Mathematics, Grade 1

One number can be shown in many ways that all mean the same amount: 23 counters, 2 full ten frames and 3 more dots, a drawing of 23 stars, the word twenty-three and the numeral 23 all show 23.

Every way of showing a number must tell the same amount.

A number broken into two parts is still the same amount: 7 counters pushed into a group of 4 and a group of 3 are still 7 counters.

Put 9 counters on the table, then slide 6 to the left and 3 to the right.

A fair share gives every friend the same amount, not just a turn: 6 cookies for 2 friends is 3 cookies each.

In math, fair means equal.

Adding and subtracting use the same three numbers, two parts and a whole: 6 + 3 = 9 puts the parts together, and 9 − 3 = 6 takes one part off the whole.

Six red counters and three blue counters make nine.

A number story can be shown three ways that agree: '23 stickers, then 8 more' is 23 counters and 8 counters pushed together, a drawing of 23 dots and 8 dots, and the number sentence 23 + 8 = 31.

Act the story out with counters first, then draw what the counters showed, then write the number sentence that matches the drawing.

A pattern has a part that repeats in the same order: star, star, moon, star, star, moon repeats star, star, moon, which is three things long.

Read the pattern from the start and stop where the same part begins again.

Some everyday amounts can change, like the temperature, your height and how many children are in the room, and some always stay the same, like the days in a week and the wheels on a bicycle.

Look around: the cars in a parking lot change all day, and the leaves on a tree change with the seasons.

Code is a list of instructions that a robot or a computer follows one at a time, in order: 'forward 2, turn right, forward 1' is three steps done one after another.

A robot does not guess.

The part that repeats can be made of a colour, a shape, a size, a texture or a turn: in a row of arrows pointing up, down, up, down, only the way the arrow points changes.

Look at each thing in the pattern and ask what changes and what stays the same.

Some things change quickly and some change slowly, and slow change is still change: a puddle dries up in an afternoon, while a tree grows taller over many years.

Make two lists.

A sorting rule uses one attribute, and every item goes into exactly one group: buttons sorted by colour make a red group and a blue group, and the rule is 'I sorted by colour'.

Choose one attribute, like colour, and look only at that.

Certain means it will always happen, like the sun setting tonight; impossible means it can never happen, like a cat growing wings; possible means it might happen, like rain tomorrow.

Three words tell how likely something is.

The same set sorts into different groups under different rules: 12 buttons by colour make red 7 and blue 5, and by size make big 8 and small 4.

Sort by colour, mix the buttons up, then sort by size, then by shape.

Two questions decide the word: an event that can never happen is impossible, one that must always happen is certain, and one that can happen but does not have to is possible, so a number cube showing 4 is possible.

First ask: can it ever happen?

A sorting rule can be worked out from the groups: a pile of red buttons of all sizes beside a pile of blue buttons of all sizes was sorted by colour, not by size.

Look at what every item in one group has in common, and what makes it different from the other group.

Flat shapes and solid objects belong in different groups: a paper square is a flat 2D shape and a cube is a 3D object, even though the cube's faces are squares.

A 2D shape is flat: it can be drawn on paper or cut out, and it lies flat on the table.

A position word tells where one thing is compared to another thing: 'the cat is under the table' names the cat, the table and how they sit.

' needs a second object to answer: under the table, on the chair, beside the door.

Some things about an object can be measured and some cannot: a bottle's height and how heavy it is can be measured, but its colour and its name cannot.

Something can be measured when you can ask how much of it there is and compare more or less.

Shapes and objects have attributes you can see or count, like corners, straight sides, flat faces and round parts, and a sorting rule uses one of them.

Pick up a block and look for what you can count or check: its corners, its flat faces, whether any part is round.

Position words come in opposite pairs, like above and below, in front of and behind, and inside and outside, while 'between' needs two landmarks.

Practise the pairs with one toy and one box: the toy is above the box, then below it; in front of it, then behind it; inside it, then outside it; beside it, then far from it.

Each Canadian coin has a name, a value and a picture: the nickel is worth 5 cents and shows a beaver, the dime 10 cents with a sailing ship, the quarter 25 cents with a caribou, and the 50-cent coin shows the coat of arms.

Say the name and the value together: 'nickel, 5 cents', 'dime, 10 cents', 'quarter, 25 cents', 'fifty-cent coin, 50 cents'.

The loonie is a coin worth 1 dollar, and the toonie is a coin worth 2 dollars: the loonie is gold-coloured with a loon and eleven sides, and the toonie has two colours and a polar bear.

Dollars are a bigger unit than cents, so a loonie is worth more than any coin counted in cents.

Canadian bills are worth more dollars and each has its own colour: the $5 bill is blue, the $10 purple, the $20 green and the $50 red.

Each bill has its value printed on it in big numbers, and its colour helps you know it at a glance.

A bigger coin is not always worth more: the dime is the smallest coin but is worth more than the nickel, and the 50-cent coin is a little bigger than the loonie but worth less.

Size does not tell value.

Canadian money can be put in order by value: nickel 5¢, dime 10¢, quarter 25¢, 50-cent coin, loonie $1, toonie $2, then the $5, $10, $20 and $50 bills.

To compare two coins, compare their values, not their sizes or colours.