Levels 1–2: Place-value
Materials:
Instructions:
Bold type indicates what should be said.
Stretch out rope in front of the student ( anchor ends if necessary)and say, “Let’s imagine all of the numbers from 0 to 100 are on this rope.” As you say this, peg the ‘0’ card at the beginning of the rope and the ‘100’ card at the end of the rope.
Place the ‘48’ card in front of the student and say, “Can you peg this card on to the rope to show where you think that number would be? Can you tell me why you put it there?” Note where the card is placed and student’s response/strategies.
Repeat with the 67 and 26 card. Note responses and strategies.
If hesitant or unable to proceed at any point , remove the 100 card and replace it by the 20 card. Say, “Okay, now let’s imagine all of the numbers from 0 to 20 are on this rope.”
Place the ‘8’ card in front of the student and say, “Can you peg this card on to the rope to show where you think that number would be? Can you tell me why you put it there?” Note student’s response/strategies.
If done reasonably well, place the 16 card in front of student and ask them to peg that on the rope as well. Note student’s strategies.
Advice Rubric
This task involves partitioning and should only be used where students have demonstrated a good grasp of 2-digit place–value and have some appreciation of halving. Student responses to this task indicate the extent to which students can locate a 2-digit number in relation to a given range of numbers. This is an important aspect of number sense (proportion) and underpins later work with division and fractions.
Partitioning at this level is a form of visual division. In this case, it is evident if students use their knowledge of halves and halving to make an informed (usually reasonably accurate) judgement about where to locate 48 (“it’s about half”) and 26 (It’s just a bit more than a quarter”). For 67, students may know that this “is about 2 thirds”, but they are more likely to reason on the basis of what they know about halves and quarters in relation to 100, eg “it’s between a 50 and 75 but closer to 75”.
| Observed response |
Interpretation/Suggested teaching response |
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Some difficulty locating numbers larger than 20 but reasonable attempt for numbers less than 20 on the 0 to 20 rope, may attempt to locate or justify placements by counting intervals from 0 using card width as a measure |
Suggests numbers beyond 20 not well understood in terms of relative magnitude, possibly seen only as count of ones
- Consolidate 2-digit place-value by making, naming, recording, comparing etc (see above)
- Model and practice ordering and sequencing 2-digit numbers, eg, Place-Value Game (pdf - 16.36kb)
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Numbers larger than 20 placed more or less correctly, but actions and/or reasons given suggest counting rather than halving or partitioning strategies |
Suggests numbers understood additively, that is, as a count from left to right, may not see interval marked by 0 to 100 as something that can be partitioned to locate numbers
- Review and discuss every-day halving, eg, halving an orange, a length of paper tape, a piece of paper etc,
- Review doubling and halving, discuss numbers in terms of their relationship to other numbers, eg, 10 is half of 20, 30 is half of 60 and so on, demonstrate in class using a 3-4 metre length of rope, number cards and pegs
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Cards placed fairly accurately with relatively little hesitation, explanations based on partitioning, eg, halving and/or fraction fact knowledge |
Suggests sound knowledge of relative magnitude of 2-digit numbers in relation to 100 and basic fraction fact knowledge of halves and halving
- Make the halving strategy more explicit by using a range of materials such as coloured square paper, paper streamers, counters etc and discussing the implications of successive halving
- Consider introducing the thirding and fifthing partitioning strategies (see Partitioning Paper (pdf - 199.51kb))
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