Published about 2 months ago by Ann Baker
So, do your kids trust the count? Do they have place value? Are they beginning to think multiplicatively? How will you find out?
Hopefully not from a boring, one-size-fits-all test delivered on a worksheet or through one-to-one time-consuming testing.
Back to school and we urgently need to find out what our students can do, know and are ready to take on next.
The following informal assessment springs from a NAPLAN question a few years ago where Year 3 students were asked to write the number one hundred and twenty three in numerals. Sadly, many children were unable to respond correctly. Common responses among those that couldn't included 10023, 1023 and 100203.
At the end of last year, I was working with a group of Year 4 and 5 teachers who were surprised when I suggested that they might have students in their classes who:
So off into the classroom we went with the following task:
The outcome was surprising (well, not really).
There were students at every level: from not able to write or show 123 or draw it confidently, to students who planned to use place value knowledge or multiplicative strategies to show 123.
To see the range of responses (see the Teacher Notes below) and to understand what each informs us about.
The beauty of this type of activity is that it has multiple entry and exit points, it is open-ended, and it works with just about any grade level - simply change the number.
Why not give it a go and get authentic data not from a test but from a purposeful activity and get whole class data in one hit.
Let us know how you go.
Natural Maths has two online courses that focus on the extremely important foundation skills of number sense and multiplicative thinking. Preventing the Numeracy Gap for Preschool & Foundation and Preventing the Numeracy Gap for Year 1 both show you how to create strategies for collecting informative data quickly and effectively and how to acton the data speedily.
Despite the recommended grade level, teachers of older students find them beneficial too, so why not
Do it now!
Sample 1, perhaps the lowest level entry point.
Note the 'count all' shown with dots, followed by a recount of them all to 28. I suggested that 28 be written as a reminder of where the count finished. The next row of marks was quickly drawn , not lined up in any way and then a recount from I was made, not a count on from 28. This is a clear example of not trusting the count.
Sample 2, getting organised for 10s but not using them.
I watched as this student drew and counted 10 in the first row, then counted as she drew 10 in the next row. Asked if she made another row lined up again how many would be in the row then, she paused , smiled and said 'Oh 10'. I waited for her to do the third row and then asked 'how many so far 3?' She touched and counted in 10s. Prompted counted, 10, 20, 30 and said, "I'll count in 10s next time".
She is moving toward trusting the count and beginning to skip count in 10s but is not applying place value . After completing 7 rows did not say 7×10, counted, 10,20, … 70.
Sample 3 - flexible multiplicative place value thinking.
The tallies were drawn downwards in columns, 20 in a column, skip counting kept the total and 123 was clearly shown.
Sample 4 - shows instant use of place value
A 10 × 10 grid was drawn but not filled in dot by dot. 23 then added as 2×10 and 3 more. Asked for a mathematical number sentence enabled this student to demonstrate 10 × 10 = 100 and 2×10 and 3 as matched number sentences.
Clearly this student trusts the count, understands the place value pattern for multiplying by 10 and looks for efficient ways to diagram.
Any one class will have such a range with students at different stages in the journey and with very different needs. If we pinpoint those needs early then we can plan with intent to scaffold learning that is needs based.
About the money
Only from such questions will we see what students know about money and how to make money amounts.
Students interact with 'real' money less and less. Since money is place-value based, we do need to connect money with other place value activities or we might see, as I often do, students drawing $1 coins and counting in 1s.
### Have a great informed year of maths in 2019!
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