H. Salvo
1
Table of Contents Unit 1: Numbers
Unit 7: Geometry
Place Value ............................................................................................................................ 4 Sequences .............................................................................................................................. 5 Odd and Even Numbers ....................................................................................................... 6 Rounding ................................................................................................................................ 7 Ordering and Comparing...................................................................................................... 8 Factors .................................................................................................................................... 9
Unit 2: Fractions and Decimals Halving and Doubling Fractions ......................................................................................... 10 Equivalence Between Fractions and Decimals ................................................................ 11 Improper Fractions and Mixed Numbers ........................................................................... 12 Fractions as Percentages ..................................................................................................... 13 Fractions as Proportions and Ratios ..................................................................................... 15
Unit 3: Addition Near Multiples........................................................................................................................ Quick Addition ....................................................................................................................... Adding Decimals ................................................................................................................... Written Method With 2-Digit Addition.................................................................................. Written Method With 3-Digit Addition....................................................................................
16 17 19 20 21
Unit 4: Subtraction Near Multiples ....................................................................................................................... 22 Written Method With 2-Digit Subtraction ............................................................................ 24 Written Method With 3-Digit Subtraction ........................................................................... 25 Subtraction With Decimals .................................................................................................. 26
Unit 5: Multiplication Multiplying by 10 and 100 .................................................................................................... 28 Multiplication Facts ................................................................................................................ 29 Squared Numbers ................................................................................................................ 30 Multiplication .......................................................................................................................... 31 Multiplying Decimals ............................................................................................................... 32 Multiplying by 19 and 21 ...................................................................................................... 33
Triangles ................................................................................................................................ Symmetry .............................................................................................................................. 3D Shapes ............................................................................................................................ Parallel and Perpendicular ................................................................................................ Angles ..................................................................................................................................
Unit 8: Positions, Perimeter and Area Coordinates ......................................................................................................................... 48 Reflection ............................................................................................................................. 49 Translations ............................................................................................................................ 50 Polygon Perimeters .............................................................................................................. 51 Area ...................................................................................................................................... 52
Unit 9: Measuring Measuring ............................................................................................................................. 54 Unit Conversion ..................................................................................................................... 55 Ordering Measurements ...................................................................................................... 56 Rounding Measurements ..................................................................................................... 57 Drawing and M easuring ..................................................................................................... 58
Unit 10: Data Data Analysis ........................................................................................................................ 60 Graphs .................................................................................................................................... 61 Mode ..................................................................................................................................... 64 Probability ............................................................................................................................... 65
Unit 11: Time Time Units .............................................................................................................................. 66 24-Hour Clocks ...................................................................................................................... 67 Time Intervals ........................................................................................................................ 69
Unit 12: Mental Maths Single-Step Word Problems ................................................................................................. 72 Multi-Step Word Problems .................................................................................................... 73 Number Stories ...................................................................................................................... 74 Number Puzzles ...................................................................................................................... 75
Unit 6: Division Dividing by 10 and 100 ........................................................................................................ 34 Divisibility Test .......................................................................................................................... 35 3-Digit Division ....................................................................................................................... 37 3-Digit Division With Remainders ..........................................................................................38 Order of Operations .............................................................................................................. 39
42 43 45 46 47
Review 2 Review 2 .............................................................................................................................. 78
Review 1 Review 1 ................................................................................................................................ 40
2
3
you k
Place Value now? Millions
Hundred Ten Thousands Thousands
1
2
Sequences
Thousands Hundreds Tens Ones Tenths Hundredths
4
3
5
6
7
Did
Whole Numbers
8
9 Decimals
A list of numbers in a special order is called a sequence. We can also call them number patterns.
Example: The number sequence 1, 4, 7 and 10 is counting by 3s. It starts at 1 and jumps 3 numbers every time.
A place value is where a digit is located in a number. Any number to the left of the decimal is a whole number. Any number to the right of the decimal is a part or fraction of a whole number.
Example: In the number 1,456,980.32, the 1 is in the millions place, the 4 is in the hundred thousands place, the 5 is in the ten thousands place, the 6 is in the thousands place, the 9 is in the hundreds place, the 8 is in the tens place and the 0 is in the ones place. The 3 and the 2 after the decimal represent a part of a whole number. The 3 is in the tenths place, and the 2 is in the hundredths place.
thousands
19,213
ones
123.45
109,674 31,312
747,380 69,333
7.89 24.68
975,250
252,454
135.79
87,567 456,789
46,912 396,864
1.23 34.56
hundredths
2. Each number has been partitioned. Write the missing numbers. 196,851 555,555 1,234,789 4
? + 90,000 + 6,000 + ? + 50 + 1 ________________________________________________________________ ? + 50,000 + ? + 500 + 50 + ? ________________________________________________________________ ? + 200,000 + ? + 4,000 + ? + ? + 9 ________________________________________________________________
1
2
3
4
5
6
7
8
9
10
3. Count by ones. 1,097
1,098
1,099
4. Count back by ones. 5,432
1. What does each red digit represent? Write. 59,156
0
5,431
5. Count by tens. 10,790
6. Count back by tens. 67,850
7. Count by hundreds. 1,530
8. Count back by hundreds. 55,380
9. Count by thousands. 75,678
10. Count back by thousands. 97,087 5
Odd and Even Numbers
Rounding
11. Colour the odd-numbered balloons red and the even-numbered balloons blue.
The purpose of rounding numbers is to make them simpler while staying close to the original number. We can round numbers to the nearest ten, hundred, thousand, etc. If the digit is 5 or more, then round up. Round down if the digit is less than 5.
Example:
nearest ten
495
325
75
1,000
nearest hundred
nearest thousand
round up
17
20
168
200
8,786
9,000
round down
13
10
349
300
7,320
7,000
When rounding to the nearest whole number, pay attention to the decimal places.
Example: 1 decimal place round to nearest whole number
25
545
740
320
910
230
650
680
17.3
17
2 decimal places 9.59
10
12. Round the numbers to the nearest 10, 100 and 1,000. Number
Nearest 10
Nearest 100
Nearest 1,000
2,917 6,159 11,864 35,675 9,213 29,415 79,919
2,920
2,900
3,000
13. Round to the nearest whole number. Number
50
6
195
215
840
1.19 7.8 18.14 23.07 46.68
Nearest whole number
1
Number
89.57 99.99
Nearest whole number
90
1.7 58.86 33.49 7
Ordering and Comparing
Factors
Ordering numbers is fun! We order numbers according to a pattern (least to greatest, greatest to least, etc.). When ordering negative and positive numbers, the negative number will always be less than the positive number. We use > (greater than) and < (less than) to compare numbers.
Example: Order the following numbers from least to greatest:
A factor is a whole number that divides into another number evenly. The greatest common factor (GCF) is the highest number that divides evenly into two or more numbers.
Example:
Factors
7, -1, 2, 4, 3, 0, 6, 1, 5, -2.
28 35
-2,-1, 0, 1, 2, 3, 4, 5, 6, 7
187 > 165
-5 < 0
40
14. Order the lists of numbers from least to greatest. (456,789) (135,987) (246,135) (357,025)
42 1
66 1
1
2
(1,000,000) (999,990) (471,036) (257,764)
4 5
8
(4.9) (4.8) (4.6) (4.7)
10
20
(45.69) (45.70) (45.68) (45.71)
40
17. Find the greatest common factor (GCF) for each pair of numbers.
15. Compare the numbers using > or <.
8
7 is the GCF
16. Look at the factor tomato and find the factors for the remaining tomatoes.
Compare the following numbers using > or <.
-15 < 15
1, 2, 4, 7, 14, 28 1, 5, 7, 35
59,789
57,989
908,754
789,123
5,321
-79
79
415
-754
-7
6,123 0
3.90
3.97
7.86
5.76
11.43
11.34
3.5
7.1
6.1
9.1
8.3
4.4
18, 36
28, 49
27, 33
16, 64
18_____________________ 28_____________________ 36_____________________ 49_____________________ GCF___________________ GCF___________________ 27______________________ 16_____________________ 33_____________________ 64_____________________ GCF___________________ GCF___________________
24, 36
24_____________________ 36_____________________ GCF___________________
36, 54
36_____________________ 54_____________________ GCF___________________ 9