Investigation Ideas from Jan Cavanagh

Investigation Ideas from Jan Cavanagh

Chance & Data

N Counters

Play “N-Counters” – chance of data - language of chance at different levels

Create a graph (using counters) – throw 2 dice and graph the number of times each of the numbers from 1-12 to discover the “normal curve” (there are more options in the middle numbers than there are at the extremities)

Create a frequency table from the data (Level 4)
Discuss the “chance” of rolling particular numbers using Level 4 language (eg ‘buckley’s chance)
Repeat activity (2) and record the number on each die (eg 1 and 1; 4 and 6 etc). Record the two numbers rolled over the total (eg 4, 4 over 8). It is important to know which die is being called first so that ‘turnarounds’ can be included (eg 2, 4 and 4, 2). This also creates a normal curve which shows all of the different ways each number can be attained.

Calculate the number of ways to roll each total (ie 1 way to roll a 2; 6 ways to roll a 7). Calculate the “probability” of rolling each number (eg P7 = 1 in 36).
Discuss “Expected/Theoretical Probability” and “Experimental Probability” (Level 5/6)

**Don’t forget to use this game for data collection as well (make graphs, tables etc)

Dice Difference (on Let’s Be Fair website)

Play “Dice Difference – A Fair Go?”
Figure out why Jane is expected to win (create a list of the possible combinations of each answer)
Calculate the chance of Jane rolling a winning combination or
Is the game fair?
How could you make the game fair?
Can you think of another way?
What would happen if you included the zero difference
What if …
How about you try…

**To numerically justify whether or not this game is fair, students must be at Level 4/5

**You may use this to teach drawing a chart, make a table etc (to record possibilities)

Measurement

Measurement Mat

Create different shapes which use 12 squares

Measure the perimeter of each – discover that long thin shapes have a longer perimeter than small (round) shapes – why

Why does it cost more to fence a long thin block of land than a short square block of land?
Why were early houses build in square shapes, rather than long thing shapes?
There are only 2 rectangles which have the same numeral for their perimeter and their area. What are they? 4cm x 4cm (perimeter = 16cm; area = 16cm2) and 3m x 6m (perimeter = 18m; area = 18m2).

Put lots of shapes on a piece of butcher’s paper. Allow students time to discover which have the smallest area and which have the largest area?

Number

Basic Facts

Beads (May be purchased from “Making Sense of Maths” – Basic Fact Beads). Use for turnarounds, doubles, double plus 1, add ons). Also available for multiplication.

Input-Output machines – “Magic Gadgets” (made from milk cartons). May also use to calculate formulae/identify patterns (eg put in 1, 1 comes out, put in 2, 4 comes out, put in 3, 6 comes out. The “magic gadget” is doubling)

**Could also use the Magic Gadget to teach literacy (eg contractions - can not becomes can’t; antonyms – black becomes white; synonyms – small becomes little)

Money Spinner

Create a “Money Spinner” and graph the results.

How could I make this spinner unfair?
Every child has 3 spins. How much money did you get? (Discuss strategies for adding money)

Hundreds Chart

Use a hundreds chart to show the “area” of money (a 20 cent coin covers 20 squares, a 50 cent coin covers 50 cents.
How much does a 50 cent and a 20 cent cover?
Use envelopes with stamps – “I paid 60 cents to post this envelope” Show 50c and 10c on the hundreds chart. “How else could I have made 60 cents.

“One day when I went to buy a stamp, I didn’t have 60 cents, I only had a dollar. Could I still buy a 60c stamp?” Overlay the $1 on the hundreds chart. Put your finger on the 60 and overlay other coins to show the change received.

**Hundreds board and money overlays may be purchased from “Making Sense of Maths”

3D Towers

Create 3D towers from 1-10
Are there ways to rearrange any of the towers so that they are still rectangular shapes? (eg 4x1 may be changed into 2x2)
These numbers are composite numbers.
Identify factors by looking at towers which fit into each other - factor and fit (eg take the tower of 2 and put it beside the 2x2 tower or the 3x2 tower)
Identify multiples - multiple and many (multiples have factors which fit in many times)
Discuss the difference between prime and composite numbers by looking at numbers which may only be made by creating towers (these are prime)
Talk about 1 – put it in a group with square numbers (numbers whose towers can be rearranged to make squares)
Talk about 1- put it in a group with cubic numbers (numbers whose towers can be rearranged to make cubes)
Introduce square notation by showing the “direction” numbers operate in – square numbers operate in 2 directions – ie 4 = 2 in one direction and 2 in the other direction (makes a square).
Introduce cubic notation by showing the “direction” numbers operate in – cubic numbers operate in 3 directions – ie 8 = 2 in one direction, in another direction and 2 in a third direction – making a cube
Make the connection to measurement: perimeter (length – one direction); area – two dimensional; volume – three dimensional. Introduce the notation cm2 etc (the 2 shows that the number operates in two directions). There is also a blurb about this connection in the Maths Syllabus Support Materials (U188)

Grids

Use the measurement mat to create a grid with numbers 0-9 across the top and counting in tens from 0-50 down the left hand side.
Stand on a square within the grid. Identify the number you are standing on by looking across at the tens and up to the ones (eg the point 20, 3 would be square 23)

Use the grid to add and take away. Eg : “What is 23 plus 35?” (find the answer by walking down 3 tens and across 5 ones to the point 50, 8. 23 + 35 is 58)
Be sure to stand in every square.
To show carrying eg 28 + 22. Begin at 28, walk down two tens, across one and walk outside the mat (not on the squares) across one more to the 50.
Could also do this activity using the ones first to compliment teaching the formal algorithm.

**Measurement mats can also be used for making people graphs, calendars etc

**The mat may be rearranged so that the numbers at the top begin at 1 and end at 10 for topics such as money.

Shape

Use a measurement (grid) mat and coloured elastics to create 2D and 3D shapes. Discuss the properties of the shapes created.

Assessment Ideas:

After completing a class activity, ascertain individual student knowledge by asking them to write/draw what they have learned.
Instead of asking children to “write” what they know use a cloze activity which requires students to fill in appropriate words to show their mathematical knowledge.
Use the Frayer Concept Model to have students communicate their understandings.

When Playing Dice Games

Give students a numeral and a dot dice – that way students will use the numeral and count on the dots.

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