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 Mathematics Workshop Notes Section 1 By Jason Caldwell B.Ed,Dip.Tch.
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Introduction
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Great Maths Links
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Why do some students seem to find Maths difficult?
For 95% of students who are underachieving in mathematics, research suggests several common findings.
Students who struggle in Mathematics usually lack:
1. A strong relational understanding of place value
(1s,10s,100s…)
2. A relational understandings of the four basic operations
(+, -, x, /)
3. Or have missing links or keys that underpin new
concepts they are trying to work through.
These three problems create maths anxiety, as students find themselves working through problems by following prescribed steps or a formula but not having a clue how it works and what is it all for.
Strategies for Building Strong Relational Understandings
Counting and number games.
Make a game of counting anything that surrounds you. Activities such as; counting buttons, counting 1 at a time then two, three, four or five at a time. This helps children get a picture of a “lot of” or a “set of” a number. Using a “stop watch” strategy adds a fun dimension and turns the activity into a game e.g. “Count as many buttons as you can in thirty seconds…”
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The BBC Maths site is great for brief but clear explainations and examples for every term: Click Here
Junior Maths Dictionary: Click here
Rain Forest Maths by Jenny Eather This is an excellent Queensland Maths Site with help and support for Grades Prep to 6/7.
Exciting Geometry links:
Word Document of nets that can be printed out for students to meke their own 3D shapes.
Animated Geometry learning tools, fantastic site where parents and student can have a lot of fun!
Great geometry games and learning activities.
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Teaching Strategy:
Talk about students beating their own time (PB) and making progress rather than comparing to others and attainment.
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If a student can count beautifully to 100 but cannot count 6 objects, are they really counting? |
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Place Value
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Obviously “rote counting” is important but, just the first step. Activities in counting that use concrete or semi-abstract materials (drawing) help students to get a picture in their heads of what numbers mean. Knowledge of how they work will naturally follow.
Another fun activity is to count steps, jumps or actions. Adding the physical helps make counting meaningful. You may create your own dance sequence together with different numbers of steps or actions.
I like to use “Finger flash” to get students quick at number conservation and recognition.
e.g. “How many fingers am I holding up?” Then add fingers and ask, “now how many?”…
Other Ideas:
Blow and count bubbles, make a tower out of blocks and count the levels, head count,
Extension: Measuring using a ruler…
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Place value is the system that underpins all decimal system mathematics. I usually use a place value table and MAB blocks (ones, tens and hundreds blocks, if you have the Math U See blocks they are great) to demonstrate to young students the concept of numerals representing a vastly different value depending upon which column they are in. I draw this table out large on a white board or on card and laminate so that it can be written on.
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Example of a Place Value Table:
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Millions
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Hundreds of Thousands
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Tens of Thousands
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Thousands
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Hundreds
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Tens
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Ones
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Tenths
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Hundred ths
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Thousand ths
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To make this usable it needs to be drawn out large on a white board or card chart...
Students also need to see concrete representations of numbers and it is a good idea to model amounts or draw them in picture form…
When learning to do simple addition or subtraction, the place value table is very important.
MAB or Place Value Blocks can be purchased from:
Billylids Innovative & Educational Toys
3 Dennis Rd Springwood 4127 - (Behind KFC)
(07) 3808 9800
Click here to go to their online ordering site.
Place Value Game
A game that I have found very helpful is the “Place Value Game”. You tell the students that you are going to throw a dice five times and each time they can decide to make the number worth “ones”, “tens”, “hundreds” or “thousands” and they have to add their numbers together to get as close as they can to one thousand. Have the students work in columns to write and add their numbers together.
For example if the first throw is 5, they can write down either 5 or 50 or 500. If the next number is 2, they can write down and add 2 or 20 or 200. Parents are to play this game as well, modeling the process. The winner is the person who gets the closest to 1000 without exceeding 1000.
As they get better at this you can increase the number of throws and the target number, I have had classes working towards a million with ten throws.
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 The 4 Main Operations -Addition, Subtraction, Multiplication and Division
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Addition = + = adding
= increase = plus…
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Teaching Tip: |
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If you can add single digit numbers easily then you can add anything.
It is fine to use your fingers so long as they are helping and useful, not just a security blanket. You can also use a number line and place value blocks and chart.
I like to use "finger flash" and start holding up two lots of fingers, one just after the other…
Just as with counting, the use of concrete materials is important for students to see and understand the relationship of adding numbers…
To build speed and knowledge of patterns I like to use 10x10 grids. Use random numbers down the side and numbers across the top that encourage students to use patterns and systems. Have students work down the columns.
It is also a good idea to give Maths activities exciting names and to model an enjoyment for Mathematics.
E.g. Addition Blaster! (Great name...)
"in column one +1 just count on,
column two +10 add 1 to the 10’s column,
+9 in column three = + 10-1…
Students enjoy learning addition patterns that take advantage of the decimal system and build strong mental maths skills in an activity I call “The Easy Way”.
I write up a list of equations that encourage students to put numbers together to make sets of 10,20,50 or 100. these numbers are then added together easily.
E.g.
1+9+2+8+7+3+4+6…=____ -sets of ten.
4+8+8+6+4+7=___ -requires splitting the 4 to add onto
the 8’s to make two sets of ten…3+4+6+7+9+3+1= ___ mixed up pairs and have leftovers.
13+7+44+6+9+5+3=___ and just keep going…
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Students need to be risk takers and know that it is alright to get something wrong… and teachers need to know that there is often more than one way of doing things and sometimes more than one correct answer…
Another great activity is giving 30 seconds to find pairs of numbers that equal 10 or 20 or 50 or 100. Write the numbers in a box all mixed up. E.g.
Subtraction = - = Takeaway
And don’t show the student the Numbers until you start timing.
I never teach subtraction until students are strong with their addition. I have never meet a student who had good addition skills who struggled with subtraction.
This is because subtraction is the same as addition, it is just backwards. “Backwards Addition”
E.g. 4+5=9 ---9-4=5
When it comes to building speed in subtraction Grids are great as you can draw out the patterns and as student try to improve their times they will be forced to use the patterns.
E.g.
-1 just count back, -10 take 1 from the 10’s column, -9 = - 10+1, -11= -10-1, -15=-5-10…
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Click here to go to Section 2
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