Place Value Disks: Free Virtual Disks and Place Value Chart
Updated · By Edulist · 4 sources
Keyboard and touch help
- Drag a piece from the tray onto the board, or press a tray button (Enter) to add it in the next spot.
- Tab to a piece. Arrow keys move it (Shift for bigger steps). Space adds it to the selection.
- D duplicates, R rotates, G trades up a group, B breaks a piece apart, Delete removes it.
- Ctrl+Z undoes and Ctrl+Shift+Z redoes (Cmd on a Mac).
- Drag across empty space to select several pieces. Drop pieces on the trash or back on the tray to delete them.
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How to use it
- Choose a disk set
Whole numbers use 1, 10, 100 and 1,000 disks. Decimal disks use 0.01, 0.1, 1 and 10. Switch with the buttons above the board.
- Build a number on the chart
Drag disks into their columns, tap a tray disk (or press Enter) to add it in the next spot, or type a number into Build a number.
- Regroup and break apart
When a column has 10 or more disks, press the trade button under the value, or select 10 disks and press Trade up. Select one disk and press Break to get 10 of the next smaller place.
- Work the task cards
Fourteen cards across the two sets cover building numbers, adding with regrouping, subtracting across zeros, multiplying and decimals. Each checks itself as you go.
Printables to go with it
What place value disks teach
Place value disks are the step after base ten blocks. Every disk is the same size, and its value is printed on it: 1, 10, 100, 1,000, or 0.1 and 0.01 for decimals. Because the size no longer shows the value, children have to think about the label and the column, which is exactly what reading a written number asks them to do.
The rule never changes: ten of one disk make one of the next disk to the left. That single idea covers regrouping in addition, decomposing in subtraction, the "times 10" pattern in multiplication, and decimals. The board on this page applies the rule exactly. Trading never changes the value, and the readout shows the number and its expanded form as you work.
How to use place value disks
- Build a number. Put disks in their columns. For 1,352 that's 1 thousand, 3 hundreds, 5 tens and 2 ones. Say it out loud and check the value.
- Regroup. If a column reaches 10 or more, trade 10 disks for 1 disk in the next column. The counts at the bottom of the chart turn red when a column needs a trade.
- Decompose. To subtract, break one disk into 10 of the next smaller value. A disk dropped one column to the right breaks apart on its own, because a hundreds disk can't sit in the tens column.
- Record. Write each step: the little numbers in the standard algorithm are the disks you traded.
Place value disks by grade
| Grade | What children do |
|---|---|
| 2nd | Build numbers to 1,000; add and subtract within 1,000 by composing and decomposing tens and hundreds (2.NBT.B.7). |
| 3rd | Round to the nearest 10 or 100; add and subtract within 1,000 fluently; multiply one-digit numbers by multiples of 10 (3.NBT.A.3). |
| 4th | Read and compare multi-digit numbers; see that a digit is ten times the value of the same digit one place to its right (4.NBT.A.1); multiply up to four digits by one digit; divide with remainders. |
| 5th | Extend the pattern to decimals: a digit is 1/10 of the digit to its left (5.NBT.A.1); read, write and compare decimals to thousandths; add and subtract decimals to hundredths. |
Eureka Math, one of the most common programs to use them, starts with real disks in 2nd grade, moves to drawn disks with values written inside, then to the "chip model": dots on a labeled chart. This board sits between those steps: the disks are real objects to drag, and the chart labels the columns.
Activities to try
- Fewest disks. Build 2,040 with any disks, then trade until you have the fewest. That version matches the written number, zero and all.
- Subtract across zeros. Build 503 and take away 128. With no tens to break, start with a hundred. This is the step many children find hardest on paper.
- Multiply by repeated groups. Make 4 groups of 23, push them together, and regroup. The result is 4 × 23 = 92, and the regrouping is the carried 1 in the algorithm.
- Times ten. Build 34, then replace every disk with the disk one column to its left. 34 becomes 340. Multiplying by 10 moves every digit one place, which is why we "add a zero."
- Share and divide. Build 72 and share it equally among 3 groups. Each group gets 2 tens with 1 ten left over; break it into 10 ones, and now 12 ones share as 4 each. 72 ÷ 3 = 24.
- Decimals. Switch to Decimal disks and show 2.46. Then add 0.6 + 0.7 and trade 10 tenths for 1 one.
Tips for teachers and parents
- Say the value, not just the digit. "5 tens" or "fifty", not "5". The habit carries over to paper.
- Keep the chart columns in order. Highest place on the left, ones on the right, decimals after the ones. The chart is the written number laid out flat.
- Use the trade suggestion sparingly. The button under the value does the trade for you. For practice, select the 10 disks yourself so the counting stays with the child.
- Connect to drawings. After a few problems on the board, have the child draw disks as circles with values, then as dots on a chart. That's the path to the written algorithm.
- Mix it with blocks. Children who are still shaky about why ten ones make a ten benefit from going back to base ten blocks, where the size shows it.
Common mistakes disks reveal
| What you see | What it means | Try |
|---|---|---|
| Puts 12 ones in the ones column and writes 12 in the ones place | Doesn't trade yet | Ask, "Can a column hold 10?" and press Trade up together. |
| Breaks a disk and loses value (one hundred becomes one ten) | Thinks "break" means "make smaller" | Count the 10 tens that come out of a hundred, then compare values in the readout. |
| Reads 1,050 as "one hundred fifty" | Ignores an empty column | Build it and point to the empty hundreds column: that's the zero. |
| Lines up decimals by the last digit | Treats decimals like whole numbers | Build both numbers on the decimal chart, where tenths only go in the tenths column. |
Using disks for multiplication and division
Disks are especially good for the 4th grade standards on multiplying and dividing, because the groups stay visible. To multiply 3 × 142, build 142 three times and push the groups together: 3 hundreds, 12 tens and 6 ones. Trade 10 tens for a hundred and the product, 426, appears. Each partial product (300, 120 and 6) is sitting right there on the chart, which is the same idea as the area model and the partial products method.
Division runs the other way. To divide 426 by 3, share the hundreds first, then break any leftover hundred into tens and share those, then the ones. Every "bring down" step in long division is a disk being broken and shared. Children who have done this a few times can explain what the steps of long division mean, not only how to do them.
For paper practice, print a place value chart or a decimal place value chart and draw disks as circles in the columns. The Montessori stamp game is a close cousin of place value disks, with color-coded tiles instead of labels.
Choosing an activity
Grade bands describe possible curriculum connections, not an assessment of an individual learner. Start with an example the learner can explain, then change one feature at a time. The activity suggestions here are editorial teaching ideas, not results from a classroom trial of this software. Use the model alongside written work and physical materials when useful. The linked standards describe learning objectives; they do not endorse Edulist or require this particular tool.
Sources
Questions
What is the difference between place value disks and base ten blocks?
Base ten blocks are proportional: a ten is ten times as big as a one. Disks are all the same size and carry their value as a label, so they work for big numbers and decimals where blocks get unwieldy. Children usually start with blocks and move to disks around 2nd or 3rd grade.
Are place value disks the same as place value chips?
Yes. Disks, discs, chips and number disks are names for the same idea. Some programs draw them as dots in columns, which Eureka Math calls the chip model.
How do you subtract across zeros with place value disks?
Break a disk from the first place that has one. For 503 − 128, break a hundred into 10 tens, then a ten into 10 ones. Now there are enough ones and tens to take away. Task card 4 walks through exactly this.
Can place value disks show decimals?
Yes. Switch to Decimal disks for tenths and hundredths. Ten hundredths trade for one tenth, and ten tenths trade for one, the same rule as whole numbers.
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