ST. MICHAEL’S CE
SCHOOL
PARENT WORKSHOP - 20th OCTOBER 2015
EXTENSION IDEAS FOR MATHS
EXTENDING YOUR CHILD’S
MATHS SKILLS
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This is not about comparing them to other children - it is about
thinking where they are at and what their next steps are.
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What knowledge, problem solving skills do they need to be
able to approach more complex questions.
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National Curriculum Levels have gone!
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No Level 6 paper any more. 2 x reasoning papers. 1 x
arithmetic
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ASSESSMENT tab on our website.
ANGLES LEVEL 3
Q5.
1 mark
Complete the table.
shape
number of right angles
...............................
...............................
231 mark
SKILLS/KNOWLEDGE
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How to identify/measure a right angle.
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What a right angle is. Know that it is 90 degrees.
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Methodically check their work.
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Use a protractor/set square to check.
ANGLES LEVEL 4
Q4.
This shape is three-quarters of a circle.
How many degrees is angle x ?
SKILLS/KNOWLEDGE
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That a complete turn is 360 degrees.
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Know that a letter (x) can indicate an unknown amount/measurement/
number.
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Not be phased by ‘no numbers’ on the diagram - lots of children are very
put off by this as they have spent so long thinking Maths is numbers!
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That 3/4 of 360 is 270 degrees or be able to calculate 3/4 by doing: (360
divided by 4) x 3.
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Understand the importance of check their work - perhaps with an inverse
operation. 360 - 90 = 270.
SKILLS/KNOWLEDGE
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That a complete turn is 360 degrees. That all of the angles of the sections in
a pie-chart therefore total 360 degrees too.
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To know that in a pie chart 360 degrees = 100% and the related facts e.g.
10% = 36 degrees, 50% = 180 degrees, 25% = 90%
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Not be phased by ‘no numbers’ on the diagram - lots of children are very
put off by this as they have spent so long thinking Maths is numbers!
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Willingness to draw on the diagram to make estimates. Use tracing paper.
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Good comprehension skills: questions are longer. Ensure they put the %
and not the measurement of the angle of the paper section.
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Ability to use a protractor.
(c)
Other windmill patterns can be made into regular polygons in the same way by drawing
extra triangles, with angles h, j and k.
Can you predict what angles h, j and k will be when you know angles c and d?
ANGLES LEVEL 5
Without working it out for every windmill pattern, how can you be certain your prediction will
always work?
Q2.
This pie chart shows the different ways that wood is used in the world.
Use the pie chart to estimate the percentage of wood that is used for paper.
%
1 mark
ANGLES LEVEL 5
Q3.
Here is an equilateral triangle inside a rectangle.
Calculate the value of angle x.
Do not use a protractor (angle measurer).
2 marks
SKILLS/KNOWLEDGE
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Good comprehension skills: questions are longer.
•
Know that a letter (x) can indicate an unknown amount/measurement/
number.
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Know the properties of an equilateral triangle - write these down at the side.
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Know that all of the angles in a triangle always add up to 180 degrees - so in
equilateral they must each be 60 degrees.
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Able to solve multi-step problems. Accurate subtraction techniques.
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Know that the corner is a right angle and that this is 90 degrees.
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Use brackets for calculations: 90 - (60 + 12) = 90 - 72 = 18 degrees
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Methodical approach to working - show working out. Even if they get the final
answer incorrect - they may get a mark for correct working out.
ANGLES LEVEL 5/6
Turning triangles – task 1
Q1.
(a)
This regular pentagon is made from 5
isosceles triangles that fit together
around a point.
The triangles fit with no gaps and no
overlaps.
Work out the angles in one of the
triangles.
(b)
A regular decagon can be made from 10 isosceles triangles that fit together around a point
with no gaps and no overlaps.
Work out the angles in one of these triangles.
(c)
All regular polygons can be made from isosceles triangles that fit together around a point
with no gaps and no overlaps.
Only 12 of these regular polygons have isosceles triangles in which all the angles are
whole numbers, and all the angles are whole numbers than or equal to 10°.
How many sides do these polygons have, and how can you be certain that there are no
more than 12 of these polygons?
Turning triangles – task 2
(a)
Isosceles triangles can fit together
around a point in a different way to
make ‘windmill’ patterns. The
triangles fit with no gaps and no
overlap.
Work out the angles in the triangle.
ANGLES LEVEL 5/6
(b)
This windmill pattern has been
made into a regular pentagon by
drawing five extra triangles.
Work out the angles in each
triangle.
(c)
Other windmill patterns can be made into regular polygons in the same way by drawing
extra triangles, with angles h, j and k.
Can you predict what angles h, j and k will be when you know angles c and d?
Without working it out for every windmill pattern, how can you be certain your prediction will
always work?
ANY QUESTIONS?