Practical questions · Original activities
Number, operations and fractions
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Number, operations and fractions
A bigger counter does not make a bigger collection
Separate how many objects there are from how large those objects look.
Number, operations and fractions
A fraction of a shape and a fraction of a set
State the whole clearly in both models before comparing the fraction named.
Number, operations and fractions
A missing addend is a quantity to find
Make the unknown part visible as a space to be filled, not a cue to guess.
Number, operations and fractions
A remainder needs an interpretation, not just a label
Keep leftover units visible and explain what they mean in the particular problem.
Number, operations and fractions
Addition starts with two quantities we can identify
Record the two starting groups and the resulting whole with a matching equation.
Number, operations and fractions
An estimate should have a reason behind it
Make an estimate before counting and compare it with the checked quantity.
Number, operations and fractions
Arrays: see the repeated grouping in rows and columns
Make the row and column structure visible and connect it to the total.
Number, operations and fractions
Before and after: locate the reference number first
Connect adjacent positions with the counting sequence using a clearly labelled line.
Number, operations and fractions
Counting on without losing track of the added amount
Keep the first quantity in mind and count the added units from that point.
Number, operations and fractions
Division by grouping: how many groups can we make?
Ask how many complete equal groups can be formed, rather than how many each recipient receives.
Number, operations and fractions
Division by sharing: how many does each recipient get?
Divide a collection into a stated number of equal groups and check every group.
Number, operations and fractions
Doubles facts with two equal groups underneath them
Build equal groups and explain what is being doubled.
Number, operations and fractions
Equal groups give multiplication a structure
Identify the number of groups and the quantity within each before finding the total.
Number, operations and fractions
Equivalent fractions: match the amount before the labels
Compare portions of the same-sized whole before drawing conclusions from the labels.
Number, operations and fractions
Make ten and keep the leftover in sight
Move part of one group to complete ten while preserving the total quantity.
Number, operations and fractions
Near doubles: find the one-unit adjustment
Start from a known double and show the one-unit difference in the actual problem.
Number, operations and fractions
Number-line addition: what does each jump mean?
Connect the starting value, jump size and landing value with a concrete model.
Number, operations and fractions
One object, one count: make the correspondence visible
Match one spoken number to one object and make the counting path visible.
Number, operations and fractions
One part-whole model connects addition and subtraction
Use one collection to show related relationships rather than unrelated number facts.
Number, operations and fractions
Put a fraction on a line with zero and one
Partition the interval between zero and one into equal lengths and locate the fraction within it.
Number, operations and fractions
Quarters require four equal shares of the whole
Establish four equal parts and retain a visible reference to the original whole.
Number, operations and fractions
Recognising a small quantity without counting each dot
Invite recognition of a small structured quantity and an explanation of what was seen.
Number, operations and fractions
Regrouping changes the pieces, not the amount
Make an exchange visible before using a written calculation procedure.
Number, operations and fractions
Rotate an array and investigate what stays the same
Compare two grouping descriptions of the same array without changing its quantity.
Number, operations and fractions
Subtraction as taking away: show the starting amount
Show the initial collection, the removed part and the remaining part separately.
Number, operations and fractions
Subtraction can compare two collections without taking any away
Compare two quantities by matching their common part and identifying the unmatched amount.
Number, operations and fractions
Teen numbers as a ten and some more
Build a group of ten and a visible remainder rather than relying only on number names.
Number, operations and fractions
Tens and ones: explain what the digits stand for
Represent a two-digit number with grouped tens and remaining single units.
Number, operations and fractions
The equals sign connects equal amounts on both sides
Compare the values on both sides instead of treating the symbol as an instruction to give an answer.
Number, operations and fractions
The last count tells us how many altogether
Ask what the final counting word tells us about the whole collection.
Number, operations and fractions
Two pieces are not automatically two halves
Check equality of the parts before naming them halves.
Number, operations and fractions
Zero belongs in the collection story
Show an empty collection alongside collections containing objects.
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