Mathematics K–6 · Years 3–4
Renaming with base-10 materials: numbers to tens of thousands
Number and algebra
This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.
The idea
Each place is ten times the place to its right, so a number can be traded into different combinations of thousands, hundreds, tens and ones without changing its value.
What you need
- base-10 materials: 30 unit cubes, 30 ten-rods, 30 hundred-flats and 3 thousand-cubes
- a place-value mat with columns ten thousands, thousands, hundreds, tens, ones
- a set of digit cards 0 to 9
- a recording sheet
How to do it
- Build 2347 on the mat with 2 thousand-cubes, 3 flats, 4 rods and 7 units. Read it aloud and write it.
- Trade one thousand-cube for 10 flats. Read the mat as 1 thousand, 13 hundreds, 4 tens and 7 ones. Check by counting that the total is unchanged.
- Trade one flat for 10 rods and one rod for 10 units. Record every renaming in the sheet.
- Build 2047 and 2407 and say what the zero does in each. Then show what 10 flats become when placed together.
- Use the digit cards to make the largest and smallest four-digit numbers from 3, 0, 8 and 5, write both, and build the smaller one on the mat.
What you should see
2347 can be shown as 2 thousands, 3 hundreds, 4 tens, 7 ones; as 1 thousand, 13 hundreds, 4 tens, 7 ones; or as 23 hundreds, 4 tens, 7 ones, and the material count is 2347 units in every case. Ten flats stack into the shape of a thousand-cube. In 2047 the zero holds the hundreds place so that the 2 stays in the thousands; without it the number reads 247. The largest number from 3, 0, 8, 5 is 8530 and the smallest four-digit number is 3058.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- A zero in the middle of a number can be left out without changing the number.
- Each place is one more than the place beside it, not ten times as much.
Safety card
Hazards
- unit cubes are small
Controls
- count cubes back into the tub at the end
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
Sources
The pages the author read to write this activity.