B1.1 Reading and building numbers to 10 000
A four-digit number has thousands, hundreds, tens and ones: 3251 = 3000 + 200 + 50 + 1. We write a space in five-digit numbers: 10 000. Populations, prices of cars and distances in kilometres use numbers this size.
Example
Write 3251 in expanded form, then decompose it a second way.
- Expanded: 3000 + 200 + 50 + 1.
- Another way: 3200 + 51.
- Both sum to 3251. A zero keeps its place: 4 037 has 0 hundreds.
B1.2 Comparing and ordering to 10 000
Example
Order 8082, 7082, 7332 from greatest to least.
- Compare thousands first: 8082 has the most.
- 7082 and 7332 share thousands; compare hundreds: 7332 is bigger.
- Greatest to least: 8082, 7332, 7082.
- Thousands.
- Then hundreds.
- Then tens, then ones.
- Same number of digits? Compare the first digit that differs.
B1.3 Rounding to the nearest ten, hundred or thousand
Example
Round 3251 to the nearest thousand, hundred and ten.
- Thousand: neighbours 3000 and 4000; the hundreds digit 2 decides (5 or more → up).
- Hundred: neighbours 3200 and 3300; the tens digit 5 decides.
- Ten: neighbours 3250 and 3260; the ones digit 1 decides.
B1.4 Fractions: numerator and denominator
Example
What fraction is shaded, and what does each number mean?
- Shaded: .
- The denominator 5 names the size of the pieces: the whole is cut into 5 equal parts.
- The numerator 3 counts how many of those pieces.
B1.5 Comparing fair shares
Example
3 pizzas among 4 friends or 2 pizzas among 3 friends — which gives the bigger portion?
- 3 among 4: each gets of a pizza.
- 2 among 3: each gets of a pizza.
- Draw both on same-size circles: three quarters covers more than two thirds. .
B1.6 Counting by unit fractions
Example
Count by fourths from 0 to 2.
- 1/4, 2/4, 3/4, 1, 1 1/4, 1 2/4, 1 3/4, 2.
- Four fourths make a whole; 8 fourths make 2.
- The same works for thirds, fifths, sixths, eighths and tenths.
B1.7 Decimal tenths
A tenth is one of ten equal parts of a whole. We write it after a decimal point: 0.6 means 6 tenths. A whole and 6 tenths is 1.6. To compare, look at the whole part first: 1.2 is more than 0.9 even though 9 is bigger than 2.
Example
Order 1.2, 0.6, 0.4 from least to greatest.
- Whole parts: 1.2 has 1; the others have 0. So 1.2 is greatest.
- Tenths: 0.4 has 4 tenths; 0.6 has 6 tenths.
- Least to greatest: 0.4, 0.6, 1.2.
B1.8 Rounding decimals to the nearest whole
Example
Round 4.7 and 4.3 to the nearest whole number.
- Look at the tenths digit: 5 or more rounds up, 4 or less rounds down.
- 4.7 → tenths digit 7 → rounds up to 5.
- 4.3 → tenths digit 3 → rounds down to 4.
B1.9 Fractions and tenths that mean the same
Example
Write 6 tenths as a fraction and as a decimal. Then write one half and one fifth as tenths.
- .
- One half = 5 tenths = 0.5. One fifth = 2 tenths = 0.2.
- A fraction with denominator 10 and a decimal tenth are two ways to write one amount.
Summary
- Thousands, hundreds, tens, ones to 10 000.
- Round from the digit to the right.
- Denominator names the piece; numerator counts pieces.
- Tenths: compare the whole part first.
- n/10 = 0.n.