Spatial Reasoners?

response to build a number (1)IMG_0369When students use the materials at hand as thinking tools they demonstrate how they are making sense and constructing meaning. Both these students were quite clear how to explain the number they were dealing with and both had no trouble explaining overall how many tens are in their number. 551 has 55 tens, but 50 of them are packed into hundreds. So you can also say 5 hundreds.


This student drew it first, then separated out the pieces in the second part of the drawing to be sure I understood 294 is composed of 2 hundreds, 9 tens ten less than a hundred, so easy to draw) and 4 ones. Again this student had no trouble explaining there are 29 tens in this 3 digit number. 



The struggles I see for students when it comes to place value are all built around a lack of imagery due to lack of experience with the BUILD. We must take time to allow students to build the units, right from the 10 to the 10 000, then backwards to the thousandth.  When we do, the pay-offs are immense. Students understand the positions are based on a proportional growth change. They learn to think before they calculate. They make sense of the “zeroes” and are not forced to “line up” the digits, when they add.

You cannot learn this BUILD on a computer. You have to experience first hand with concrete materials. Every classroom Grade 1, 2 and 3 needs to be equipped with snap cubes ( I like “unifix”). Enough for every student to build to the thousand. Not “base ten” blocks. Snap cubes… Base ten blocks should only come out once students have demonstrated they can be flexible with the units…

When students are challenged to visualize, imagine and then build with snap cubes and paper models they experience how numbers are related and the power of trusting units. The experiences support their understandings of magnitude, density, direction, proportional growth.  Linear, vs area, vs volume. Making one thousand with strips of ten is incredibly different than making the thousand with squares of one hundred. And the thousand cube is impossible with a flat model.

Thousand on wall area

This picture shows the thousand being constructed 3 different ways. Most adults are astounded to see the difference with the linear thousand. The picture only captured to the first 300.





Mystery Bag numbersThis is only one hundred in blocks, can you imagine the length for 1000?

Spatial skills and spatial reasoning engage students in the learning. Flexible thinking, mental fluency, confidence, risk taking, these are the skills that student’s develop. If you want students to build and apply common sense, to develop a foundation of practical math skills engage them spatially.