NPPS Park Numeracy Framework Planning Format for Year 6: Date: 9 January 2013 – 2 weeks
Block: A2 (Counting, partitioning and calculating)
Units Objectives
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Explain reasoning and conclusions, using words, symbols or diagrams as appropriate
Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including
calculator use
Use decimal notation for tenths, hundredths and thousandths; partition, round and order decimals with up to three places, and position them on the number line
Use knowledge of place value and multiplication facts to 10 × 10 to derive related multiplication and division facts involving decimals (e.g. 0.8 × 7, 4.8 ÷ 6)
Calculate mentally with integers and decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U
Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two-digit
and three-digit integers by a two-digit integer
Use a calculator to solve problems involving multi-step calculations
Use approximations, inverse operations and tests of divisibility to estimate and check results
Participate in a whole-class debate using the conventions and language of debate
Key aspects of learning: focus for the block
Building on previous learning
Check that children can already:
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Enquiry
Problem solving
Reasoning
Creative thinking
Information
processing
Evaluation
Self-awareness
Managing feeling
explain reasoning using text, diagrams and symbols
Social skills
Communication
Motivation
Empathy
solve one- and two-step problems involving whole numbers and decimals
and all four operations, choosing and using appropriate calculation strategies
order positive and negative numbers in context
explain what each digit represents in whole numbers and decimals with up to two places, and partition, round and order these numbers
multiply and divide whole numbers and decimals by 10, 100 or 1000; multiply pairs of multiples of 10 and 100 and derive corresponding division facts
use mental methods to find sums, differences, doubles and halves of decimals (e.g. 6.5 ± 2.7, halve 5.6, double 0.34), to multiply a two-digit by a one-digit number, to
multiply by 25 and to subtract one near multiple of 1000 from another (e.g. 6070 - 4097)
use efficient written methods to add and subtract whole numbers and decimals with up to two places, to multiply HTU × U, TU × TU and U.t × U, and to divide HTU ÷ U
use a calculator to solve problems, interpreting the display correctly
use rounding and inverse operations to estimate and check calculations
1
Day OMS
Shared
Group
Plenary
1
Learning Objective: To create word problems.
Success Criteria: I can create word problems starting with the solution. I can solve problems involving more than one step.
(See OMS
Rolling
Programme)
Tell the children that when there is a real life word problem it
usually contains units and is usually based on x + - / %
fractions. Problems at their level are usually multi-step.
Discuss: What different types of units do word problems
usually have?
capacity – litres, ml,
mass – kg, g,
length – km, m, cm, mm,
money - £, p
time – hours, minutes, seconds
Show children the following answer to a problem and have
children work brainstorm some different questions:
Children make up word problem that
could be solved using the calculations.
Task is differentiated. However, HA could
extend the problems and add extra parts
to the solution.
G+T to make up their own solutions to
test class in plenary.
Level 5 APP Targets
I can use brackets correctly ( ).
I can solve a variety of word problems and
investigations checking results that they
are reasonable.
2 hours – 45 minutes.
e.g.
The film was 2 hours long; the projector broke 45 minutes
before the end. How long into the film did it break?
or:
I was supposed to do my homework for 2hours, but I started
playing my PlayStation for 45 minutes. How long did I do my
homework for?
Go over some of the
trickier answers to
check understanding.
of
the
were
See some if anyone
created
their
own
solutions that we can
now work out the
problems for.
Go
over
Success
Criteria, targets and Self
Assess.
Why was it useful for us
to come up with
problems? (so we can
see the process of
creating word process –
usually we just solve
them)
Could the problem be extended? E.g. If the film started at
5PM what time did it crash?
6:15
2
Word
Problems
Calculate
See if any
problems
extended
What was important
when creating the
questions?
(Good
English, we didn’t give
away the answer, the
problem made sense).
1 hour, 15 minutes.
Vocabulary Resources
Operator
Sheet
of
calculation
answers.
Day OMS
Shared
Group
Plenary
Vocabulary Resources
2
Learning Objective: To estimate with larger numbers.
Success Criteria: I can estimate with larger numbers. I can make reasonable assumptions. I can take part in a whole-class debate.
(See OMS
Rolling
Programme)
This will probably take 2 lessons. It is a good opportunity for
the children to make a display/presentation based on their
Fermi question* and all the steps they took.
Our modelled question (It might take most of the lesson):
How many packets are needed to measure a single line of
M&Ms to a distance of 100m?
What do we need to consider when answering this?
Children should come up with a list similar to below:
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What information do we need to know? How many
M&Ms in 1 packet. How long is each one?
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Is the information fixed or does it depend on variable
factors? Do you always get the same number in each
packet? Are they always the same length?
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What would we need to do to work out an estimate?
Work out how many are in one packet. How much length
would that give you? Divide 100 by this and round to see
how many packets you need.
Can it be worked out accurately or do we need to give an
upper and lower limit i.e. between? You could give the
most packets needed and the least, based upon the most
M&Ms in a packet with the longest m&m, and also the
least M&Ms in a packet with the smallest m&m, so the
answer will be between these 2 values.
Can these results be checked? Only if we actually do this!
Also the answer should be in our range, but in reality the
packets will always be variable as they are measured in
grams
Children show their estimation skills by trying to solve it.
Then, give the children calculators to try and give an upper
and lower limit for an answer.
MA - How long would it take to drive to
the moon (if you could!)?
HA - How many people could you fit into
the classroom? How many soccer balls?
G+T - If all the people in Australia joined
hands and stretched themselves out in a
straight line, how long would it reach?
How many times around the world would
it reach?
Extension: Children come up with their
own Fermi questions
Level 5 APP Targets
I can solve a variety of word problems and
investigations checking
I can recognize important information,
break a problem down into steps, and
consider different methods to solve.
I can draw simple conclusions with
explanation of methods, examples and
identifying patterns.
*Fermi questions often require students to
make reasonable assumptions and estimates
about the situation in order to come up with
an approximate answer. Students should be
reminded of the need to be able to explain and
justify what they did when coming up with
their solutions. Students’ answers may differ
from each other, but if students have made
sensible estimates and assumptions then the
different answers should be “close” to each
other. Take advantage of opportunities to
discuss students’ different solution strategies
and the effect of assumptions and estimates.
3
Depending on how far
you are up to in this
lesson, either go through
how the children got on
answering the example
question or let them talk
about their own group’s
questions.
Did anyone make up
their own Fermi
question?
What did we learn by
looking at Fermi
questions?
Go over Success Criteria,
targets and Self Assess.
Tell the children what
they are doing
tomorrow. (Continue
with Fermi
presentations/display)
Estimate
Assumption
Fermi
Question
Useful
information
sheet which
has
some
assumption
for MA and
G+T question
3
Learning Objective: To estimate with larger numbers.
Success Criteria: I can estimate with larger numbers. I can make reasonable assumptions. I can take part in a whole-class debate.
(See OMS
Rolling
Programme)
Continue with Fermi Questions. (There are more in resource
folder if everything from yesterday is done)
Children can present their work and have a debate about
whether their answers are accurate
e.g. when driving to the moon, did they take into account
using different cars/speeds or even different gravity as we
leave the atmosphere.
Children could also make a display showing their steps,
assumptions and diagrams to solving the problem
4
Learning Objective: To order real world decimals numbers.
Success Criteria: I can use decimal numbers with up to three places and order them.
(See OMS
Rolling
Programme)
Play the little Guess the number game with decimals. (See
folder)
MA to put the runners in order with
both reaction time and race result.
Revise how we work out if decimals are higher than others –
Look at place value of each decimal digit – not how many
digits.
i.e. 9.7 is bigger than 9.67 and 0.54 is smaller than 0.6
HA to do same as MA but also put the
race cars in order for both Q1 and Q2
Look at the runners - Who had the fastest reaction time?
Who had the slowest? Who came first in the race? Last?
Look at the Formula 1 racing cars – Who was quickest in
Qualifying 1, Qualifying 2? Who was quickest overall?
How can we put the runners and racing cars in order? Again,
we look at place value of the tenths, hundreds and thousands
if necessary. What about comparing 2 decimals that are not
of the same length?
G+T : In addition, work out the
differences each person is from the
leader. e.g.
1st Bolt 9.54
2nd Blake +0.34
3rd Bailey + 0.67
(not correct values compared to sheet)
Quick finishers. Do the same for the race
cars for Q1.
Level 5 APP Targets
I can understand place value to 1000
including decimals.
I can order decimals.
4
Go over the answers to
see if children have
ordered decimals to 3 dp.
Do the KS3 quiz about
decimals (see link).
Why is it useful to be
able to order decimals?
Go over Success Criteria,
targets and Self Assess.
Decimal
place value
Guess the
decimal
game
Runners and
race car
times sheet.
5
Learning Objective: To understand basic algebra.
Success Criteria: I can balance equations. I can explain my reasoning and conclusions, using symbols to represent unknown numbers
(See OMS
Rolling
Programme)
Discuss: What is algebra and why is it important?
Take the children through the modelling at this link.
http://www.bbc.co.uk/schools/gcsebitesize/maths/alge
bra/equationsrev1.shtml
If they need a visual representation of how to balance
equations, here are 2 scales:
http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html
http://www.mathsisfun.com/algebra/add-subtractbalance.html
Remind children what happens when we do
+ x + = positive, - x - = positive, - x + = negative, + x - =
negative
Activity is differentiated.
MA to do first section.
HA to do all sections.
G+T can also break out the brackets
in the extension activity.
Level 5 APP Targets
Bytesize Class Quiz:
http://www.bbc.co.uk/ap
ps/ifl/schools/gcsebitesiz
e/maths/quizengine?quiz
=equationstest&template
Style=maths
Algebra
Equation
Balancing
Equation
sheet
Why is it useful to be able
to solve equations?
I can use simple formulae with
unknowns e.g. n-2.
Go over Success Criteria,
targets and Self Assess.
I can use brackets correctly ( ).
I can check solutions by using inverse
or estimation.
Check children are ready to start activity by going
through some examples.
6
Learning Objective: To understand basic algebra.
Success Criteria: I can expand brackets and balance equations. I can explain my reasoning, using symbols to represent unknown numbers
(See OMS
Rolling
Programme)
Revise what we did yesterday. Go over any difficulties.
Today we will learn how to continue the extension work
from yesterday – multiplying out brackets in equations.
Go through the modelling here:
http://www.bbc.co.uk/schools/gcsebitesize/maths/alge
bra/equationsrev3.shtml
If this is too easy for G+T, print them
this extension:
http://www.bbc.co.uk/schools/gcsebites
ize/maths/algebra/trialimprovementrev
1.shtml and get them to solve the
equation at the bottom.
MA to do questions 1+2
HA to do all questions
Level 5 APP Targets
How do we solve the
equation x/2 − 4 = 3?
One way is to multiply
everything by 2:
x/2 − 4 = 3
x-8=6
x = 14
Or, alternatively, add 4
and then multiply both
sides by 2:
x/2 − 4 = 3
x/2 = 7
x = 14
I can use simple formulae with
unknowns e.g. n-2.
I can use brackets correctly ( ).
I can check solutions by using inverse
or estimation.
See Testbase questions
5
Algebra
Equation
Brackets
Expanding
Brackets
sheet
7
Learning Objective: To use a calculator
Success Criteria: I use a calculator to perform a trick and explain it to the class. I can use a calculator to solve problems involving more than one step
To start, as a
class play
the broken
calculator
game:
http://www.
mathsisfun.c
om/games/b
rokencalculator.ht
ml
8
This lesson will probably take 2 lessons to complete due Give the children time to learn and Show as many
to the children’s presentations.
perform the tricks.
presentations as
possible.
Do the following trick with the children:
Calculator tricks are differentiated:
2's trick (answer is always 2)
What did we learn from
Think of a number. Multiply it by 3. Add 6 with the
MA – 1, 7, 8
this lesson?
getting result. Divide it by 3. Subtract it from the first
HA – 2, 3, 4, 5, 6
number used.
How can calculators
G+T can try and invent their own help us?
Why does it always work?
tricks.
How did the tricks
Level
5
APP
Targets
Tell the children they will be learning similar tricks
work?
(harder ones), using calculators. They will be performing Calculator practise
them to the class.
Go over Success
Criteria, targets and Self
Print out the PowerPoints (6 slides per page) which
Assess.
should be enough to do double sided printouts and give
them out to 8 groups of 4.
Children have the task of learning the magic trick on the
calculator and will be asked to teach the trick to the
class to perform on their calculators. The children must
learn why the trick works and explain how it works to
the class.
Calculator
Calculators
Calculator
trick sheets
Learning Objective: To use a calculator
Success Criteria: I use a calculator to perform a trick and explain it to the class. I can use a calculator to solve problems involving more than one step
(See OMS
Rolling
Programme)
Continue lesson from yesterday.
Continue presentations of tricks.
If time, q do ‘Calculator fun’ sheet, or use laptops to do
more Broken Calculator activities at harder levels.
http://www.mathsisfun.com/games/brokencalculator.html
6
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