Primary 4 Numbers to 100 000 Study Guide

Primary 4 numbers to 100 000 in six short steps: place value and words, comparing, number patterns, growing figures, repeating units and rounding. Each step has something to tap, and worked examples follow.

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How does place value work up to 100 000?

Each place is worth 10 of the place on its right.

A five-digit number has ten thousands, thousands, hundreds, tens and ones. The digit tells how many; the place tells what each one is worth. Reading a number, comparing two numbers, rounding and finding a pattern all start from the places.

In this chapter, your child learns to:

  • read and write numbers up to 100 000 in numerals and in words;
  • find the value of a digit from its place;
  • compare and order numbers, starting from the greatest place;
  • find the rule in a number pattern, a growing figure or a repeating unit;
  • round to the nearest 10, 100 or 1000, and use ≈ for an estimate.
1

Step 1

Place value and numbers in words

A digit's value is the digit times its place. In 83 506 the digit 3 stands in the thousands place, so it is worth 3 thousands, which is 3000. A place with nothing in it still keeps its 0, so the other digits stay where they belong. When a place has 10 or more, such as 14 hundreds, rename 10 of them as 1 thousand.

Tap a digit

83 506 = 80 000 + 3000 + 500 + 6
In words: eighty-three thousand, five hundred and six
Tap a digit to see its place and its value.
Try it

What is the value of the digit 6 in 26 914?

▶ Watch the lesson: Place value and wordsPractise 10 questions →
2

Step 2

Comparing and ordering numbers

The first place that differs decides. Line the numbers up by place and start at the greatest place. While the digits agree, move one place right. The first place where they differ tells which number is greater. Ascending order means smallest first; descending order means greatest first.

Ascending order: smallest first
72615
72165
71625
Arrange 72 615, 72 165 and 71 625 in ascending order. Start at the greatest place.
Try it

Which number is the greatest: 58 214, 58 241 or 58 124?

▶ Watch the lesson: Compare and orderPractise 6 questions →
3

Step 3

Number patterns: finding the rule

Find the gaps, then follow their direction. Find the gap between each pair of neighbouring terms. If every gap is the same, the rule is that amount more or less each time. If two gaps take turns, the pair of steps is the rule. Check the rule on the next term you were given.

52 30051 60050 90050 200?48 800700 less700 less700 less700 less700 less
The terms are getting smaller. How much smaller is each one?
Try it

What is the next term? 31 450, 32 450, 32 400, 33 400, 33 350, ___

▶ Watch the lesson: Number patternsPractise 6 questions →
4

Step 4

Growing patterns with figures

Figure 1 starts it; every gap adds the same. Count what each figure holds and put the counts in a table. When the difference between neighbouring figures stays the same, each gap adds that amount. From figure 1 to figure 12 there are 11 gaps. To work back from a count, minus figure 1's count first, then divide by the amount each gap adds.

Figure 1Figure 2Figure 3
Figure
1
2
3
…
?
Matchsticks
4
+3
7
+3
10
…
61
Figure 1 uses 4 matchsticks, figure 2 uses 7 and figure 3 uses 10. Which figure uses 61?
Try it

Figure 1 uses 4 matchsticks and each figure adds 3 more. How many matchsticks does figure 15 use?

▶ Watch the lesson: Growing figuresPractise 7 questions →
5

Step 5

Repeating patterns and positions

Cut the pattern where it begins again. Find the group of items that repeats, and count how many it holds. Divide by that number to find the whole units; the remainder is the start of an unfinished unit. Read the leftover items off the start of the unit. A remainder of 0 means the last item ends a whole unit.

…1 unit = 7 shapes1 unit again84 shapes12 whole units6 left over
90 shapes repeat: 4 circles, then 3 squares, and so on. How many squares are there?
Try it

A pattern repeats A, B, B, C, A, B, B, C, and so on. What is the 30th letter?

▶ Watch the lesson: A repeating unitPractise 8 questions →
6

Step 6

Rounding to the nearest 10, 100 or 1000

The next digit decides. Find the place you are rounding to, then look at the digit just to its right. 5 and greater than 5 rounds up; 4 and smaller than 4 rounds down. Put zeros in the places after it. Write ≈ for a rounded answer, with the place in brackets.

6385263 80063 900halfway63 852
63 852 ≈ 63 900 (to the nearest 100)
The next digit is 5, in the tens. 5 and greater than 5 rounds up.
Try it

Round 49 960 to the nearest 100.

▶ Watch the lesson: RoundingPractise 8 questions →

Primary 4 numbers to 100 000 questions, worked step by stepWork each one out on paper, then open a hint or reveal the working line by line.

Place value and wordsBasic

Write 4 ten thousands, 23 hundreds and 7 ones in numerals and in words.

23 hundreds is more than one digit can hold. Rename 20 of the hundreds as thousands.
  1. 4 ten thousands = 40 000.
  2. 23 hundreds = 20 hundreds and 3 hundreds = 2300.
  3. 40 000 + 2300 + 7 = 42 307. There are no tens, so the tens digit is 0.
  4. In words: forty-two thousand, three hundred and seven.
Answer: 42 307, forty-two thousand, three hundred and seven
Number patternsBasic

Find the missing term in the number pattern. 86 450, 85 200, ____, 82 700, 81 450

Find the gap between the first two terms, and check it on the last two.
  1. 86 450 − 85 200 = 1250. The terms are getting smaller.
  2. Check: 82 700 − 81 450 = 1250. Each term is 1250 less.
  3. 85 200 − 1250 = 83 950.
  4. Check: 83 950 − 1250 = 82 700, the next term given.
Answer: 83 950
RoundingIntermediate

A museum had 49 652 visitors in June and 38 471 visitors in July. Round each number to the nearest 1000, then estimate the total number of visitors.

For the nearest 1000, the hundreds digit decides. Round first, then add.
  1. 49 652: the hundreds digit is 6, so round up. 49 652 ≈ 50 000.
  2. 38 471: the hundreds digit is 4, so round down. 38 471 ≈ 38 000.
  3. Estimated total: 50 000 + 38 000 = 88 000.
Answer: about 88 000 visitors
Growing figuresIntermediate

Identical squares of side 3 cm form a pattern. Figure 1 has 3 squares, Figure 2 has 5 squares and Figure 3 has 7 squares. Find the area of Figure 30.

Find how many squares each gap adds, and how many gaps there are from Figure 1 to Figure 30.
  1. 5 − 3 = 2 and 7 − 5 = 2, so each gap adds 2 squares.
  2. From Figure 1 to Figure 30 there are 30 − 1 = 29 gaps.
  3. Squares in Figure 30: 3 + 29 × 2 = 61.
  4. One square: 3 × 3 = 9 cm². Area: 61 × 9 = 549 cm².
Answer: 549 cm²
A repeating unitChallenge

Siti makes a string of 100 beads. The beads repeat in this order: 3 blue, 2 yellow, 1 green. How many yellow beads are there, and what colour is the 100th bead?

One repeating unit is 6 beads. Divide, then read the leftover beads off the start of a unit.
  1. 1 unit = 3 + 2 + 1 = 6 beads. 100 ÷ 6 = 16 R 4.
  2. 16 whole units hold 16 × 2 = 32 yellow beads.
  3. The 4 left over are 3 blue and 1 yellow. Yellow beads: 32 + 1 = 33.
  4. The 100th bead is the 4th bead of a unit, which is yellow.
Answer: 33 yellow beads; the 100th bead is yellow
7

Step 7

Check yourself

Five quick questions from across the chapter. Nothing is saved; each reply points to the practice set that fits.

1. Which is seventy thousand, three hundred and eight in numerals?

2. Which number is the smallest: 90 512, 90 152 or 90 215?

3. Figure 1 has 6 squares. Each figure has 4 more squares than the one before. Which figure has 46 squares?

4. Shapes repeat: circle, circle, square, triangle, and so on. What is the 24th shape?

5. Which number rounds to 25 000 to the nearest 1000?

0/5
Answer all five to see where to practise next.
For parents

Using the steps together. Before each tap, ask your child to say what they expect: which place decides, which gap comes next, how many are left over. Then tap and compare. Saying numbers aloud in words, such as forty-two thousand, three hundred and seven, helps your child hear where each zero belongs.

The worked examples begin with place value and patterns and end with a string of beads. Let your child write the working first, then reveal one line at a time and check each line against theirs.

More study guides

Before this: Primary 3 Numbers up to 10 000Next: Factors and MultiplesPrimary 5 Numbers to 10 MillionPrimary 4 Decimals study guidePrimary 4 Four Operations of Whole Numbers study guide
Lessons and practice

P4 Numbers to 100 000 lessons and practice

6 lesson videos and 48 questions across six subtopics, from Basic to Challenge, each with a worked solution.

Watch and practise →