Embedded Files
Inspired from a workshop run by Peter Newall
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically.
They will solve problems and model situations that require them to..... NZC
GM 3-2: Find areas of rectangles by multiplication using whole numbers
Know some basic facts (NA 3-2) and maybe deduce some more
Recognise a rectangle: (GM2.2) go on a rectangle hunt around the "hood", take photos & tell a story
The task : Rectangles and Cuisenaire rods
The task : Rectangles and Cuisenaire rods
Make a rectangle from 2 brown and 2 green Cuisenaire rods.
Can you make a different rectangle?
How many different rectangles can you make ?
Are the areas of each one the same ( note the inside and outside)
Teaching points /Look fors
Teaching points /Look fors
What rectangle are students focusing on , the inside or outside?
How are they finding the area of each rectangle?
What connections are children making eh multiplication leads to areas if it 3 groups of 8 ?or 8 groups of three?
The task : A rectangle has an area of 24 square units.
What could its dimensions be?
The task : A rectangle has an area of 24 square units.
What could its dimensions be?
Materials: rulers/straight edge, squared paper, calculator if needed
Scaffolds:
Materials : squares cut out/ tiles for children to manipulate or cover pre drawn rectangles
Materials : Squared paper with rectangles drawn on them so they can identify the ones with the same area by counting, multiplying or other method
Link to Number:
Multiply & divide by 10, 100, 1000
[mm, cm, m]Factors and multiples
Draw Factor Bugs
24 Bug 36 Bug 3 bug 16 bug
Squares / primes/ odd /even
nzmaths Prime Search
Learning goals
Model the numbers from 1 to 50 as rectangular arrays.
Identify the factors of the numbers 1 to 50.
Identify prime numbers from 1-50
[NA 3-2, 3-6]
Figure it Out - The great Factor hunt
This activity uses spreadsheets to find factors [NA4-1]
Link to Algebra:
Finding patterns & relationships
Record you results in a systematic way (in a table), what do you notice ?
Plot on graph, what do you notice
Generalise to the rule for area of a rectangle
Extend the task to exploring the perimeter of rectangles of area 24 ( an appropriate number for the group) or exploring patterns in rectangles with a given perimeter
Extend further by linking the area of a triangle to the area of a rectangle.
How can this pattern be generalised?
Taking it up a level
Taking it up a level
Decimal lengths this could come from the students themselves or the great factor hunt spreadsheet activity above
Rectangle Fractions
Rectangle Fractions
Use different shapes and start with the statement
If this [show shape] was 1 third what would the whole look like?
How many ways can you make 1 using your shape?
This build understanding of fractions as parts of a whole and the whole is not always a rectangle or a circle.
You can use materials or draw on paper or use the mathlearning centre pattern shapes app
Rectangles in art
Rectangles in art
Mondrian is a well know artist from the Netherlands who creates using rectangles. You could use squared paper and add constraints like equivalent fractions, a proportion of the total red etc.
Maybe a stained glass window project
Other works for inspiration: Photos taken by Robyn
Darren George, Waru
Ohinetahi Garden's Banks Peninsula
Building at night, Milano
Ben Nicholson 1939
Auckland Art Gallery
Fatu Feu'u
https://chambers241.wordpress.com/2012/09/21/fatu-feuu-absolute-power/What mathematical skills & knowledge are involved ?
Thinking mathematically
Work systematically
Recording findings
Recognise a pattern
Generalise a pattern
Download Learning to work like a mathematician
Read setting up positive norms in a maths classroom from Youcubed
Download and use some of the 100 questions for promoting discourse in your mathematics & statistics class
Download and browse Nix the Trix a booklet compiled by Tina Cardone and the #MTBOS community highlighting many of the tricks I have used and why I should not of used them.
More...
More...
Mathlearning centre app ; Partial product finder illustrates multiplication
Magic rectangle From making math moments
and just for fun... how does this work ?
Google Sites
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