Base-Ten Blocks Widget

Base-ten blocks put ones, tens, hundreds and thousands on a mat. Students read a number someone built, build one themselves, group a pile of loose ones into tens, break a piece apart or make a new one, add to or take away from a number, and say which of two numbers is greater. With tens as the largest piece, everything works up to 120; with hundreds, up to 1,200; with thousands, up to 20,000.

A ten is one piece, so building 47 is 4 taps on the tens tray and 7 on the ones tray, not 47 single cubes. A hundred is one piece too, so 355 is 13 taps. For free building with snap-together cubes in Kindergarten, use connecting cubes instead.

Select the widget on the canvas and click the floating ⚙ Configure button to set it up. The dialog asks things in order:

1. What students do: pick one of the seven modes below.
2. How the pieces look: cubes, blocks or a drawing, the largest piece (tens, hundreds or thousands), and what a small cube is worth.
3. The mode's own setup: The model, The start, The pile, The two models, or Number A and Number B.
4. How it's checked: the answer row, the target, or the pieces to trade to.
5. What students build with: the trays, and whether students can break and make tens.
6. How the mat is laid out: tens first or ones first, and how the ones are arranged.

Settings most lessons never change are under More options at the bottom.

Three looks

Under How the pieces look, Look decides how a ten and a one are drawn. The math, grading and attempt page are the same in every look. Use one look for the whole lesson, so a child never sees towers turn into rods partway through.

The piece colors are fixed for each look and a lesson's theme never changes them, so a ten looks the same in every lesson. The Style & Layout section in the sidebar still colors the background, the mat, the trays and the text.

Hundreds, thousands and what a small cube is worth

Under How the pieces look:

• Largest piece: Tens (Grade 1 and Grade 2's tens units: 100 is 10 tens), Hundreds (adds a hundred, up to 1,200) or Thousands (adds a thousand, up to 20,000). Each look draws them its own way: a flat (a 10 × 10 square) and a big cube in blocks, a hundred square and a thousand cube of connecting cubes, and in the quick drawing a square for a hundred and a cube outline for a thousand. In Lines and dots, a hundred is still a square, a ten a line and a one a dot, as students draw them on paper.
• A small cube is worth: 1 (the default), 10, 100 or 1,000. It changes only the numbers students see, type and hear, never the pieces: with a small cube worth 10, 1 big cube, 3 flats, 2 rods and 5 small cubes read 13,250. Use it for Grade 4's "the same blocks can show 1,325 or 13,250", and to build numbers like 120,450 (12 big cubes, 4 rods and 5 small cubes, with a small cube worth 10). Targets are typed as students will read them (13,250), in steps of the small cube's worth.
• Piece labels: a key above the mat that says what each piece is worth ("small cube = 10, rod = 100, flat = 1,000"). Turn it on whenever a small cube is worth more than 1. Screen readers always hear what a small cube is worth ("Each small cube is worth 10."), with or without the key.

Breaking and making work at every size: a hundred breaks into 10 tens, 10 tens make a hundred, and a thousand breaks into 10 hundreds. Group and count is always a tens task, so it doesn't show these settings.

Classroom examples:

• Grade 3, "355 is 3 hundreds 4 tens 15 ones": Show a model of 3 flats, 4 rods and 15 small cubes with □ hundreds □ tens □ ones, and how many in all. Students answer 3, 4 and 15, and 355.
• "Build 355 two ways": Build with target 355 and Any form. 3 hundreds 5 tens 5 ones and 3 hundreds 4 tens 15 ones are both right.
• Trading for the standard algorithm: Trade from 3 hundreds 5 tens 5 ones to 2 hundreds 15 tens 5 ones. Students break a hundred into 10 tens.
• For thousands, make the widget full width, so the pieces stay big enough to tap. The dialog warns you when they aren't.

Seven modes

Each mode in What students do is tagged Graded or Not graded.

Explore, and a Show with no answer row, never count toward a score. Scoring stays on and is marked Not graded, because that's what sends the child's mat to their attempt page.

Explore

The trays are open and nothing is checked. Use it to get students comfortable with the pieces: "Build your age. Now build a number bigger than 20."

Show

You build the model on the dialog's mat, and students read it.

• The model: use the + and − buttons (like + Tower of ten and − Single cube) to set the pieces, and Break apart a ten or Make a ten to change their form. Same number, standard form tidies the model into at most 9 ones. Any form works, so you can show 65 as 6 tens 5 ones or as 5 tens 15 ones.
• Marks: choose Ring, tap pieces, give the ring a label like "10" or "new ten", and press Add ring. Ring 10 ones to show where a new ten comes from, or ring 10 towers and label it "100". Choose Cross out to cross pieces out for a take-away picture. Students are asked about the pieces left: 82 with 9 ones crossed out is 73.
• Answer: No answer (just look), How many?, □ tens □ ones, or □ tens □ ones, and how many in all. Tens and ones are checked as the pieces show them, so 5 tens 15 ones is answered 5 and 15, not 6 and 5.
• Flash the model: the model shows for 0.5 to 3 seconds (Seconds), then a cover slides down and students say how many they saw, like a quick look with tens and ones. Offer Look again lets them peek once more; looking again never counts as an attempt.

Classroom example: show 3 tens and 4 ones with Order set to Ones first, and ask How many?. A child who reads the ones first and answers 43 shows you they're reading digits in the order they see them, not by place.

Build

Students build Target, a number from 0 to 120, then tap Done. In this form decides what counts:

• Any form: any pieces worth the target. 47 can be 4 tens 7 ones or 47 ones.
• Standard: at most 9 ones, so 47 must be 4 tens 7 ones.
• Exactly: the exact pieces you set on the little mat below it.

Classroom example: "Build 65" with the tens tray limited to 5 (see What students build with). Students who can't get a sixth ten have to use 15 ones, which is exactly the thinking Grade 1 is after.

Step-by-step: Build a three-digit number with base-ten blocks builds 243 from flats, rods and small cubes in Standard form, with a hint on a wrong Done.

Group and count

The mat starts with a pile of Loose ones (1 to 120), laid out the way Ones under How the mat is laid out says. Students tap Make a ten to gather 10 loose ones into a ten, as many times as they like, then answer how many there are.

• Answer is How many?, □ tens □ ones, or both. There's no "just look" here: the point is the count.
• Must group is off by default, so only the answer is graded, and you still see on the attempt page whether the child made tens. Turn it on when making every full ten is the lesson: students then tap Done, and the answer only counts once all the tens are made.

Classroom example: a pile of 52 ones. A child who makes 5 tens and answers 52 shows you they used the tens to count. A child who answers 51 without making any tens probably counted one by one and lost track, and the attempt page says so.

Trade

The mat starts with The start, and students break or make tens until the mat shows Trade to, then tap Done. The number never changes, only its form: 3 tens 7 ones can become 2 tens 17 ones. Trade needs Can break and make tens on.

Classroom example: "Show 37 another way." Start at 3 tens 7 ones and trade to 2 tens 17 ones.

Add or take away

Under The change, Students can Add, Take away, or Either. Start with is One model or Two numbers.

• One model: the mat starts with The start, and students change it until it shows Target. Take-away students break a ten themselves when there aren't enough ones.
• Two numbers: Number A and Number B sit side by side. Students tap Put together to join them, make a new ten if they can, and tap Done.

Classroom examples:

• 82 − 9: start with 8 tens 2 ones, Take away, target 73. Students must break a ten to take 9 ones away.
• 47 + 8: Two numbers, A is 4 tens 7 ones, B is 8 ones, target 55. After Put together, a child who makes a new ten ends with 5 tens 5 ones; one who doesn't ends with 4 tens 15 ones. Both are right with Any form, and the attempt page tells you which one happened. Choose Standard if making the ten is required.

Step-by-step: Add two-digit numbers by making a new ten builds 38 + 25 with Two numbers and Standard form, with a cheer on On Ten Made and a hint on a wrong Done.

• 17 + ? = 48: start with 17, Add, target 48. The attempt page shows what the child added (31).

Compare

Set Model A and Model B on two little mats, and pick a Question: Which is greater?, Which is less? (both also offer Same), or Same or not? (Same and Different). Students tap their answer.

Classroom example: A is 5 tens 32 ones and B is 7 tens 2 ones. A has fewer tens, but it's 82, which is greater than 72. Students who pick B are comparing the tens alone.

Under More options, Name the models shows them as A and B, or By their numbers (the buttons then read "82" and "72").

What students build with

These show in every mode where students change the mat (all but Show and Compare).

How the mat is laid out

• Order: Tens first (left) or Ones first. Ones first is a good check that students read by place, not left to right.
• Ones: Rows of 5, In a column, or Scattered, a loose pile for counting or estimating.

More options

If you turn on Count aloud on a scene whose narration also asks "how many?", the dialog warns you. If the pieces come out too small for young fingers, it warns you too: make the widget bigger, or use a smaller number.

How students use it

• Add a piece: tap a tray, or drag from a tray onto the mat. A tray that's run out is greyed, and says why. With hundreds or thousands, the trays sit on their own row above the buttons.
• Select a piece: tap it. Then tap Take away, or Break apart (cubes) or Trade for 10 … (blocks and drawing): Trade for 10 ones for a ten, Trade for 10 tens for a hundred.
• Make a ten: tap Make a ten when there are at least 10 loose ones. With Speak on, it counts 1 to 10 as it gathers them. Make a hundred and Make a thousand gather 10 tens or 10 hundreds the same way.
• Take away and put back: taken pieces go into Put back, which shows what was taken (crossed out in the drawing look). Tap it to put the pieces back on the mat. Dragging a piece onto it takes it away too.
• Put together: joins Number A and Number B into one mat.
• Clear empties the mat (Explore and Build).
• Answer: tap a box under the mat, type on the number pad, then tap Check (or Done with Must group). With hundreds, the boxes read □ hundreds □ tens □ ones.
• Keyboard: Tab moves through the trays, the mat, the buttons and the answer row. Arrow keys move between pieces, and Enter or Space selects one. Dragging is never required.

Screen readers hear the mat as pieces, like "4 towers of ten and 7 single cubes", and each piece by its place ("tower of ten, 3 of 4"). They never hear the total while the widget asks how many. Tens and ones differ in shape and size, never only in color.

Grading, attempts and the attempt page

• Build, Trade, Add or take away, and Group and count with Must group record an answer each time a student taps Done. Every piece added, taken away, broken or made goes into the record of how they did it instead of counting as a try, so building 47 is 1 attempt, not 11.
• Show and Group and count record an answer each time a student taps Check, never while they type.
• Compare records each answer tap, like a multiple choice question.
• Grading is recomputed on the server from the pieces and your lesson's settings. A mat the child couldn't have built with your trays (6 tens when the tray only had 5) is marked wrong, so it can't be faked from the browser.
• The attempt page draws the mat and sums up how the child got there in plain words, like "Made 5 tens · 2 left over · answered 52 ✓", "Started 82 · broke 1 ten · took away 9 ones · 73 ✓", or "47 + 8: 4 tens 15 ones = 55 ✓ · no new ten made".

A widget whose setup can't work, like a target the trays can't reach or a Trade to a different number, can't be published. The dialog lists each problem and the setting that fixes it.

Logic

Use the mat in behaviors and conditions:

• Triggers: On Blocks Change (a student adds, takes away, breaks or makes a ten, or puts the numbers together), On Done (a student taps Done or Check, or answers a Compare question), and On Ten Made (a student makes a new ten, great for a "That's a new ten!" cheer).
• Properties: Total (as students read it, so 13,250 when a small cube is worth 10), the pieces of each kind on the mat (named for the look, like Towers of ten or Flats), Zone A total, Zone B total, New tens made, Tens broken, New hundreds made, Hundreds broken, New thousands made, Thousands broken, Value added, Value taken away, Is in standard form, Answer, Done taps, Is correct and Is answered. Use them in {{variables}} too.
• Methods: Reset, Clear, Show the target, Break a ten and Make a ten (demonstrations for a "Watch me" button, which never count as the child's work), Count aloud, and Flash the model.

See widget properties and methods for more.