Grade 4/5 Patterns and Equations

Pattern Detectives

100

What comes next? 2, 4, 6, 8, ___

10

200

Is this pattern increasing or decreasing? 100, 90, 80, 70...

Decreasing

300

What is the difference between a growing and a repeating pattern?

Growing pattern: gets larger each term

Repeating pattern: Has a part that repeats again in the same way.

400

What is the 10th term in the pattern: 3, 6, 9, 12...?

30

500

A student is stacking books in a pattern.

• In the first stack, there are 3 books.
• In the second stack, there are 6 books.
• In the third stack, there are 9 books.
• In the fourth stack, there are 12 books.

1. Make a t-table with this information.
2. How many books will be in the 7th stack?

Show me your t table.

There will be 21 books in the 7th stack. 

Equation Explorers

100

Solve: 3 + x = 7

x=4

200

Solve: x - 5 = 10

x = 15

300

Solve the equation 4x−2=10

x=3

400

A pack of markers costs $5. Emma buys some packs and spends $35.Write an equation to find how many packs she bought.

Equation: 5x=35

500

A school orders boxes of pencils. Each box has 12 pencils. They receive a total of 108 pencils.Write an equation to find how many boxes were ordered, AND solve it.

Equation: 12b=108

Solution: b=9

Pattern Rule Builders

100

What is the pattern rule for 2,4,6,8

Start at 2 and add 2 each time

200

Write the first 5 terms for the pattern rule start at 10 and add 10 each time. 

10, 20, 30, 40, 50

300

What is the pattern rule?

2, 3, 5, 8,12

Start at 2 and add one, then increase by one more each time. 

400

One magazine is $4.00. I want to figure out how many magazines I can get for $16.00. Write the pattern rule using a variable and then find the answer. (two parts - both have to be correct).

16 ÷ 4 = x

x= 4

I can buy 4 magazines with $16.00

500

A gardener plants flowers in rows. In the first row, there are 2 flowers. In the second row, there are 6 flowers. In the third row, there are 10 flowers. The pattern continues in the same way.

1. What is the pattern rule?
2. How many flowers will be in the 6th row?

1. Pattern Rule: Start at 2, then add 4 each time → Add 4
   (Or: y = 4x - 2, where x is the row number and y is the number of flowers)

2. 6th row:
   Using the rule y = 4x - 2 → y = 4(6) - 2 = 22 flowers

Algebra Adventures

100

What is a variable?

A symbol (like x) that represents a number

200

Write an expression for “5 more than a number x”

x + 5

300

Write an equation for: “A number doubled is 14”

2x = 14

400

Write an expression for: “Triple a number, then subtract 4”

3x - 4

500

A movie theatre sells tickets for $8 each. One day, they made $72 from ticket sales.

1. Write an equation using a variable to represent the number of tickets sold.
2. Solve the equation to find out how many tickets were sold.

1. Let t represent the number of tickets sold.
   Equation: 8t = 72

2. 9 tickets were sold

Word Problem Wizards

100

Sam has 5 apples. He buys 3 more. How many does he have?

8

200

A number plus 7 equals 12. What is the number?

5

300

If 4 pencils cost $2, how much do 10 pencils cost?

$5

400

A group of students are making friendship bracelets. Each bracelet takes 4 beads to make. If they have 28 beads, how many bracelets can they make?

1. Write an equation using a variable to represent the number of bracelets.

1. Let b represent the number of bracelets.
   Equation: 4b = 28

500

Ms. Carter is organizing a school art show. She wants to hang student artwork in rows. Each row has 6 pieces of art. She doesn’t know how many rows she’ll need yet, but she knows she has 54 pieces of art in total.

1. Write an equation using a variable to represent the number of rows.
2. Solve the equation to find out how many rows Ms. Carter needs.

1. Let r represent the number of rows.
   Equation: 6r = 54

2. Solve:
   Ms. C needs 9 rows