Number Multiplication and Division
NZC LEVEL 2
Number Strategies NAS2-1 Use simple additive strategies with whole numbers and fractions. Number Knowledge NAK2-1 Know forward and backward counting sequences with whole numbers to at least 1000. NAK2-2 Know the basic addition and subtraction facts. NAK2-3 Know hoe many ones, tens, and hundreds are in whole numbers to at least 1000. NAK2-4 Know simple fractions in everyday use. |
NZC LEVEL 3
Number Strategies NAS3-1 Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages. Number Knowledge NAK3-1 Know basic multiplication and division facts NAK3-2 Know counting sequences for whole numbers. NAK3-3 Know how many tenths, tens, hundreds, and thousands are in whole numbers. NAK3-4 Know fractions and percentages in everyday use. |
NZC LEVEL 4
Number Strategies and Knowledge NA4-1 Use a range of multiplicative strategies when operating whole numbers. NA4-2 Understand addition and subtraction of fractions, decimals and integers. NA4-3 Find fractions, decimals and percentages of amounts expressed as whole numbers, simple fractions and decimals. NA4-4 Apply simple linear proportions, including ordering fractions. NA4-5 Know the equivalent decimal and percentage forms for everyday fractions. NA4-6 Now the relative size and place value structure of positive and negative integers and decimals to three decimal places. |
NZC LEVEL 5
Number Strategies and Knowledge NA5-1 Reason with linear proportions. Use prime numbers, common factors and multiples and powers (including square roots). NA5-3 Understand operations on fractions, decimals, percentages, and integers. NA5-4 Use rates and ratios. NA5-5 Know commonly used fraction, decimal, and percentage conversions. NA5-6 Know and apply standard form, significant figures, rounding, and decimal place value. |
In this unit you will learn:
1) Multiplying by tens, hundreds and thousands
2) Multiplication and Division using Proportional Adjustment
3) Partitioning using Place Value
4) Multiples, Primes and Squares
5) Using Algorithms to Multiply
6) Powers
7) Multiplying and Dividing Integers
8) Order of Operations
1) Multiplying by tens, hundreds and thousands
2) Multiplication and Division using Proportional Adjustment
3) Partitioning using Place Value
4) Multiples, Primes and Squares
5) Using Algorithms to Multiply
6) Powers
7) Multiplying and Dividing Integers
8) Order of Operations
Understanding Multiplication and Division
- X, multiply, times, of, product and lots of all mean multiplication.
- The order of multiplication does not matter, e.g. 2 x 3 = 3 x 2.
- A basic fact can be written in at least four different ways.
- Two numbers that multiply together to give a number are called its factors, e.g. 2 x 3 = 6, so 2 and 3 are factors of 6.
- Division is the opposite of multiplication.
1) Multiplying and Dividing by tens, hundreds and thousands
- Using multiples of tens can simplify some multiplication and division problems.
2) Multiplication and Division using Proportional Adjustment
- When multiplying, doubling on number and halving the other gives the same answer.
- Doubling and halving is a multiplication strategy that recombines the factors of numbers.
- Thirding means dividing a number by 3.
- Trebling means multiplying a number by 3.
- Proportional adjustment is the name given to these strategies.
- Halving and halving a number is the same as dividing it by 4.
3) Partitioning using Place Value
- Numbers can be split up (or partitioned) according to their place value to make multiplication and division easier. For example, 213 can be written as 200 + 10 + 3. 213 x 6 = is the same as 200 x 6 + 10 x 6 = 3 x 6.
- A multiplication table or (array) can be used to set out a multiplication problem.
4) Multiples, Primes and Squares
- If a number only have two factors, it is called a PRIME number.
- A number multiplied by itself is a square number. e.g. 9 is 3 x 3 or 3 squared.
- Skip counting gives the multiples of a whole number. The multiples of 2 are 2, 4, 6, 7, 8, 10, 12, 14, 16,...
Check out these great websites on Factors, Multiples and Primes. Have fun!
http://www.romsey.hants.sch.uk/maths/number_c.html
http://nrich.maths.org/8705
http://nrich.maths.org/5448/solution
5) Using Algorithms to Multiply
- We can multiply bigger numbers using a grid or the standard algorithm.
- The standard algorithm is called long multiplication because the calculation is set out longways down the page.
- Understanding place value is important for long multiplication.
- It is important to estimate the answer before working it out so you can check your answer is sensible.
Have a look at the video clip to talk you through the stages or go to these sites and have a go!
http://www.homeschoolmath.net/teaching/md/multiplication_algorithm.php
https://www.khanacademy.org/math/arithmetic/multiplication-division/multi_digit_multiplication/v/multiplication-6-multiple-digit-numbers
http://faculty.atu.edu/mfinan/2033/section13.pdf
http://www.homeschoolmath.net/teaching/md/multiplication_algorithm.php
https://www.khanacademy.org/math/arithmetic/multiplication-division/multi_digit_multiplication/v/multiplication-6-multiple-digit-numbers
http://faculty.atu.edu/mfinan/2033/section13.pdf
6) Powers
- A power is also called an exponent or an index. If we talk about more than one power, we say powers, exponents or indices,
- Numbers in index form have a base and an index.
- Squaring means to the power of 2. 4 squared is the same as 4 x 4.
- The inverse of squaring is taking the square root.
- There are other powers, e.g. cubed and cubed root.
7) Multiplying and Dividing Integers
- When two positive numbers are being multiplied or divided the answer is positive.
- When a positive and a negative number are multiplied together the answer is negative.
- When one number is divided by another, if one of the numbers is negative the answer is negative.
- Khan Academy is a great site to visit to walk you through adding and diving integers.
- Here is another brilliant site...
8) Order of Operations
The accepted order of operations is remembered by the word BEDMAS
B Brackets comes first (3 + 4 ) = 7
E Exponents (or indices)
D Division and Multiplication come next, working left to right across the page
M 2 x 6 divided by 3 = 12 divided by 3 = 4
A Addition and Subtraction come next, working left to right across the page
S 4 + 7 - 3 = 11 - 3 = 8
B Brackets comes first (3 + 4 ) = 7
E Exponents (or indices)
D Division and Multiplication come next, working left to right across the page
M 2 x 6 divided by 3 = 12 divided by 3 = 4
A Addition and Subtraction come next, working left to right across the page
S 4 + 7 - 3 = 11 - 3 = 8