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B. Number · Number Sense: Numbers to One Million, Integers, Decimals and Fractions

Number Sense: Numbers to One Million, Integers, Decimals and Fractions: Unit Review

A1 B1.1 B1.2 B1.3 B1.4 B1.5 B1.6About 40 minutes
Learning goals
  • I can read, write, build, compare and order whole numbers to one million.
  • I can read, represent, compare and order integers on horizontal and vertical number lines.
  • I can read, write, compare, order and round decimals to thousandths.
  • I can show how fractions and decimals to thousandths are related.
  • I can compare and order integers, decimals and fractions together.

Words to know

one million
1 000 000, or 1000 thousands.
integer
A whole number, its opposite, or zero, like −4, 0 or 7.
opposites
Two integers the same distance from zero on opposite sides, like −6 and 6.
thousandth
One of 1000 equal parts: 1/1000 = 0.001.
repeating decimal
A decimal with digits that repeat forever, like 0.333…
simplest form
A fraction whose numerator and denominator have no common factor except 1.

Let's review!

In this unit you read, wrote, built and compared whole numbers up to one million and described how big numbers are used. You met integers, the numbers below zero, on horizontal and vertical number lines. You worked with decimals to thousandths, rounded terminating and repeating decimals, and connected fractions and decimals. Finally, you put integers, decimals and fractions in order together.

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.

Integers, decimals and fractions on one line−2−10120.31/2= 0.50.751 1/4= 1.25least ← negatives, then 0, then positives → greatest
Order: −1, 0.3, 1/2, 0.75, 1 1/4. Changing fractions to decimals (1/2 = 0.5, 1 1/4 = 1.25) makes them easy to place among the decimals.
Up is greater, down is less−12−8−404850−4−9greaterless← zero
From least to greatest, read up the line: −9, −4, 0, 5. The negative integer farther from zero is the lesser one.

Reading and Writing Numbers to One Million

1

Write 609 084 in words.

2

Write "four hundred thousand thirty" as a numeral.

3

Count forward by 100 000s: 700 000, 800 000, ___, ___

Place Value: Building and Breaking Apart Numbers to One Million

1

Write 358 207 in expanded form.

2

How many thousands are in 358 207? How many hundreds?

3

What number is 6 hundred thousands + 14 ten thousands + 9 ones?

Comparing, Ordering and Using Big Numbers

1

Use >, < or =: 408 950 ___ 480 590

2

Order from least to greatest: 99 900, 909 000, 900 900

3

Is a bus route number used to count, measure or label?

Integers: Numbers Below Zero

1

Write as an integer: 14 degrees below zero.

2

What is the opposite of −30?

3

On a vertical number line, is −5 above or below −2?

Comparing and Ordering Integers

1

Use >, < or =: −11 ___ −6

2

Order from least to greatest: 3, −7, 0, −2

3

Which is warmer: −18 °C or −8 °C?

Decimal Thousandths: Reading, Writing and Showing

1

Write 4.056 in words.

2

What is the value of the 9 in 0.219?

3

Write 1250 g in kilograms.

Comparing and Ordering Decimals to Thousandths

1

Use >, < or =: 0.7 ___ 0.698

2

Order from least to greatest: 2.3, 2.03, 2.303, 2.033

3

Write a decimal between 0.81 and 0.82.

Rounding Decimals: Terminating and Repeating

1

Round 5.274 to the nearest tenth and the nearest hundredth.

2

Round 0.555… to the nearest hundredth.

3

Round 19.6 to the nearest whole number.

4

Is 0.125 terminating or repeating?

Fractions and Decimals to Thousandths

1

Write 7/8 as a decimal.

2

Write 0.36 as a fraction in simplest form.

3

Write 3 1/4 as a decimal.

4

Write 1/3 as a decimal.

Comparing and Ordering Integers, Decimals and Fractions Together

1

Use >, < or =: 3/8 ___ 0.4

2

Order from least to greatest: 0.7, −2, 2/3, 1/2

3

Which is greater: 4/5 or 0.79?

Just for fun

Why are decimal points so good at arguments?

They always know how to make a point!

How to use this review

  • Do one or two sections at a time. You don't have to finish in one sitting.
  • Try every question before you look at the answer. Write your work on paper.
  • Put a check mark beside the ones you got right and a star beside the ones you missed.
  • For each starred question, go back to that lesson, read the worked examples again and try a few more practice questions.
  • Then take the quiz below. Mistakes are information: they show you exactly what to practise next.
Check your understanding

Quiz

1.

How do you write five hundred thousand sixty as a numeral?

2.

How many hundreds are in 74 500?

3.

Which is greatest?

4.

Which integer is least?

5.

What is the opposite of 7?

6.

How do you write "twenty-one thousandths"?

7.

Which is true?

8.

Round 2/3 = 0.666… to the nearest hundredth.

9.

What is 5/8 as a decimal?

10.

Which list is in order from least to greatest?

For parents and teachers

Use the review to find what to practise. Look at which questions your child missed, then revisit:

  • Reading or writing six-digit numbers, missing zeros ("forty thousand six" as 4006): Reading and Writing Numbers to One Million.
  • Expanded form, "how many hundreds/thousands", or regrouping (14 ten thousands): Place Value: Building and Breaking Apart Numbers to One Million.
  • Comparing whole numbers with different numbers of digits, or deciding if a number counts, measures or labels: Comparing, Ordering and Using Big Numbers.
  • Writing integers from words (below zero, below sea level), opposites, vertical number lines: Integers: Numbers Below Zero.
  • Thinking −11 > −6: Comparing and Ordering Integers.
  • Reading or writing thousandths (0.21 for twenty-one thousandths), metric conversions: Decimal Thousandths: Reading, Writing and Showing.
  • Thinking a longer decimal is always greater (0.405 > 0.45): Comparing and Ordering Decimals to Thousandths.
  • Rounding errors, chain rounding, rounding 9s, repeating decimals: Rounding Decimals: Terminating and Repeating.
  • Fraction–decimal conversions (3/8 written as 0.38), simplest form: Fractions and Decimals to Thousandths.
  • Ordering a mixed list of integers, decimals and fractions: Comparing and Ordering Integers, Decimals and Fractions Together.

Celebrate effort and progress, not just right answers. Calculations with these numbers (adding, subtracting, multiplying, dividing, ratios, rates and percents) are in the separate Operations unit.