Form simple expressions involving an unknown

What you will learn

• Form simple expressions involving an unknown

Models used: number sentences, stories, tables.

Before you start

• Letters and balanced equations

Use a letter for a hidden amount

Each bag has the same hidden number of counters. Call that number x.

1. Matching bags hold the same amount. A level balance means both sides have equal value.

   Each bag has the same hidden number of counters. Call that number x.

   A letter can take a numerical value. Like terms count the same unknown-sized unit; substitution replaces it consistently.

   x

   x

   x = x · balanced

2. Matching bags hold the same amount. A level balance means both sides have equal value.

   Three bags contain x + x + x counters. We write that more briefly as 3x.

   x + x + x = 3x

   Equality is a relationship between both sides. Adding or removing the same amount on both sides keeps that relationship true.

   xxx

   xxx

   3x = 3x · balanced

3. Matching bags hold the same amount. A level balance means both sides have equal value.

   Add two loose counters. The total is 3x + 2, whatever number is hidden in each bag.

   3x + 2

   Equality is a relationship between both sides. Adding or removing the same amount on both sides keeps that relationship true.

   xxx

   xxx

   3x + 2 = 3x + 2 · balanced

Worked example: A new example, together

Each packet has x stickers. Write an expression for 4 packets and 3 loose stickers.

1. Count equal unknown units. Read each value with the heading above its column.

   Say what one letter means before grouping terms or substituting a value.

   A coefficient counts equal copies of the unknown amount.

   Count equal unknown units

   Quantity	Expression
   4 packets	4x
   Loose stickers	3

2. Count equal unknown units. Read each value with the heading above its column.

   One packet has x stickers.

   Count equal unknown units

   Quantity	Expression
   4 packets	4x
   Loose stickers	3

   Each packet has x stickers. Write an expression for 4 packets and 3 loose stickers.

   4x + 3

3. Count equal unknown units. Read each value with the heading above its column.

   One packet has x stickers.

   Count equal unknown units

   Quantity	Expression
   4 packets	4x
   Loose stickers	3

4. Count equal unknown units. Read each value with the heading above its column.

   4 packets have 4x stickers.

   Count equal unknown units

   Quantity	Expression
   4 packets	4x
   Loose stickers	3

5. Count equal unknown units. Read each value with the heading above its column.

   Add the loose stickers: 4x + 3.

   Count equal unknown units

   Quantity	Expression
   4 packets	4x
   Loose stickers	3

6. Count equal unknown units. Read each value with the heading above its column.

   Check the result against the question we started with.

   If x = 5, the expression is 4 × 5 + 3 = 23.

   We found 4x + 3. A coefficient counts equal copies of the unknown amount.

   Count equal unknown units

   Quantity	Expression
   4 packets	4x
   Loose stickers	3

Common mistakes to discuss

• Writing the numbers in the order heard. “Three more than x” is x + 3, while 3x is three lots of x.

Check your understanding

• Form simple expressions involving an unknown
• interpret and use an expression through the meaning of its unknown
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.