SJO PW - Język angielski ogólnotechniczny, Poziom B2
DLA LEKTORA
Opracowanie: A. Ryszkiewicz, A. Pisarek, J. Mirowska,
B. Maśluszczak, B. Grzybowska, E. Kopryna
Lekcja 2 B
____________________________________________________________________________________
MATHEMATICS
Order of Operations
In order to prepare students for the following lesson, ask them to read and try to memorize the rules of the order of
operations:
Homework:
Examples:
12 ÷ 4 + 32
12 ÷ 4 + 9
3+9
12
Exponent first
Multiply or Divide as they appear
Add or Subtract as they appear
(42 + 5) - 3
21 - 3
18
Everything in the brackets first
Add or Subtract as they appear
20 ÷ (12 - 2) x 32 - 2
20 ÷ 10 x 32 - 2
20 ÷ 10 x 9 - 2
18 - 2
16
Everything in the brackets first
Exponents
Multiply and Divide as they appear
Add or Subtract as they appear
How will you remember this order?
Learn the following acronyms and remember what they stand for:
PEMDAS: Please Excuse My Dear Aunt Sally (Parenthesis, Exponents, Multiply, Divide, Add,Subtract)
PEDMAS: Pink Elephants Destroy Mice And Snails (Parenthesis, Exponents, Divide, Multiply, Add, Subtract)
BEDMAS: Big Elephants Destroy Mice And Snails (Brackets, Exponents, Divide, Multiply, Add, Subtract)
Complete the table: (KEY IN BRACKETS)
to multiply
to divide
to add
to subtract
multiplication
(DIVISION)
(ADDITION)
(SUBTRACTION)
In class:
ORDER OF OPERATIONS
Task 1: Ask students to complete a task based on their homework. They should do it individually. They can use their
homework handout.
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
DLA LEKTORA
Opracowanie: A. Ryszkiewicz, A. Pisarek, J. Mirowska,
B. Maśluszczak, B. Grzybowska, E. Kopryna
Lekcja 2 B
____________________________________________________________________________________
Task 1: Complete the rules of order of operations: (Key underlined.)
1. Do all operations within parentheses first.
2. Multiply and divide in order from left to right.
3. Add and subtract in order from left to right.
Task 2: Ask students to go over the following example individually. They should provide the missing numbers and
compare the answers with a partner.
(Key in bold.)
Task 2: Find the value of each expression. Complete the expressions with the missing numbers:
a.
(5.5 + 6.5) ÷ 6 x 3
Add 5.5 and 6.5 within the parentheses.
(5.5 + 6.5) ÷ 6 x 3 = 12 ÷ 6 x 3
Divide 12 by 6.
=2x3
Multiply.
=6
b.
20 - 5 x 8 ÷ 2
Multiply 5 by 8.
20 –5 x 8 ÷ 2 = 20 - 40÷ 2
Divide 40 by 2.
= 20 -20
Subtract.
=0
Task 3: Divide students into pairs and ask them to take turns to solve the following examples. They should read the
expression to their partner and explain to each other each step of their performance.
(Key on the right in bold in brackets)
Task 3: Find the value of each expression. Read the expression to your partner and explain the order of operations:
1) -9 + 3 - 5
(= -11)
2) 10 - 3 + 9
(= 16)
3) (26 + 5) x 2 - 15
(= 47)
4) 5 + (21 - (- 3))
(= 29)
5) 18 ÷ (2 + 7) x 2 + (-1)
(= 3)
6) 21 ÷ (3 + 4) x 3 - (-8)
(= 17)
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
DLA LEKTORA
Opracowanie: A. Ryszkiewicz, A. Pisarek, J. Mirowska,
B. Maśluszczak, B. Grzybowska, E. Kopryna
Lekcja 2 B
____________________________________________________________________________________
MATHEMATICAL SYMBOLS - OPERATIONS
Each Student’s Page with the tasks for Student A and Student B needs to be prepared before the beginning of the
exercise: either cut in two or folded along the marked line in the middle.
Task 1. (Do NOT reveal the name of the game to the students : A GREY ELEPHANT IN DENMARK)
Students work in pairs. Student A gives the following instructions to Student B.
1. Think of a number from 2-9
2. Multiply it by 9
3. Add the 2 digits together
4. Subtract 5
5. Think of that number as a letter of the alphabet
6. Think of a European country beginning with that letter
7. Think of an animal beginning with the second letter of that country
8. Think of a typical colour for that animal
The result Student B should obtain is: A GREY ELEPHANT IN DENMARK
Task 2. SAME SUM EACH TIME
Students work in pairs. Student B gives the following instructions to Student A.
1. Take any three digit number in which the first digit is larger than the last digit.
2. Reverse the number.
3. Subtract the smaller number from the larger one.
4. Reverse the result.
(If the result from step 3 is a two-digit number, simply put a 0 in front of the two-digit number before reversing it.)
5. Add this number to the result.
Student B checks whether the number Student A has obtained is 1,089.
It should be 1,089 every time. If it is not, they go through the calculations again, \until the mistake(s) is/are corrected
and the answer is 1,089.
Example for the teacher:
For example, use the number 725. The reverse of the number is 527. Subtract 527 from 725 to get 198. The reverse
of the result is 891. Add this number to 198 –and the answer is 1,089. If the result from step 3 is a two-digit
number, such as 99, simply put a 0 in front of the 99 before reversing it (the reverse of 099 is 990). The answer will
still be the same.
Next class, perform the following test to check how much your students remember. Students can do the test in pairs.
(Key on the right in brackets)
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
DLA LEKTORA
Opracowanie: A. Ryszkiewicz, A. Pisarek, J. Mirowska,
B. Maśluszczak, B. Grzybowska, E. Kopryna
Lekcja 2 B
____________________________________________________________________________________
TEST:
1. Complete each gap with ONE word:
In Mathematics, the order in which mathematical problems are solved is extremely important.
Rules:
1. Calculations must be done from (1) ___ _______ to right. ~ (left)
2. Calculations in (2) __________ are done first. When you have more than one set of brackets, do the inner
brackets first. ~ (parentheses)
3. (3) __________ (or radicals) must be done next. ~ (Exponents)
4. Multiply and (4) __________ in the order the operations occur. ~ (divide)
5. Add and (5) __________ in the order the operations occur. ~ (subtract)
Remember to:
~ Simplify inside groupings of parentheses, (6) __________ and braces first. Work with the innermost pair, moving
outward. ~ (brackets)
~ Simplify the exponents.
~ Do the (7) __________ and division in order from left to right. ~ (multiplication)
~ Do the (8) __________ and subtraction in order from left to right. ~ (addition)
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