Resources • 1cm grid paper • 10 x 10 grid floor mat • Various 2D shapes • BLM worksheets h<p://www.worksheetworks.com/math/geometry/counBng-‐area.html h<p://www.superteacherworksheets.com/area.html • Mats (1m x 1m) • Leaves • Blank A4 size paper • FISH Kit Review Ac-vity Process 1. Brainstorm and discuss various units of measurement the students
can recall.
2. Using various units of length (mm, cm, m, km) ask students to suggest objects that would be measured using these units of length.
Review Ac-vity Process 1. Explain what is meant by the term ‘one dimension’ (measurement in
length, width, and thickness) and explain that measuring length is using ‘one dimension’(a figure having only length, such as a line) Area of a 2D shape is the measure of its interior
(a point has no dimension only posiBon)
2. Encourage students to make connecBons, ask them to think of possible examples for the noBon ‘two dimensions’ (2D) Record eg.
two dimensional shapes have, length and width, but lacking depth, A figure (shape) that only has two dimensions (such as width and
height) has no thickness.
Ac-vity Process-‐Exploring Area 1. Introduce the term ‘area’ and ask students to share their
mathemaBcal understanding of this concept.
2. Create a class definiBon of what ‘area’ is.
3. Discuss that area can also be measured using mm, cm, m , km etc. of 2D shapes
4. Students list a range of objects where the area can be calculated eg. Desk top, books, basketball court, football field.
5. Explain to students that an easy way to calculate the area of a 2D shape is through the use of squared grids. Highlight the importance of the squares being iden6cal with no gaps. Eg. Area = 30 units
6. Give students coloured construcBon paper and ask them
to create a straight sided regular 2D shape, (polygons) these become a general resource for the acBvity
7. Students are given a transparent square cm grid to place over the ‘regular’ 2D shapes and asked to esBmate the area of each and compare which shape they think will cover the most/least area.
Australian Curriculum Year 4 ACMMG290 Compare objects using familiar metric units of area and volume Spotlight-‐What is a Key Idea It is a statement of an idea that is central to the learning of the big ideas of mathema6cs, one that links mathema6cal understandings increasingly into a coherent whole. Understanding key ideas: • is moBvaBng. • promotes connected understanding to big ideas. • promotes memory. • influences beliefs. • promotes the development of autonomous learners. • enhances transfer. • reduces the amount that must be remembered. Big Idea: Some a<ributes of objects are measurable and can be quanBfied using unit amounts. Key Ideas: • Measurement involves a selected aFribute of an
object (length, area, mass, volume, capacity) and a comparison of the object being measured against a unit of the same aFribute.
• The magnitude of the aFribute to be measured and the accuracy needed determines the appropriate measurement unit.
4.2.4 Word Wall: esBmate, area, grid, idenBcal, square cenBmetres/cenBmetres squared, square metres/metres squared, square kilometres/kilometres squared, dimensions, boundary, 2D, region, units, perpendicular, properBes. polygon
DRAFT-‐This is a work in progress. MAG wriBng project 2012-‐2013
Note CounBng can be used as a strategy to find the area of a polygon on a grid where the inside of the shape (interior) can be covered by whole square unit. If part of the shape includes parBal square units then it is necessary to EsBmate parts = ? When the shape is a rectangle or a Square finding the area can be Linked to the noBon of arrays and Using mulBplicaBon strategies MulBplying the number of rows by squares in each row eg. 6 X 5 = 30 square units Ac-vity Process-‐Part 2 1. Students then trace and count the area in square cm and compare
their esBmaBon. This would be a good opportunity to demonstrate how to write area squared.
2. Explore any issues or quesBons that arise from these acBviBes, such as half squares, incomplete squares etc. Look at strategies for solving these problems. (see note)
3. Show 2 shapes (such as rectangles) that have a different shape but cover the same amount of area.
4. Pose quesBons such as: Which shape would cover the greatest area and why? Which shape would cover the smallest area and why?.
5. Explore the idea that different objects can have the same area. Use hands as another example. Two hands are not always similar eg. One person may have thicker thumbs and shorter fingers.
Digital Learning Area Explorer h<p://www.shodor.org/interacBvate/acBviBes/AreaExplorer/ Paving Slabs h<p://www.ngfl-‐cymru.org.uk/vtc/ngfl/maths/cynnal/slabs/saesneg/paving_slabs.swf Contexts for Learning Inves-ga-on: Clarify their understanding of ‘two dimension’ as mulBplying length and width Explain that this only works for squares and rectangles. Revise the rule for triangles.
Using the rule of squares and rectangles: Use a 1 square metre mat or material Ble and esBmate how many metres squared a secBon of your school is. Eg. Basketball court, classroom, stage. Show how much room one square takes up and students use strategies to come up with suitable esBmates.
Students can then use a trundle wheel or count how many mats it takes to measure the length, then width, the use the rule to mulBply them together to get an accurate answer.
Real Life Context:
A cube has 6 faces (sides) and all angles are right angles. What are the advantages of using this shape, at school, at home, and at work?
Extension and Varia-ons 1. Using grid paper, ask students to draw as many different shapes that have an area of a certain number of squares such as 4 or 8.
Experiment with finding the area of irregular shapes and ways we can work out suitable esBmates. Use a leaf, hand or other accessible irregular shape and trace or glue onto grid paper.
Count the number of square completely inside the shape.
Combine other parts into squares
Add to find the total area.
Look at area of triangles and explore the properBes of triangles.
2. Give students a sheet of paper and ask them to idenBfy its shape. Ask them to think about how they could make two idenBcal shapes with three straight sides from the rectangular paper. Eg. cut it diagonally into two triangles. Ask students to describe what this proves eg. that a square or rectangles equal two triangles.
Discuss how this knowledge would help us work out the area of a triangle. Length x height /2
Introduce the term ‘perpendicular’ and explain how it relates to finding the area of triangles.
3. Brain Teaser
h<p://greatmathsgames.com/number/item/33-‐brain-‐teasers/78-‐chessboard-‐puzzle.html Using a chessboard and 8 pawns the teacher explains how the pawns must be placed on the board so that there is only one pawn occupying each verBcal, horizontal and diagonal. ie there cannot be any other piece on the same line as another.
Assessment-‐open ques-ons (students choice) 1. A chessboard that has both black and white Bles. Which area is greater-‐the area for the black Bles or the area for the white Bles? 2. Give more than one answer to the quesBon. ‘A shape has an area of 200 square cm. What could its length and width be? Show how you have worked out your answers and explain the strategies you used. Background
Area is the calculated space within a boundary (interior) of a shape. A square grid and/or grid paper can be a useful way to work out area. The size of a grid cells (units) needs to be consistent with no gaps.
Some children invent rules for finding the area of familiar shapes, like length X width = area for squares or rectangles. They can then apply these rules with understanding. Teaching students these rules before they have experiences (explaining before exploring) leads to rote measurement skills with li<le understanding of why the rule works.
Volume measures the amount of space in an object. The volume formula for a rectangular prism is mul6plying the height/length of each dimension by each other-‐length how long, by width how wide by height how high
While some learners may understand the basic formulae to find the formula of a rectangular prism, the focus at this year level is on understanding the concept of volume
Links to other MAGs MAG 4.1.3
MAG 4.2.1