Mathematics notes, unit 1

Numbers up to 100

Textbook Mathematics Year 1 (DLP), Textbook Part 1 and Part 2, pages 1–54

What this chapter covers

You can say which group has more and which has fewer, and match things one to one (1.1)
You can count, say, read and write the numbers 0 to 100 in numerals and in words (1.2, 1.3)
You can show how two numbers make a bigger number, such as 4 and 6 make 10 (1.4)
You can say the place value and the digit value of a digit in a two-digit number (1.6)
You can say which number is more or less, and use "1 more than" and "1 less than" (1.2)
You can arrange numbers in ascending and descending order, and count on and back in ones, twos, fives and tens (1.5)
You can finish simple number patterns (1.9)
You can estimate with "about", "more than" and "less than", and round off to the nearest ten (1.7, 1.8)
You can solve simple number problems (1.10)

1.1Many and few

We can compare two groups. Match the things one to one. The group with things left over has more. The other group is less.

A row of 8 blue counters above a row of 5 orange counters — The blue row has 8 and the orange row has 5. Blue is more. Orange is less.

If two groups match one to one with none left over, they are equal.

There are 6 cups and 6 plates. Are they equal or not equal?

Show answerHide answer

Equal. Each cup has one plate.

1.2Numbers 0 to 20

Count the things, then say the number. Zero (0) means none.

0	1	2	3	4	5	6	7	8	9	10
zero	one	two	three	four	five	six	seven	eight	nine	ten

11	12	13	14	15	16	17	18	19	20
eleven	twelve	thirteen	fourteen	fifteen	sixteen	seventeen	eighteen	nineteen	twenty

For 11 to 20, make a group of 10 first. Then count on. 10 and 3 is 13.

How do you write 16 in words? What is 10 and 8?

Show answerHide answer

sixteen. 10 and 8 is 18.

1.3Making numbers

Two small numbers can make a bigger number. This is a combination.

4 blue counters and 2 orange counters — 4 and 2 make 6. There are 6 counters altogether.

7 blue counters and 3 orange counters — 7 and 3 make 10.

Combinations of 10
0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5

Order does not matter. 7 and 3 make 10, and 3 and 7 make 10 too.

6 and ___ make 10.

Show answerHide answer

4. 6 and 4 make 10.

1.4Numbers 21 to 100

Count in groups of ten. 3 groups of ten is 30. Then count on in ones: 30, 31, 32, 33, 34.

10	20	30	40	50	60	70	80	90	100
ten	twenty	thirty	forty	fifty	sixty	seventy	eighty	ninety	one hundred

Say and write 34 and 45

30 and 4 is 34: thirty-four.
40 and 5 is 45: forty-five.

Watch the spelling. It is forty (no "u" in four), and fourteen keeps the "u".

10 tens make 100 (one hundred).

Write 72 in words.

Show answerHide answer

seventy-two.

1.5Place value and digit value

2 tens blocks and 4 ones blocks — 24 is 2 tens and 4 ones.

A digit is one of the numbers 0 to 9. The number 24 has two digits, 2 and 4.
Place value is the place of the digit: tens or ones.
Digit value is what the digit is worth. In 24, the 2 is worth 20 and the 4 is worth 4.

Number 58	Digit 5	Digit 8
Place value	tens	ones
Digit value	50	8

67 and 76 use the same digits, but they are different numbers. Look at which digit is in the tens place.

In 83, what is the digit value of 8?

Show answerHide answer

8 is in the tens place, so its digit value is 80.

1.6More than and less than

Which is less, 38 or 45?

Compare the tens first. 3 tens is less than 4 tens, so 38 is less than 45.
If the tens are the same, compare the ones: 57 is more than 53.

Number line from 36 to 47 — On a number line the numbers get bigger to the right. 45 is to the right of 38, so 45 is more.

Say it in a sentence: "45 is more than 38. 38 is less than 45."

Which is more, 74 or 69?

Show answerHide answer

7 tens is more than 6 tens, so 74 is more.

1.7Arranging and counting

Ascending order: from the smallest to the biggest, like 1, 2, 3, 4, 5.
Descending order: from the biggest to the smallest, like 5, 4, 3, 2, 1.

1 more than 38 is 39 (the number after).
1 less than 38 is 37 (the number before).
The number between 38 and 40 is 39.

Jumps of 5 from 0 to 25 — Count on in fives: 0, 5, 10, 15, 20, 25.

Jumps of 10 backwards from 90 to 40 — Count back in tens: 90, 80, 70, 60, 50, 40.

Arrange 25, 45 and 35 in ascending order.

Show answerHide answer

25, 35, 45.

1.8Number patterns

A number pattern repeats or follows a rule.

Boxes 3, 8, 3, 8, 3, 8 — 3 and 8 come again and again: 3, 8, 3, 8, 3, 8.

Counting patterns follow a rule too. 82, 84, 86, 88 goes up in twos. 100, 90, 80, 70 goes down in tens.

What comes next? 6, 1, 6, 1, 6, ___

Show answerHide answer

1. The numbers 6 and 1 take turns.

1.9Estimating and rounding off

To estimate is to make a good guess. Use the words about, more than and less than. A bigger box holds more things than a smaller box.

Round off to the nearest ten

Number line from 60 to 70 with 67 marked — 67 is nearer to 70, so it becomes 70.

Number line from 60 to 70 with 65 marked in the middle — 65 is in the middle. A middle number goes up, so it becomes 70.

Look at the ones digit. 0, 1, 2, 3, 4: stay at the tens (22 becomes 20). 5, 6, 7, 8, 9: go up (28 becomes 30).

Round off 74 and 85 to the nearest ten.

Show answerHide answer

74 becomes 70. 85 becomes 90.

1.10Solving problems

Read the problem. Draw a picture or a number line. Then find the answer.

Ali has 45 marbles. Kumar has 5 fewer.

Kumar has 5 less than 45. Count back 5 from 45: 44, 43, 42, 41, 40.
Kumar has 40 marbles.

Make numbers with cards 7 and 2

Put 7 in the tens place: 72. Put 2 in the tens place: 27. The biggest is 72.

Use the cards 4 and 9. What is the biggest two-digit number you can make?

Show answerHide answer

94. Put the bigger digit in the tens place.

Summary

Match one to one to find which group has more or less.
Numbers up to 100 are made of tens and ones. Say and write them in words.
Combinations: 4 and 6 make 10.
Place value is tens or ones. Digit value is what the digit is worth (the 5 in 58 is 50).
Compare the tens first, then the ones.
Ascending is small to big. Descending is big to small.
Estimate with "about", "more than" and "less than". Round off by looking at the ones digit.

Based on the Year 1 textbook, pages 1 to 54.