Download Algebra GFED - Dynamic Learning

Situation
Choose the activity(ies) that best suit
your students’ learning needs.
A short activity to get students
thinking about the information in a
Warm
up – ideal for the beginning
question
of the lesson
What are
Four questions to encourage
students to think about alternative
the possibilities?
questions using the same
information
Four questions to encourage
students to use higher order
Thinkingthinking
harder
skills to consider question
alternatives
Three more questions to practise
theto
same
Some more
tryapproach in different
contexts
An opportunity for students to
assess and reflect on their
Reflection
progress, including the grade they
are working at
Content covered
Test
Key points which can be printed
and
at home or in pairs in the
yourselfused
cards
classroom
Algebra GFED
Situation – Content covered
Reflection
F
Algebra
Solve linear equations with one operation
E
Algebra
Simplify by adding and subtracting terms
E
Algebra
Use simple formulas
E
Algebra
Form simple algebraic expressions
D
Algebra
Simplify by multiplying and dividing letters and numbers
D
Algebra
Solve linear equations with two or more operations
D
Algebra
Expand single brackets
Algebra GFED
Situation – Warm up
Answers
4x
2
3y + 1
5C + 25
x−3
y−4
3
5
-2x + 7y
2x − 1
p+9
p
7p
()
2y
()
-8
9y
x+2
C+5
6x
8xy
+
+
−
−
1. Simplify 4x + 2x − 1 + 5 (The answer is not in the box.)
2. Which of the expressions above are divisible by 5?
3. Which two expressions have a difference of 5?
4. Write and answer a simple question using some of the expressions above.
Algebra GFED
×
÷
Situation – What are the possibilities?
Answers
4x
2
3y + 1
5C + 25
x−3
y−4
3
5
2x − 1
p+9
p
-2x + 7y
7p
()
2y
()
+
-8
9y
x+2
C+5
6x
8xy
+
−
−
×
÷
Question
3
1. Write an equality by combining some of the above to form the
left-hand
side.
2. (i) Solve 3y + 1 = 7 (ii) Simplify 7p + p + 3 − 5
3. Make up a mark scheme for this question.
4. Write a contextualised exam question that uses some of the
Prompts
Thinking
prompts
Algebra GFED
Three kinds of marks can be
given:
[4 marks]
B for something being correct,
irrespective
Question 4 of method
Use the Prompts button to help
M
for carrying
out unfamiliar
a correct step
students
who are
expressions
with this style ofabove.
question.
A for a correct answer
Use the Thinking prompts
button to help students be more
creative with their questions.
Situation – Thinking harder
Answers
4x
2
3y + 1
5C + 25
x−3
y−4
3
5
-2x + 7y
2x − 1
p+9
p
7p
()
2y
()
+
-8
9y
x+2
C+5
6x
8xy
+
−
1. Write two equalities using the items above.
2. Write two equalities that involve 8xy.
3. Write two false statements using the items above.
4. Write three statements that might be true using the items above.
Give reasons for your choices.
Algebra GFED
−
×
÷
Situation – Some more to try
1.
Answers
Jack hires a cordless hammer drill for £20, plus £15 per day.
Write an expression for the cost of hiring it for N days.
How much will it cost to hire for 3 days?
2.
(x + 3)
(x − 4)
(x + 7)
(2x − 1)
(x − 3)
(x + 1)
Which pair, when added together and simplified, gives 2x − 3?
3.
2x + 3
3x − 7
4−x
=1
=9
=2
Pair up the three equations with the three answers so that x has the same value for each
equation. What is this value of x?
Algebra GFED
Situation – Reflection
Click below the button to reveal
the grades.

I can
Simplify by adding and subtracting terms
Simplify by multiplying and dividing letters and numbers
Solve linear equations with one operation
Solve linear equations with two or more operations
Use simple formulae
Self assess
• Find or write some evidence to support your assessment.
• Write down your next steps.
• You may wish to use the Test yourself cards.
Algebra GFED


E
D
E
D
E
Situation – Test yourself cards
These cards contain
some of the key
terms and skills you
will need to answer
algebra questions.
Copy down the
ones you need or
ask your teacher
for a printout.
What does term mean?
What does simplify mean?
A ‘small’ chunk of algebra, e.g. 7y
Collect like terms or cancel
What does solve mean?
What is an equation?
In the case of an equation, find the value (or
values) of the unknown
Two expressions with an = sign between
them
How do you solve equations?
What does expression mean?
By getting the unknown on its own on one
side of the equation by using inverses or
doing the same to both sides
a ‘larger’ chunk of algebra with multiple
terms joined by operations, e.g. 3p − 7y
How do you simplify expressions?
How do you substitute?
By doing the sums that you can do i.e.
collecting like terms
Replace the letters in an expression or
formula by numbers
Algebra GFED
Situation – Answers for Warm up
1. 6x + 4
2. 5C + 25 and 5
3. x + 2 and x − 3
4. Possible simple questions are:
– Simplify 7p × 2y [answer 14py]
– Simplify x − 3 − 8 [answer x − 11]
– Solve y − 4 = 3 [answer y = 7]
– Multiply out 3(x + 2) [answer 3x + 6]
Algebra GFED
Situation – Answers for What are the possibilities?
1. Some true statements you could write down are:
7p + p = 8p
C+5−5=C
y − 4 + 2y = 3y − 4
3y + 1 + y − 4 + -2x + 7y − 4x + 6x = 11y − 3
2. and 3.
(i) 3y + 1 = 7
3y = 6
1 mark
y=2
1 mark
(ii) 7p + p + 3 − 5
8p − 2
2 marks
Examiner note: ‘ 8p’ scores 1 mark and ‘− 2’ scores the second mark.
4. The exam questions would normally be a selection to test techniques and do not
need to have any connection with each other.
Possible exam questions, in addition to those in Warm up question 4, are:
– Solve 2x − 1 = 5
[2 marks, grade E]
– Solve p + 9 = -8
[1 mark, grade E]
– Simplify 3y + 1 + y − 4 − 2y
[2 marks, grade E]
– Simplify 9y × 7p
[1 mark, grade D]
Algebra GFED
Situation – Answers for Thinking harder
1. e.g.
5(C + 5) = 5C + 25
2+3=5
x+2−5=x−3
6x – 4x + 3 − 2 = 2x − 1
6x – 4x + 9y – 2y = -2x + 7y
3y + 1 – (y – 4) = 2y + 5
2. 2 of: 8xy ÷ 4x = 2y
8xy ÷ 2y = 4x
4x × 2y = 8xy
3. Some false statements include:
p+9=p
subtract p from both sides to get 9 = 0
3y + 1 − 2y = y − 4
simplify and subtract y from both sides to get
1 = -4
x+2=x−3
subtract x from both sides to get 2 = -3
4. e.g.
p+9=5
y − 4 = 2y
2x − 1 = x + 2
(true when p = -4)
(true when y = -4)
(true when x = 3)
Algebra GFED
Situation – Answers for Some more to try
1.
Jack hires a cordless hammer drill for £20, plus £15 per day.
15N + 20
£65
Write an expression for the cost of hiring it for N days.
How much will it cost to hire for 3 days?
2.
(x + 3)
(x − 4)
(x + 7)
(2x − 1)
(x − 3)
(x + 1)
(x − 4)
(x + 1)
Which pair, when added together and simplified, gives 2x − 3?
3.
2x + 3
3x − 7
4−x
=1
=9
=2
x=3
Pair up the three equations with the three answers so that x has the same value for each
equation. What is this value of x?
Algebra GFED
Situation – Prompts
Think of a
really easy
question…
Think of a
really short
question…
Think of a really
obvious question…
Think of a
really hard
question…
Algebra GFED
Think of a
really boring
question…
Think of a really
strange question…
Situation – Thinking prompts
Could I make a
question with
fractions in it?
Is there a question
that would mean
adding some of the
numbers?
Is there a
question that
would mean
dividing?
Could I make a
question with an
answer less than 1?
Could I make a
question worth 5
marks?
Is there a
question that
would involve the
number 90?
Could I make a
question worth 2
marks?
Is there a question
that would involve
multiplication?
Algebra GFED