Mathematics 1

The last number said when counting tells how many there are: touching five blocks while saying 1, 2, 3, 4, 5 means there are 5 blocks, and 'five' names the whole group.

Counting is not a song: each number word goes with one thing, and the last word is the size of the whole group.

A numeral is a symbol for a number: the numeral 7 stands for seven, whether it is 7 cars, 7 claps or 7 dots.

Numerals are how numbers are written.

Two amounts are equal when they have the same number of things: 5 cups and 5 straws are equal, because matching them gives every cup a straw with none left over.

Equal means the same amount.

Adding finds the whole when parts are put together: 6 red blocks and 4 blue blocks pushed into one pile make 10 blocks.

Two parts joined make a whole.

Two ten frames show a teen number as ten and more: one full frame and 4 dots in the second frame is 10 and 4, which is 14.

Fill the first ten frame before starting the second.

A circle is round with no corners, and a triangle has 3 straight sides and 3 corners: a clock face is a circle and a yield sign is a triangle.

Run a finger round a circle: it never bumps a corner.

A composite shape is made of two or more shapes put together: a house drawn as a square with a triangle on top is one composite shape made of 2 shapes.

Many pictures and objects are made of simple shapes joined edge to edge.

A square has 4 straight sides all the same length and 4 square corners, while a long rectangle has 4 square corners with 2 long sides and 2 short sides, like a door.

Squares and rectangles both have 4 sides and 4 square corners, so counting is not enough to tell them apart.

Shapes can be put together to make new shapes: two matching triangles placed edge to edge can make a square, and two squares placed side by side make a rectangle.

Slide, turn and flip shapes until their edges line up with no gaps and no overlaps.

A shape keeps its name in any size and any position: a triangle standing on its point is still a triangle, and a giant triangle still has 3 sides.

Cut out a triangle and turn it: point up, point down, lying on a side, tilted.

Length is how far it is from one end of a thing to its other end: a pencil's length goes from its eraser to its point.

Every object has two ends, and its length is the fixed space between them.

Distance is the length between two points: the space between two chairs, between a tree and a rock, or between your home and your school is a distance.

A distance is a length that is not part of one object; it is the space between two things or places.

Two lengths are compared by laying the things side by side with their starts on the same line: the one whose other end reaches farther is longer.

Put a red ribbon and a blue ribbon flat on the table with one end of each touching the same line; the edge of the table works.

Distances are all around: between two people in a line, between two cars in a parking lot, and on the land between a tree and a river or a tent and a lake.

Some distances are inside a room: from your desk to the door, or between two people sitting in a circle.

The starts must be lined up for a fair comparison: a crayon placed farther ahead looks longer than a marker even when it is shorter, until both are slid back to the same line.

Put a short crayon and a long marker on the table with the crayon starting closer to you; its tip is ahead, and it looks like the longer one.

A pattern core is the part of a repeating pattern that comes back again and again as a unit: in circle, square, square, circle, square, square the core is circle, square, square.

Read the pattern from the start and watch for the first place it begins again.

A cycle is a repeating pattern of events that goes around in the same way forever: day, night, day, night never stops, and each turn is just like the last.

Some patterns end, like a line of beads on a string.

A list with nothing coming back is not a repeating pattern: red, blue, green, yellow, purple never repeats, but red, blue, red, blue does, because its core comes back.

Ask whether anything comes back in the same order.

Cycles include day and night, the four seasons, life cycles like a frog growing from an egg, and the calendar's days and months, which come around again and again.

Each cycle has a core that repeats.

The pattern core is the shortest part that copies itself: in red, blue, red, blue, red, blue the core is red, blue, not red, blue, red, blue and not red alone.

Red, blue, red, blue does repeat, but it is two copies of a smaller part, so it is too much.

Time can be noticed through changes we can see: an ice cube melting into water, a puppy growing into a dog, and shoes that no longer fit all show that time has passed.

You cannot see time itself, but you can see what it does.

Some changes come back again and again, and those changes show a cycle of time: the sun rising each morning shows that a new day has begun.

Many changes happen only once: a sandcastle washes away and does not come back.

A day goes around in a cycle: morning, afternoon, evening and night come in the same order every day, and after night comes morning again.

The parts of a day always follow one another.

The day's meals are part of its cycle: breakfast in the morning, lunch at midday and supper in the evening come around again every day, in the same order.

The time of day can be told by what is happening.

Day and night take turns and keep taking turns: light comes, dark comes, and then light comes again, over and over with no end.

Yesterday had a day and a night, today has a day and a night, and tomorrow will too.

Data is information that is collected, and it can be the answers people give to a question: 'Do you like apples, bananas or grapes best?' asked of 20 classmates gives 20 answers of data.

When you ask a question and keep the answers, you have data.

A wondering is something you want to find out about people, things or events: 'I wonder what pets my classmates have' is a wondering that a question can answer.

Data starts with being curious.

A data question offers a few choices so every answer fits one: 'Apple, banana or orange?' works, but 'What food do you like?' can give a different answer from every person.

Before collecting, make sure the question has choices.

Exactly one answer is kept for each person: going down the class list in order with one cube for each answer, 20 classmates leave 20 cubes.

Gathering data is a counting job, and the count has to match.

A few people cannot answer for a whole class: three friends who all pick apple do not show that the whole class picks apple, so everyone is asked.

Data answers only for the people who were asked.