LESSON PLAN

Numbers from Thousandths to Billions

Apothem Team

Grade 6 · Number

LESSON AT A GLANCE

Warm-up

5 min

Explore

15 min

Consolidate

10 min

Practice

12 min

Exit ticket

3 min

Warm-up

What is 1,000 times 1,000,000? (1,000,000,000 = 1 billion.) What is 1/1,000 of 1? (0.001 = 1 thousandth.) How many thousandths in 1 million? (1,000,000,000 = 1 billion thousandths.) This number chain builds the complete place value picture.

Explore

Large and small number investigation: each group researches one large-number context (population, national debt, distance) and one small-number context (cellular size, medication dose, wavelength). Represent on a place value chart, order alongside each other, and estimate a related computation.

Consolidate

Practice

Students represent 6 numbers from context in standard form, order 5 numbers from least to greatest, and solve 2 estimation problems at large scales. Exit ticket: write 2.5 billion in standard form.

Exit ticket

Students represent 6 numbers from context in standard form, order 5 numbers from least to greatest, and solve 2 estimation problems at large scales. Exit ticket: write 2.5 billion in standard form.

TIP Use real-world contexts consistently. Abstract large numbers are hard to reason about; large numbers attached to real things (populations, distances, budgets) are memorable and motivating.

WORKED EXAMPLES

Write 4.7 billion in standard form.

4.7 billion = 4,700,000,000. Count: 9 digits after the 4 and 7... billion has 9 zeros, so 4,700,000,000.

Order from least to greatest: 3.6 million; 36,000,000; 3,600; 0.36 billion.

3,600 < 3,600,000 < 36,000,000 < 360,000,000. 0.36 billion = 360,000,000.

MATERIALS

•Place value charts (thousandths to billions)

•Large and small number context cards

•Calculators for large-number operations

•Scientific notation reference (preview)

WATCH FOR

!Students may write billions incorrectly: 4.7 billion becomes 47,000,000 instead of 4,700,000,000. Require students to write out the full number on a place value chart before converting.

!Students may not recognize that 0.36 billion = 360 million: same number, different expression.