Download Number Rules - Planet Maths

TOPIC
Number Rules
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Strand:
Strand unit:
Curriculum Objectives
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Know simple properties and rules about brackets and priority of operation.
Identify relationships and record symbolic rules for number patterns.
Looking back: What the 5th class programme covered
1. Exploration of simple rules and properties about brackets and priority of operation.
2. Identification of number patterns.
Maths skills used in this topic
1. Reasoning: Reason, investigate and hypothesise with patterns and relationships in mathematics.
2. Understanding and recalling: Understand and recall facts, definitions and formulae.
Concrete materials
Grid of small squares (for activities on top of page 167)
Vocabulary
Square (a number)
Teaching points
1. In the absence of brackets, the rules governing operations are as follows:
If there are only + and – signs, work from left to right. x or ÷ signs take precedence over +
and – and must be worked first. Hence BOMDAS:
1. Brackets
2. Of
3. Multiply
4. Divide
5. Add
6. Subtract
However, this is not to say that addition precedes subtraction, not necessarily. When x and ÷
have been worked, proceed from left to right. For example:
10 – 8 ÷ 2 + 9 =
10 – (8 ÷ 2) + 9 =
10 – 4 + 9 =
(10 – 4) + 9 = 15
Note that many variations of BOMDAS exist, including some which use O for Orders (powers
– exponents).
2. Encourage children to use brackets all the time to avoid ambiguity. Brackets make maths a lot
easier because the rule is simple.
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Oral and mental activities
Fans:
Add 9 to a variety of low numbers (add 10 take 1 away). Use larger the numbers, e.g. 178 add 9,
and repeat with lots of numbers, adding 90 (add 100 take 10 away). Show the first 3 multiples of a
variety of tables. Count back in a variety of multiples from a large number. Show the product of a
variety of factors. Show the factors for various multiples.
Choir of number:
Counting in 10s, 100s, 1,000s, 10,000s forwards and backwards.
Topic suggestions
1. Place lots of emphasis on the importance of brackets.
2. Have children experiment with 3-number questions to see the effect of having the brackets in
different positions, e.g. compare (9 – 5) – 2 with 9 – (5 – 2).
Activity A
1. Look at the horizontal line of numbers. Questions such as:
(d) Find 4 multiples of 9. (27, 36, 45, 81)
(a) Find the greatest prime number. (43)
(e) What is the third odd number? (21)
(b) Find the smallest prime number. (11)
(f) What is the fourth even number? (64)
(c) Find 4 square numbers. (36, 49, 64, 81)
(g) Add the second number to the second last number. (112)
2. Look at the list of symbols. What are their names and where might they be used or seen?
(a) backslash – used in computing
(b) forward slash seen in website addresses
(c) pi, letter of Greek alphabet 3.14 approximately
(d) not equal to
(e) club – suit in deck of cards
(f) diamond – suit in deck of cards
(g) heart – suit in deck of cards
(h) spade – suit in deck of cards
(i) musical note – quaver, a half-beat
(j) female – Venus (think of it as a lady with a cross in front of a mirror praying for her
knight to return safely)
(k) male – Mars (think of it as a knight going into battle with sword and shield)
(l) per cent
(m) US dollar
(n) pound sterling
(o) degrees (of temperature or angle measure)
(p) infinity
(q) square brackets
(r) curly brackets, braces
(s) approximately
(t) therefore
Note: The numbers 1–20 are there only to help you refer to the symbols: symbol 1,
symbol 2, etc.
Differentiation
Lower attainers:
Separate activity sheet
Higher attainers:
1. Separate activity sheet
2. The % sign is also a mathematical sign for ‘modulus’ which is the remainder when 2 numbers
are divided.
Thus:
20 % 3 = 2 (20 ÷ 3 = 6 r2)
20 % 5 = 0 (20 ÷ 5 = 4 r0)
20 % 6 = 2 (20 ÷ 6 = 3 r2)
20 % 7 = 6 (20 ÷ 7 = 2 r6)
20 % 8 = 4 (20 ÷ 8 = 2 r4)
This operation is used by computers to compute random numbers of a certain magnitude.
The computer first computes any random number. If the programmer wants a random
number between 1 and 10 s/he then programs the computer to output the random number
% 10. This generates a number between 0 and 9 (i.e. the only possibilities when a number
is divided by 10 is a remainder of 0, 1, 2 ... 9) A unit is then added to this number to ensure
the number is between 1 and 10.
Topic
Topic
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1. Make patterns similar to the ones in your book.
1. Work out the answers by doing the question inside the brackets first.
(a) (9 + 3) – 8 = ___ (b) (10 + 4) – 5 = ___ (c) (8 + 8) – 1 =
___ (d) (10 – 2) + 5 = ___
(e) (8 – 7) + 6 = ___ (f) (7 – 7) + 6 = ___ (g) 12 + (10 – 3) = ___ (h) 8 + (7 – 2) = ___
(i) 9 + (6 – 6) = ___ (j) 11 – (4 + 4) = ___ (k) 12 – (5 + 6) = ___
(l) 9 – ( 4 + 5) = ___
2. (a) (4 x 7) + 6 = ___ (b) (2 x 8) + 5 = ___ (c) (8 x 9) + 12 = ___
(d) (7 x 7) – 6 = ___
(e) (6 x 8) – 5 = ___ (f) (5 x 10) – 1 = ___ (g) 8 + (4 x 4) = ___
(h) 7 + (5 x 5) = ___
(i) 6 + (7 x 7) = ___ (j) 50 – (3 x 7) = ___ (k) 50 – (4 x 6) = ___
(l) 50 – (5 x 8) = ___
3. (a) (12 ÷ 2) + 3 = ___
2. Decode this Masonic coded message.
(b) (21 ÷ 7) + 5 = ___
(c) (24 ÷ 3 ) + 2 = ___
(d) (48 ÷ 6) + 4 = ___
(e) (56 ÷ 8) + 7 = ___
(f) 20 – (63 ÷ 7) = ___
(g) 20 – (54 ÷ 6) = ___
(h) 20 – (49 ÷ 7) = ___
(i) 20 – (45 ÷ 9) = ___
4. Make a pattern similar to the ones in your book.
3. Match the symbol with its meaning.
forward slash
within the range
male
#
multiply by (computer term)
greater than or equal to
&
clubs
infinity
±
copyright
sad
©
tilde
female
5. Work from left to right.
sharp or how many?
omega
spades
~
ampersand (and)
answers.
(a) 18 – 5 + 6 = ___
(b) 23 + 7 – 2 = ___
(c) 20 x 2 – 6 = ___
(e) 24 ÷ 2 + 4 = ___
(f) 63 ÷ 7 x 3 = ___
(g) 50 – 8 x 3 = ___
(h) 4 x 5 + 2 x 3 = ___
(i) 15 ÷ 3 – 20 ÷ 20 = ___
Name: _______________________________________
Date: ___________________
Page 175: Numbers Rules
(d) 10 + 10 – 10 = ___
(f) 8 + 4 – 11 = ___
(g) 12 – 10 + 3 = ___
(h) 10 – 7 + 4 = ___
(i) 9 – 8 + 6 = ___
(j) 14 – 8 + 2 = ___
(k) 15 – 5 + 1 = ___
(l) 20 – 20 + 3 = ___
6. Write these problems as word problems. Use brackets.
4. Place brackets in the following to show which items should be worked out first. Calculate the
(d) 14 + 8 ÷ 2 = ___
(a) 15 + 8 – 2 = ___ (b) 8 + 11 – 16 = ___ (c) 3 + 12 – 15 = ___
(e) 9 + 6 – 2 = ___
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(a) Molly has 1 hour to do as she pleases. She spent 15 minutes typing and 20 minutes playing
basketball. How much time has she left? _____________
(b) There are 6 eggs in a carton. Mr S. Cramble has 4 cartons of eggs and 3 more eggs.
How many eggs has he altogether? _____________
Name: _______________________________________
Date: ___________________
© Folens Photocopiables
*
© Folens Photocopiables
approximately
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Linkage
Number: Operations (adding and subtracting)
Integration
Art: Patterns
Maths at home/parental involvement
Look for signs and symbols at home and in the world around you: sign language, Braille,
keyboard symbols, road and traffic signs, universal signs, hand and body signals, facial
expressions, gestures, ancient symbols and alphabets, runes, the sign that preceded the séimhiú
in Gaeilge where the initial consonant was dotted, Chinese, Japanese, Cyrillic alphabets, etc.
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