbers was
   0.61. What might be the numbers on the jigsaw piece?




3. The numbers 0.37 and 0.59 are on the same jigsaw piece. What might the rest of the piece
   look like?
4. Use this hundredths grid, to show how you might work out the answers to these questions:
          a)    Which is larger: 0.37 or 0.4?
          b)    Round off 0.37 to the nearest tenth.
          c)    What is the difference between 0.48 and 0.6?
          d)    What is 0.43 + 0.2?


          .01     .02    .03    .04    .05    .06    .07       .08    .09    .1
          .11     .12    .13    .14    .15    .16    .17       .18    .19    .2
          .21     .22    .23    .24    .25    .26    .27       .28    .29    .3
          .31     .32    .33    .34    .35    .36    .37       .38    .39    .4
          .41     .42    .43    .44    .45    .46    .47       .48    .49    .5
          .51     .52    .53    .54    .55    .56    .57       .58    .59    .6
          .61     .62    .63    .64    .65    .66    .67       .68    .69    .7
          .71     .72    .73    .74    .75    .76    .77       .78    .79    .8
          .81     .82    .83    .84    .85    .86    .87       .88    .89    .9
          .91     .92    .93    .94    .95    .96    .97       .98    .99    1
         1.01    1.02   1.03   1.04   1.05   1.06   1.07   1.08      1.09   1.1
         1.11    1.12   1.13   1.14   1.15   1.16   1.17   1.18      1.19   1.2




          What other questions could you use the hundredths chart to answer?

				
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