Use a letter for an unknown number

What you will learn

• Use a letter for an unknown number

Models used: number sentences, stories, tables.

Before you start

• Mentally add and subtract two-digit numbers

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 6 packets and 6 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
   6 packets	6x
   Loose stickers	6

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
   6 packets	6x
   Loose stickers	6

   Each packet has x stickers. Write an expression for 6 packets and 6 loose stickers.

   6x + 6

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
   6 packets	6x
   Loose stickers	6

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

   6 packets have 6x stickers.

   Count equal unknown units

   Quantity	Expression
   6 packets	6x
   Loose stickers	6

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

   Add the loose stickers: 6x + 6.

   Count equal unknown units

   Quantity	Expression
   6 packets	6x
   Loose stickers	6

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 = 3, the expression is 6 × 3 + 6 = 24.

   We found 6x + 6. A coefficient counts equal copies of the unknown amount.

   Count equal unknown units

   Quantity	Expression
   6 packets	6x
   Loose stickers	6

Common mistakes to discuss

• The letter stands for an object. A letter stands for a number. In 6 packets with x stickers each, x is how many stickers one packet holds.

Check your understanding

• Use a letter for an unknown number
• 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.