Grade by Grade
C. Algebra · Patterns, Equality and Coding

What Changes and What Stays the Same

C2.1About 25 minutes
Learning goals
  • I can find amounts that change in real life.
  • I can find amounts that always stay the same.
  • I can explain why an amount changes or stays the same.

Words to know

quantity
An amount of something; how many or how much.
change
To become different.
stay the same
To not change, no matter what.
variable
A math word for an amount that can change.
constant
A math word for an amount that always stays the same.

Some things change, some things don't

How old are you? Next year, you will be one year older. Your age changes.

How many days are in a week? There are 7. Last week, there were 7. Next week, there will be 7. The number of days in a week always stays the same.

In math, an amount that can change is called a variable. An amount that always stays the same is called a constant.

Changes (variable) 🔄Stays the same (constant) 🔒
your agedays in a week (7)
how tall you aremonths in a year (12)
the temperature outsidewheels on a bicycle (2)
the score in a hockey gamenets in a hockey game (2)
how many leaves are on a maple treelegs on a dog (4)
how many people are on a busfingers on one hand (5)
Sorting quantities

Ask yourself

Could this amount be different tomorrow, or in a different place, or for a different person?

  • If yes, it changes.
  • If no, never, it stays the same.
Worked example

At the hockey game

At a hockey game, which of these change and which stay the same?

  • the score
  • the number of nets
  • the number of fans cheering
  • the number of periods in the game (3)
  1. The score: it starts at 0 and goes up when a team gets a goal. It changes.
  2. The number of nets: there is always one at each end. There are always 2. It stays the same.
  3. The number of fans cheering: sometimes lots of fans cheer, sometimes few. It changes.
  4. The number of periods: a regular hockey game always has 3 periods. It stays the same.

Change: the score, the number of fans cheering. Stay the same: the number of nets (2), the number of periods (3).

Changes and constants in patterns

Patterns have things that change and things that stay the same, too!

Think about the growing towers: 1, 3, 5, 7 blocks.

  • The number of blocks in each tower changes: 1, then 3, then 5, then 7.
  • The amount we add each time stays the same: always 2.
1357+2+2+2blocks in each tower: changes (1, 3, 5, 7)blocks added each time: stays the same (+2)
The towers grow: 1, 3, 5, 7 blocks. The number of blocks changes, but the jump is always +2, so the amount added stays the same.
Worked example

Bicycles and wheels

Each bicycle has 2 wheels. What changes and what stays the same as more bicycles arrive at the park?

  1. 1 bicycle has 2 wheels.
  2. 2 bicycles have 2 + 2 = 4 wheels.
  3. 3 bicycles have 2 + 2 + 2 = 6 wheels.
  4. The number of wheels on each bicycle is always 2. That stays the same.
  5. The number of bicycles and the total number of wheels change.

Stays the same: 2 wheels on each bicycle. Changes: how many bicycles there are and how many wheels there are in all (2, 4, 6...).

1 bike2 wheels2 bikes4 wheels (2 + 2)3 bikes6 wheels (2 + 2 + 2)Each bike always has 2 wheels.
Every bike has 2 wheels, and that never changes. The number of bikes changes (1, 2, 3), so the total number of wheels changes too: 2, 4, 6.
Bicycles12345
Wheels246810
As the number of bicycles changes, the total number of wheels changes. Each bicycle always has 2 wheels.

Your turn

1

Does the number of days in a week change or stay the same?

2

Does the number of snowflakes falling outside change or stay the same?

3

Does the number of corners on a square change or stay the same?

4

Does the number of books on your shelf change or stay the same?

5

Name one thing about you that changes.

6

In the pattern 5, 10, 15, 20, what changes and what stays the same?

7

Each tricycle has 3 wheels. How many wheels do 2 tricycles have? What stayed the same?

Just for fun

What if the number of days in a week could change? We could add a Funday between Saturday and Sunday! Sadly, it is a constant. Every week has 7 days.

Hands-on activity

Change detective at home

You need: paper and a pencil.

  1. Fold the paper in half. Write Changes on one side and Stays the same on the other.
  2. Look around your home. Find things to count: chairs at the table, legs on a chair, apples in the fruit bowl, people at home, wheels on a toy car.
  3. Write or draw each thing on the correct side.
  4. Talk about it: Why could the apples in the bowl change? (Someone eats one!) Why do the legs on the chair stay the same?
  5. Bonus: check the weather each day for a week. Does the temperature change?

More practice: warm-up

1

Does the number of legs on a spider change or stay the same?

2

Does the number of cars in a parking lot change or stay the same?

3

Does the number of sides on a triangle change or stay the same?

4

True or false? The number of children at school today always stays the same.

5

Does the number of eggs in the carton in your fridge change or stay the same?

More practice: on your own

1

At the skating rink, which amount changes and which stays the same?

  • the number of skaters on the ice
  • the number of skates each skater wears
2

Each cat has 2 ears. How many ears do 3 cats have? What stays the same?

3

In the pattern 50, 45, 40, 35, what changes and what stays the same?

4

Is the temperature outside a variable or a constant? How do you know?

5

Which one stays the same?

  • a) the number of snowmen on your street
  • b) the number of letters in the word CAT
  • c) the number of mittens in the lost-and-found

Challenge

1

Find the mistake! Ari says: "There are 4 apples in our fruit bowl, so the number of apples always stays the same." Is Ari right? Explain.

2

Each wagon has 4 wheels. Fill in the blanks: 1 wagon has 4 wheels. 2 wagons have ___ wheels. 3 wagons have ___ wheels. What changes and what stays the same?

3

Kai is 6 years old. His sister is 3 years old. How old will each of them be next year? What changes and what stays the same?

Check your understanding

Quiz

1.

Which amount stays the same?

2.

Which amount changes?

3.

In the pattern 10, 20, 30, 40, what stays the same?

4.

A math word for an amount that can change is...

5.

Which amount changes?

6.

Each spider has 8 legs. When more spiders come, what stays the same?

For parents and teachers

In Grade 1, children start noticing that some quantities can vary (variables) while others are fixed (constants). This idea is the foundation of algebra.

Common mistakes

  • Thinking something stays the same because it has not changed today ("there are 3 apples, so it stays the same"). Ask: Could it ever be different?
  • Mixing up the count of one thing with the total (each bike has 2 wheels, but the total wheels change). Use real objects or drawings.
  • The words variable and constant are new. It is fine if your child says changes and stays the same instead.

How to help

  • During daily routines, ask: Does this change or stay the same? (minutes until dinner, the number of eggs in a carton, the number of players on your team).
  • Connect to the seasons: the number of leaves on a tree changes, but there are always 4 seasons.