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B. Number · Number Sense: Big Numbers, Square Roots and Rational Numbers

Number Sense: Big Numbers, Square Roots and Rational Numbers: Unit Review

A1 B1.1 B1.2 B1.3 B1.4 B1.5 B1.6 B1.7About 40 minutes
Learning goals
  • I can read, write, compare and round whole numbers up to one billion, including with powers of ten.
  • I can identify perfect squares and find their square roots.
  • I can read, compare and order positive and negative fractions and decimals.
  • I can simplify fractions, find numbers between numbers, round decimals, and convert between fractions, decimals and percents.

Words to know

billion
1 000 000 000 = 10⁹.
power of ten
A product of 10s, like 10³ = 1000.
perfect square
A whole number times itself, like 49 = 7².
square root
The number that times itself gives the number: √49 = 7.
rational number
A number that can be written as a fraction of integers, like −3/4 or 2.5.
simplest form
A fraction with no common factor other than 1 in the numerator and denominator.
percent
Out of 100.

Let's review!

In this unit you read, wrote and compared numbers up to one billion, used powers of ten, found perfect squares and square roots, worked with positive and negative fractions and decimals, simplified fractions, found numbers between other numbers, rounded decimals in real situations, and converted between fractions, decimals and percents.

This review has a few questions from every lesson. Try each one, then press Show answer to check. If a part feels tricky, go back to that lesson for more practice.

Big numbers1 000 000 000= 10⁹ = one billionPeriods: billions | millions |thousands | onesEach place is 10 × the one to its rightSquares and roots555² = 25√25 = 5side = √areaarea = side²
Big ideas from the first lessons: periods and powers of ten for big numbers, and squares and square roots as opposites.
−2−101−1 1/2−3/40.4← lessgreater →3/4 = 0.75 = 75% (same amount, three forms)
Rational numbers on one line: the further right, the greater. Negatives sit to the left of 0.

Reading and Writing Numbers to One Billion

1

Write 307 040 500 in words.

2

Write ninety million two hundred six in standard form.

3

What is the value of the 6 in 462 000 000?

4

How many millions are in one billion?

Expanded Form with Powers of Ten

1

Write 10⁷ in standard form.

2

Write 5 080 000 in expanded form with powers of ten.

3

Write 3 × 10⁸ + 4 × 10⁵ + 9 in standard form.

Comparing, Ordering and Using Big Numbers

1

Use >, < or =: 340 512 000 ___ 340 521 000

2

Round 672 489 000 to the nearest million.

3

Which is greater: 9 × 10⁶ or 1 × 10⁷?

Perfect Squares

1

What is 14²?

2

Is 90 a perfect square? Explain.

3

100 = 2 × 2 × 5 × 5. Show it is a perfect square.

Square Roots of Perfect Squares

1

Find √121.

2

A square rink has an area of 225 m². How long is each side?

3

Find √729.

Rational Numbers: Positive and Negative Fractions and Decimals

1

Write a rational number for a loss of $8.50.

2

Write −7/4 as a mixed number and as a decimal.

3

Between which two integers is −0.4?

Comparing and Ordering Rational Numbers

1

Use >, < or =: −0.7 ___ −0.65

2

Order from least to greatest: −1/4, −0.3, 0.2, −1

3

Which is colder: −9.15°C or −9.5°C?

Simplifying Fractions

1

Simplify 18/27.

2

Simplify −20/48.

3

Simplify 42/28 and write it as a mixed number.

Finding Fractions and Decimals Between Two Numbers

1

Find a decimal between 3.4 and 3.41.

2

Find a fraction between 2/3 and 3/4.

3

Find a number between −0.5 and −0.4.

Rounding Decimals in Real Life

1

Round 3.096 to the nearest hundredth.

2

Round −4.25 to the nearest whole number.

3

Four friends share $15 equally. How much each?

Converting Between Fractions and Decimals

1

Write 3/20 as a decimal.

2

Write 0.875 as a fraction in simplest form.

3

Write 5/9 as a decimal.

Converting Between Fractions, Decimals and Percents

1

Write 0.09 as a percent.

2

Write 175% as a decimal and as a mixed number.

3

Write 3/8 as a percent.

4

Write 0.7% as a decimal.

Just for fun

Why was the math book so tired at the end of this unit?

It had way too many problems. Good thing you solved them!

How to use this review

  • Do the review over two or three short sittings. Each section matches one lesson.
  • Estimate first: Is the number more or less than 1? Positive or negative? Between which perfect squares?
  • Use a number line sketch for any question with negative numbers.
  • Check your answers another way: square your square root, change a fraction to a decimal, or put a rounded number back on a number line.
  • Put a star next to any question you got wrong, and go back to that lesson's practice.
Check your understanding

Quiz

1.

How do you write four hundred three million sixty thousand in standard form?

2.

What is 10⁸ in standard form?

3.

Which number is the greatest?

4.

Which number is a perfect square?

5.

A square garden has an area of 81 m². How long is each side?

6.

Which list is in order from least to greatest?

7.

What is 30/42 in simplest form?

8.

Which number is between 1/2 and 3/5?

9.

Round −6.47 to the nearest tenth.

10.

Which shows the same amount in all three forms?

For parents and teachers

Use mistakes to choose what to revisit. Each review section matches one lesson.

  • Leaves out placeholder zeros or reads big numbers wrongly: revisit Reading and Writing Numbers to One Billion.
  • Writes 10⁴ as 40, or uses the wrong power in expanded form: revisit Expanded Form with Powers of Ten.
  • Compares only the first digit, or rounds by looking at the wrong digit: revisit Comparing, Ordering and Using Big Numbers.
  • Thinks 6² means 6 × 2, or calls 90 a perfect square: revisit Perfect Squares.
  • Divides by 2 instead of finding the square root (√64 = 32): revisit Square Roots of Perfect Squares.
  • Treats −1 1/2 as −0.5, or places −1.2 between −1 and 0: revisit Rational Numbers: Positive and Negative Fractions and Decimals.
  • Says −4.5 > −4.25 because 4.5 > 4.25: revisit Comparing and Ordering Rational Numbers.
  • Subtracts instead of dividing, or stops simplifying too early: revisit Simplifying Fractions.
  • Says there is no number between 0.3 and 0.4, or between 3/5 and 4/5: revisit Finding Fractions and Decimals Between Two Numbers.
  • Rounds twice, forgets to regroup 9s, or rounds down when real life needs rounding up: revisit Rounding Decimals in Real Life.
  • Writes 3/4 as 0.34, or thinks 0.3 = 1/3: revisit Converting Between Fractions and Decimals.
  • Moves the decimal point the wrong way (0.06 → 60%), or thinks percents can't be over 100%: revisit Converting Between Fractions, Decimals and Percents.

A few mistakes are normal. Praise the strategy your child explains and the habit of checking, not only the right answer.