4 + 4 = = 1 5 x 2 = 10

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Philippa Bruce
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1 Beginning Multiplication Ask your child... "Have you ever seen a multiplication problem?" Explain: "Instead of a plus ( + ) sign or a minus ( - ) sign a multiplication sign ( x ) is used." Have child to look at the equations below and circle the multiplication sign = = 1 5 x 2 = 10 Make sure your child knows these basic symbols by the following test. Have them circle the correct sign in each row. In line 1. plus 2. minus 3. equals 4. multiplication or times 1. x - = = x 3. + x - = 4. - = + x Circle all the adding problems. Put a box around the subtraction problems. Put an x on all the Multiplication problems = 6 6 x 1 = = = = 9 2 x 2 = 4 5 x 5 = = 4 3 x 2 = 6

2 Multiplication is adding the same number to itself = 6 There are three 2 s added together. We can write this adding problem as a multiplication problem. 3 x 2 = 6 Look at this equation = 20 Count the 4 s. How many fours are there? 5 So we can write the Multiplication problem as 4 x 5 = 20 Can you make a multiplication problem for the following adding problems? = 12 How many 3 s? 3 x = = 6 How many 2 s? x = = 25 How many 5 s x = 25

3 Multiplying by zero is easy. Zero times any number is zero. 0 x 0 = 0 0 x 1 = 0 0 x 2 = 0 0 x 3 = 0 0 x 4 = 0 0 x 5 = 0 0 x 6 = 0 0 x 7 = 0 0 x 8 = 0 0 x 9 = 0 No matter what you multiply by zero the answer is zero. Do these equations. 4 x 0 = 7 x 0 = 0 x 1 = 5 x 0 = 7 x 0 = 0 x 6 = 0 x 0 = 9 x 0 = 8 x 0 = 20 x 0 =

4 Multiplying by 1 Any number that you multiply by 1 equals that number. One four is four. One nine is nine. Look at the following equations. 1 x 0 = 0 1 x 1 = 1 1 x 2 = 2 1 x 3 = 3 1 x 4 = 4 1 x 5 = 5 1 x 6 = 6 1 x 7 = 7 1 x 8 = 8 1 x 9 = 9 Now you write the answers. 1 x 4 = 1 x 9 = 1 x 5 = 1 x 8 = 1 x 2 = 1 x 6 = 1 x 3 = 1 x 1 = 1 x 7 = 1 x 0 =

5 No matter how you write the problem the answer is the same. 3 x 1 = 3 or 1 x 3 = 3 Look at the following equations, fill in the blanks, the answer is the same. The first one is done for you. 4 x 1 = 4 or 1 X 4 = 4 3 x 2 = 6 or X 3 = 6 6 x 0 = 0 or X 6 = 0 Do the following problems. 1 x 0 = 7 x 0 = 1 x 2 = 1 x 9 = 5 x 0 = 6 x 1 = 1 x 4 = 4 x 0 = 0 x 0 = 1 x 5 = 8 x 1 = 1 x 3 =

6 Multiplying by 2. Can you count by two s? If you can count by two s you can multiply by two s. Do you know what is? Right! 4 Then you know 2 x 2. A number added to itself is multiplying by 2. Work the following problems = = = = = = = = = = = 8 How many 4 s? 2 So 4 x 2 = 8 or 2 x 4 = 8

7 Multiply by two. 1 x 2 = 2 x 2 = 3 x 2 = 4 x 2 = 5 x 2 = 6 x 2 = 7 x 2 = 8 x 2 = 9 x 2 = 0 x 2 = Count by two s. 2,, 6,,, 12, 14,,, 20 Work these adding problems = = = = = =

8 Mixed problems test. 0 x 2 = 2 x 2 = 1 x 2 = 4 x 2 = 5 x 1 = 1 x 7 = 3 x 2 = 1 x 0 = 9 x 2 = 2 x 4 = 0 x 2 = 8 x 1 = 7 x 0 = 6 x 2 = 3 x 1 = 8 x 2 = 5 x 2 = 0 x 9 = 0 x 3 = 2 x 7 = 3 x 0 = 1 x 8 = 3 x 1 = 1 x 9 = 4 x 0 = 5 x 0 = 2 x 6 =

9 Two's Notice: When counting by two's the numerals 2, 4, 6, 8, and 0 keep showing up. They always will. As a matter of fact, you can tell if a number is divisible by 2. If it ends in 2, 4, 6, 8, or 0, it is divisible by 2. Look at these numbers: 214, 677, 2018, 91, 444 Which are divisible by two? (214, 2018, and 444) The other two numbers 677 and 91 don't end in 2, 4, 6, 8, or 0 Therefore, they are not divisible by 2. When you are multiplying by two and your answer doesn't end in one of these numerals, your answer is wrong. Notice the answers below. Look for 2,4,6,8,0. 2 x 1 = 2 2 x 3 = 6 2 x 4 = 8 2 x 5 = 10 2 x 6 = 12 2 x 7 = 14 2 x 8 = 16 2 x 9 = 18 2 x 10 = 20 2 x 11 = 22 2 x 12 = 24

10 Three's The 3's are great fun! Remember the numerals 3, 6, and 9, because when you get to double digits you will see them again, but they are hidden. Look at the number 12. It has a 2 in the ones place and a 1 in the ten's place. add the two numbers together. (1 + 2 = 3) Our 3 was hidden, but it was there. NOW, look at 15 (1 + 5 = 6) There's our 6. Look at 18 (1 + 8 = 9) and there's our nine. Find the hiding numbers 3, 6, and 9 in the following numbers. 21, 24, 27, 30, 33, and 36 COOL! It keeps repeating 3,6, and 9. This lesson will be even important later when we learn our six's and nine's. 3 x 0 = 0 3 x 1 = 3 3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 3 x 5 = 15 3 x 6 = 18 3 x 7 = 21 3 x 8 = 24 3 x 9 = 27 3 x 10 = 30 3 x 11 = 33 3 x 12 = 36

11 Practice x5 x 7 x8 x6 x x3 x3 x 3 x9 x3 0,1,2, and 3 s Mixed Practice x5 x 7 x8 x6 x x3 x1 x 4 x9 x0

12 Four's The same rule in multiplication applies in our 4's as with our 2's. (The answer must end with 2, 4, 6, 8, or 0) NOW LOOK! You know your 0 s, 1 s, 2 s, and 3 s so you already know (4x0 or 0x4) (4x1 or 1x4) (4x2 or 2x4) and (4x3 or 3x4) This means you already know 4 of your fours. 4 x 0 = 0 4 x 1 = 4 4 x 2 = 8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 4 x 6 = 24 4 x 7 = 28 4 x 8 = 32 4 x 9 = 36 4 x 10 = 40 4 x 11 = 44 4 x 12 = 48

13 Notice the 0,2,4,6, and 8. Practice Count by fours Fill in the blanks Practice what you ve learned x5 x 7 x8 x6 x x3 x4 x 4 x9 x4

14 Five s Counting by Five s is multiplying by five s When Multiplying by five your answer will always end in 5 or zero. ALWAYS! Lets count by five s Multiply by 5. 5x1= 5x2= 5x3= 5x4= 5x5= 5x6= 5x7= 5x8= 5x9= 5x10= 5x11 5x12

15 Six s Did you learn your three s? Good! It will help you with your six s. You can double your answer on your three s and you ve learned your six s. 3x1 = 3 6x1 = = 6 3x2 = 6 6x2 = = 12 Let s Practice. Take the answer to the three s and double them to get the answers to six s. 3x3=9 so 6x3 is the same as which is. 3x4=12 so 6x4 is the same as which is. 3x5=15 so 6x5 is the same as which is. 3x6=18 so 6x6 is the same as which is.

16 3x7=21 so 6x7 is the same as which is. More Practice: x1= 3 so 6x1= 3x2= 6 so 6x2= 3x3= 9 so 6x3= 3x4= 12 so 6x4= 3x5= 15 so 6x5= 3x6= 18 so 6x6 = 3x7=21 so 6x7= 3x8 = 24 so 6x8 = 3x9=27 so 6x9= 3x10= 30 so 6x10= 3x11=33 so 6x11= 3x12=36 so 6x12=

17 Seven s Count by 7 s Your getting to know your 1 s, 2 s, 3 s, 4 s, 5 s, and 6 s. So you already know the 7 s up to 6x7=42. Now we just have to learn the rest. Practice 7x 1= 7x 2= 7x 3= 7x 4= 7x 5= 7x 6= 7x 7= 7x 8= 7x 9= 7x10= 7x11= 7x12= x7 x 2 x3 x6 x

18 x8 x9 x1 x7 x7 Eight s Just like we doubled the answers to our three s to get the answers to our sixes we can double the answers to the fours to get answers for our eight s. ALSO... answers will end with 0,2,4,6, or 8. 8x 1= 8 4x 1 = 4 8x 2= 16 4x 2 = 8 8x 3= 24 4x 3 = 12 8x 4= 32 4x 4 = 16 8x 5= 40 4x 5 = 20 8x 6= 48 4x 6 = 24 8x 7= 56 4x 7 = 28 8x 8= 64 4x 8 = 32 8x 9= 72 4x 9 = 36 8x10=80 4x10 = 40 8x11=88 4x11 = 44 8x12=96 4x12 = 48 Practice x7 x 2 x3 x6 x4

19 More Practice x8 x9 x1 x8 x x5 x 0 x2 x6 x4 Count by 8 s Fill in the blanks Count by 4 s Fill in the blanks.

20 Nine s (The nine s are fun!) What is so fun about the Nine s? The 9! There are hidden nines in every answer. Let s look. 9x1 = 9 Here s a 9. It s plain to see. 9x2 = 18 Here s a 9 too. 18 or 1+8 equals 9 9x3 = 27 Here s another or 2+7 equals 9 9x4 = 36 Here s another or 3+6 equals 9 9x5 = 45 Here s another or 4+5 equals 9 9x6 = 54 Here s another or 5+4 equals 9 9x7 = 63 Here s another or 6+3 equals 9 9x8 = 72 Here s another or 7+2 equals 9 9x9 = 81 Here s another or 8+1 equals 9 9x10=90 Here s another or 9+0 equals 9 9x11=99 Here are two 9 s. They are plain to see. 9x12=108 Here s another or equals 9 Practice x8 x9 x1 x9 x9

21 More practice x5 x 0 x2 x6 x x3 x9 x1 x9 x x9 x 0 x2 x3 x9 Count by nine Fill in the blanks

22 Ten s You have made it to the ten s. They are so easy! All you have to do is put a zero on the number that you multiply 10 by. If you multiply 3 by 10 add a zero to the right of the number 3 and you have 30. 3x10= 30 Try the following x5 x 1 x2 x6 x x3 x9 x1 x7 x

23 x 8 x 6 x11 x12 x9 Eleven s Like the ten s, the eleven s are very easy. you can just write the number that you are multiplying 11 by two times with numbers 1-9. Look! 11x1 is 11 two 1 s 11x2 is 22 two 2 s 11x3 is 33 two 3 s 11x4 is 44 two 4 s 11x5 is 55 two 5 s 11x6 is 66 two 6 s 11x7 is 77 two 7 s 11x8 is 88 two 8 s 11x9 is 99 two 9 s Practice x5 x 1 x2 x6 x4

24 x3 x9 x8 x7 x5 More practice Count by 11 s Fill in the blanks To multiply ten with eleven just add your zero to the right of the number 11. (110) Copy the following problems 5 times. 11 x 11= x 12 = 132

25 Twelve s You already know your multiplication to 11. Remember that you can reverse a problem and it has the same answer. There is only one more problems to learn. 12x12 = 144 Let s practice x5 x 1 x2 x6 x x3 x9 x8 x7 x x12 x10 x11 x6 x4

26 x3 x9 x8 x7 x5 Practice, practice, practice! x0 x 1 x8 x6 x x3 x9 x8 x7 x x12 x10 x11 x6 x x3 x9 x8 x7 x x5 x 1 x2 x6 x4

27 x3 x9 x8 x7 x x12 x10 x11 x6 x x3 x9 x8 x7 x x5 x 1 x2 x6 x x3 x9 x8 x7 x

28 x 9 x10 x11 x6 x x3 x2 x8 x7 x x4 x 9 x8 x3 x x9 x5 x6 x7 x x1 x 4 x11 x8 x x8 x9 x3 x8 x5

Section 1.1 Patterns in Division

Section 1.1 Patterns in Division Divisibility refers to whether or not a number is divisible by another number. If a number divides evenly into another number (no remainder), then it is divisible by that