Bigger numbers.
Same playful support.

Count 10 ones, make one complete group and compare it with one ten piece.

If I call this one ten, are the ten ones still inside that idea? How could you prove it?

Rebuild one object at a time, then name the whole group together: “ten ones — one ten.”

Treating the ten piece as a new amount unrelated to ten ones.

Make two tens and explain how many ones that represents.

Explains that one ten is ten ones.

Build 10 ones, trade them for one ten, then reverse the trade.

What changed? What stayed the same? How do you know the amount is still equal?

Put ten ones beside the ten piece and match the quantities before trading.

Believing an exchange changes the quantity.

Make repeated trades with 20 or 30 ones.

Exchanges both ways and explains that quantity is unchanged.

Build several quantities from 13–29, grouping every complete ten and leaving remaining ones visible.

How many tens? How many ones left over? Can you tell me the number without counting everything from one?

Complete one group of ten first, then separate the leftovers.

Recounting every object from one after tens are formed.

Predict the tens and leftovers before building.

Reliably describes quantities as tens and ones.

Show a quantity as ones, then trade complete tens and compare both representations.

Which looks bigger? Is it actually bigger? What evidence could convince someone?

Count once, then exchange 10-for-1 without adding or removing anything.

Assuming a more spread-out arrangement means more.

Create a third representation of the same amount.

Recognises equivalence across grouped and ungrouped forms.

Choose numbers to 30, build each, trade where possible and explain the final structure.

Could you unbundle that ten? Could you bundle these ones? Would the number change?

Return to one complete group of ten and rebuild the equivalence.

Treating bundling or unbundling as changing the amount.

Show two different representations of the same number.

Unitises ten reliably and can unbundle when needed.

Choose numbers from 20–50, read each numeral, build it and describe its structure.

What does this digit tell us? How many tens? How many ones?

Cover one digit at a time and connect it to the matching physical units.

Reversing digits or building digit counts rather than digit values.

Include larger numbers approaching 100.

Converts a numeral into a structured quantity accurately.

Build numbers from 20–60 with full tens and extra ones.

What number did we build? How could you tell without counting every one?

Touch each ten and count by tens, then count only the extra ones.

Ignoring the ten structure and reverting to one-by-one counting.

Predict the train before placing any pieces.

Interprets the structured representation without recounting from one.

Match a numeral with a tens/ones representation and a spoken description.

What makes this a match? What would have to change to make it a different number?

Build the numeral physically, then compare it with the representation.

Matching by surface appearance rather than place-value structure.

Add a near-match as a deliberate distractor.

Justifies matches using tens and ones.

Build 32 as 3 tens 2 ones, then unbundle one ten to show 2 tens 12 ones.

Did we add anything? Did we take anything away? So why is it still the same number?

Make the 10-for-1 equivalence visible before changing the representation.

Thinking only the standard tens/ones form is valid.

Find a third representation where practical.

Understands non-standard partitioning with materials.

Build a spread including the 20s, 50s, 80s, 100 and 101–120.

How many tens are in 100? What changes when we go from 100 to 107?

Show 100 as ten tens before extending to 101–120.

Treating 100–120 as a completely new structure.

Choose a number for the grown-up to build and check it.

Builds and reads representative numbers across the range and explains their structure.

Build reversal pairs such as 24 and 42 and compare each digit’s value.

Show me 4 ones. Now show me 4 tens. Are those the same amount?

Build both values side by side and compare physically.

Treating a digit as having a fixed value regardless of place.

Try other reversal pairs.

Distinguishes, for example, 4 ones from 4 tens.

Build a number, place tens and ones into labelled areas and connect them to the numeral.

What does the digit in the tens place mean here? What does the ones digit mean?

Keep the physical quantity visible and move one unit type at a time.

Treating the columns as arbitrary boxes rather than representations of units.

Build the same number in a non-standard way before returning to standard notation.

Links concrete tens/ones units to positional notation.

Build a number, cover either the tens or ones digit, then infer the missing digit.

What can you see that proves your answer?

Count the relevant units only — tens for the tens digit, ones for the ones digit.

Guessing from sequence rather than using place-value evidence.

Reverse roles and make a mystery for the grown-up.

Identifies the missing digit from the tens/ones structure.

Start with at least 10 ones, trade 10 for one ten and compare the numeral representation.

Why can the written number stay equal when the pieces look different?

Revisit the physical 10-ones ↔ 1-ten equivalence.

Believing the exchange itself creates a new quantity.

Use a non-standard representation such as 2 tens 12 ones before exchanging.

Connects exchange to place-value notation.

Use pairs such as 36/63 and numbers such as 40. Build, read and explain each digit.

What does the zero tell us? What changed when the digits swapped places?

Build the values and point from each digit to its physical units.

Reading numerals correctly without understanding digit value.

Include representative numbers above 100 once secure.

Explains digit value rather than only naming the numeral.

Build two numbers, compare tens first and state the relationship in words before using the symbol.

Which has more tens? Does that settle it? How do you know?

Line up the tens in each quantity and compare them physically.

Comparing the ones digit only or relying on which way the gator faces.

Find a number greater or less than a target.

Compares tens first and uses greater than/less than accurately.

Compare pairs such as 43 and 47.

What is equal? What is different? Which difference matters?

Pair the equal tens first, then compare only the leftover ones.

Treating equal tens as meaning equal numbers.

Include very close pairs and equal pairs.

Uses ones to decide when tens are equal.

Locate 37, 68, 95, 107 and 119 using nearby tens and benchmarks.

Is it closer to 60 or 70? What must come before and after it?

Locate the surrounding tens first, then narrow the interval.

Ignoring equal numerical intervals or treating labels as isolated answers.

Estimate a location before checking structured marks.

Uses benchmarks and relative magnitude to place numbers.

Give bounds such as 45 and 52 and place several valid numbers between them.

Could there be another answer? What makes an answer impossible?

Place both bounds on the line and inspect the interval.

Relying only on memorised sequence rather than magnitude.

Use wider bounds and ask for numbers closer to one endpoint.

Generates valid examples and justifies them.

Order small sets using tens first, ones second and the number line to check.

Which clue helped first? Could you prove the order another way?

Compare two numbers at a time and build them if needed.

Correct ordering with no understanding of why.

Include reversals, same-tens pairs and 100–120 examples.

Orders flexibly and justifies using magnitude language.

Start with a known quantity such as 34 and add a small amount, counting on from 34.

What number did you start saying first? Why?

Keep 34 built and add one piece at a time while saying 35, 36…

Recounting the known starting quantity from one.

Increase the starting number while keeping the added amount manageable.

Counts on from a known total.

Remove a small amount from a known number and compare counting back with thinking about difference.

Which way felt easier for this problem? Why?

Keep the whole visible and remove only the amount being subtracted.

Recounting the entire remainder from one unnecessarily.

Compare two strategies on the same problem.

Starts from the known whole and explains a sensible strategy.

Model 32 + 14 as +10 then +4 and label each jump.

What stayed the same when you jumped +10? What changed?

Build 14 as one ten and four ones before transferring the structure to the line.

Making a +10 jump but changing the ones digit.

Try adding 20 or another structured amount.

Decomposes the addend into useful parts and tracks jumps accurately.

Build two quantities and combine tens with tens and ones with ones.

How many tens altogether? How many ones? Do we need to make any new ten?

Keep unit types physically separated and combine like units.

Mixing tens and ones as if they have equal value.

Include an example where combined ones can be exchanged for a ten.

Uses place-value structure accurately to combine quantities.

Solve a small set using counting on, tens jumps, decomposition or materials and compare choices.

Could another strategy work? Which would you choose next time?

Offer two strategy choices rather than prescribing a procedure.

Treating one method as mandatory for every problem.

Solve the same problem in two meaningful ways.

Uses at least two meaningful strategies and can explain choices; speed is irrelevant.

Model 8 + 5. Split 5 into 2 and 3, move 2 to complete 10, then add 3.

Where did the 5 go? Did we create or lose anything?

Keep the remainder visible before moving anything.

Making ten and then adding the whole second amount again.

Try 9 + 6.

Physically makes ten and recombines while conserving the total.

Use several additions crossing a ten. Partition the second amount before moving pieces.

How did you decide how much to move? Where is the remainder?

Mark the remainder bay first and place the unused part there.

Losing track of the remainder.

Predict the result before completing the physical moves.

Conserves the total while repartitioning across ten.

Model 13 − 5 by removing 3 to reach 10, then the remaining 2.

How did we split the 5? Why did 10 help?

Separate the amount to remove into the part that reaches ten and the remainder.

Removing the full subtraction amount again after reaching ten.

Try another subtraction crossing a decade.

Uses ten as a landmark and tracks the full amount removed.

Identify 30, partition 5 into 2 and 3, then recombine.

Why did you choose 30? What was left after reaching it?

Locate the starting number and nearest useful decade on the number line.

Choosing a decade without considering the direction of the calculation.

Use another example near a different decade.

Identifies a useful ten and bridges accurately.

Mix addition and subtraction examples, some suited to bridging and some better another way.

Why did you choose that strategy?

Compare two possible strategies using materials and let the child choose.

Applying the bridge procedure mechanically to every problem.

Invent a problem where bridging would be especially useful.

Uses bridging flexibly and can explain when it helps.

Make equal groups of 2, touching and describing each group before finding the total.

Are the groups equal? How could you prove it?

Fill one group at a time with exactly two pieces and compare groups.

Confusing number of groups with number in each group.

Compare 2 groups of 5 with 5 groups of 2.

Distinguishes group size, number of groups and total.

Build several equal groups of 5, then total them by tracking one count per complete group.

What does each count of five correspond to on the board?

Point to one complete group for each count word.

Chanting 5s without connecting each number to a complete group.

Change the number of groups while keeping group size 5.

Connects repeated groups of five to the total.

Build groups of 10 and connect each group to one ten unit and totals such as 20, 40 and 60.

How is this like the Number Bank work we did earlier?

Replace each complete group of 10 ones with one ten piece.

Treating counting by tens as an unrelated chant.

Connect 10 groups of ten to 100.

Sees, for example, 6 groups of 10 as 60.

Build groups of 2, 5 or 10, then point to one complete group per skip-count step.

What did the number you just said represent?

Slow down and touch one group for each skip-count step.

Reciting a sequence without one-to-one correspondence to groups.

Switch group sizes and choose the appropriate counting pattern.

Each skip-count number corresponds to another equal group.

Present equal and deliberately unequal arrangements. Identify group size, number of groups and total.

What exactly makes this unfair or unequal?

Compare groups directly, one position at a time.

Calling an arrangement equal because the total looks plausible.

Make two different equal-group arrangements with the same total.

Explains equality of groups and totals efficiently.

Solve practical build/exchange situations and let the child decide when to trade.

Why did that trade help? Did the amount change?

Build the story exactly as stated before considering any exchange.

Trading mechanically without connecting the move to the problem.

Invent a Number Bank story for the grown-up.

Unitises and trades appropriately within a story context.

Solve matched problems where counting on, tens jumps or bridging may be efficient.

What did you notice about the numbers that helped you choose?

Use the materials and ask which representation makes the relationship easiest to see.

Choosing a strategy by habit rather than number relationships.

Solve one problem two ways and compare efficiency conceptually, not by stopwatch.

Chooses and explains a sensible strategy.

Model missing-result, missing-change and missing-start situations using materials.

What do we know? What are we trying to find? How could the materials show that?

Build only the known information and identify the physical gap or unknown.

Assuming every story means “add the two numbers you can see.”

Change which part of the same relationship is unknown.

Reasons from known whole/parts and explains what the unknown represents.

Model practical grouping and fair-sharing situations, building the story before finding the total or missing part.

How can you check that the groups are fair or equal?

Act out the story one piece at a time, keeping group boundaries visible.

Losing the meaning of the numbers while calculating.

Create and solve a new equal-group story.

Represents the story faithfully and explains group size, number of groups and total.

Move through Bank, Train, House, Gator, Number Line, Bridge and Bus challenges.

Why did you choose that strategy? Could you show it another way?

Route back to the matching familiar activity rather than telling the answer.

Treating the capstone as a speed test or removing manipulatives to make it harder.

Try an alternative representation or strategy after a successful solution.

Shows broad, flexible understanding; weaker concepts route back to earlier activities.