Count amounts in dollars and cents

What you will learn

• Count amounts in dollars and cents

Models used: number sentences, stories, tables.

Before you start

• Convert between dollars and cents

The decimal point separates dollars from cents

We have one dollar, twenty cents and five cents. How do we write their total as an amount of money?

1. These are model coins. Read the cent value on each coin; counting coins alone will not give their value.

   One dollar is worth one hundred cents. These model coins show 100, 20 and 5 cents.

   100 + 20 + 5 = 125 cents

   Different coins can have different values. One dollar and one hundred cents are two names for the same amount.

2. One amount, three ways to read it. Read each value with the heading above its column.

   Keep 100 cents as one dollar. The 25 cents left go after the decimal point.

   125 cents = $1.25

   One amount, three ways to read it

   Dollars	Cents	Money notation
   1	25	$1.25

3. The zero holds the tens-of-cents place. Read each value with the heading above its column.

   There must be two cents digits. One dollar and five cents is $1.05; $1.50 would mean fifty cents after the dollar.

   The zero holds the tens-of-cents place

   Words	Correct notation
   1 dollar 5 cents	$1.05
   1 dollar 50 cents	$1.50

4. Two hundreds and thirty-five more. Read each value with the heading above its column.

   To count or convert an amount, group each hundred cents into a dollar and keep the remaining cents.

   2 × 100 + 35 = 235 cents

   Two hundreds and thirty-five more

   Dollars and cents	Cents altogether
   $2.35	235 cents

Worked example: A new example, together

Count $5 and coins of 50, 20, 10, 20 cents. Give the total in dollars.

1. The coins and notes use different units; include every stated value. Read each value with the heading above its column.

   Read every value and its unit. Keep dollars and cents distinct until you rename them.

   Using one common unit makes money values comparable and calculations consistent.

   The coins and notes use different units; include every stated value.

   Notes ($)	Coins (cents)
   5	50, 20, 10, 20

2. The coins and notes use different units; include every stated value. Read each value with the heading above its column.

   The notes make $5.

   The coins and notes use different units; include every stated value.

   Notes ($)	Coins (cents)
   5	50, 20, 10, 20

   Count $5 and coins of 50, 20, 10, 20 cents. Give the total in dollars.

   6.00 dollars

3. The coins and notes use different units; include every stated value. Read each value with the heading above its column.

   The notes make $5.

   The coins and notes use different units; include every stated value.

   Notes ($)	Coins (cents)
   5	50, 20, 10, 20

4. The coins and notes use different units; include every stated value. Read each value with the heading above its column.

   The coins make 100 cents.

   The coins and notes use different units; include every stated value.

   Notes ($)	Coins (cents)
   5	50, 20, 10, 20

5. The coins and notes use different units; include every stated value. Read each value with the heading above its column.

   Combine them: $6.00.

   The coins and notes use different units; include every stated value.

   Notes ($)	Coins (cents)
   5	50, 20, 10, 20

6. The coins and notes use different units; include every stated value. Read each value with the heading above its column.

   Check the result against the question we started with.

   Convert the result back to cents to verify the calculation.

   We found 6.00 dollars. Using one common unit makes money values comparable and calculations consistent.

   The coins and notes use different units; include every stated value.

   Notes ($)	Coins (cents)
   5	50, 20, 10, 20

Common mistakes to discuss

• Counting coins instead of values. Each coin carries its own value. Four coins can be 70 cents when they are 50, 10, 5 and 5.

Check your understanding

• Count amounts in dollars and cents
• compare, combine or rename money while preserving its value
• 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.