Week 3: Area & Time
Area: Definitions
About the MM of length and width and then multiplying L x W - this is not an understanding kids come to without completing concrete hands-on activities beforehand
Amount of cover of something - start with rectangles and put things down to cover an area, how many units cover it?
Area vs Perimeter - two are combined, but make sure kids are aware of what the difference is between them. Need direct explicit teaching as once kids have experienced it, they are unlikely to be confused E.g. take a door and run hands around the outside, and then all over.
Area: Challenges
The whole world isn't rectangular
Working out area with no gaps or overlaps - estimate and approximate
Units need to tessellate
Students need multiple copies of units to cover area
1.1 Why is it difficult for some students to comprehend the unit of time?
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Language can be confusing – quarter past six vs 6:15 – need to be consistent in early years
Digital vs analog
Prep-p – not able to use scaled instruments
Hard to see time passing
Not tangible – can't be measured in the way it's possible the tangibly measure other types of attributes
Based around 60, not the usual concept of 10
Don’t understand fractions, hard to comprehend
1.2 What 3 key aspects are needed to develop an understanding?
- Understanding the concept of time duration. E.g. using language – before, after, long, short. Time from the start of something to the end. To dev of attirbute that can be measured compare duration of events not starting at same time. Activity: offset the starts using hand claps as non-std units, not just a matter of who finishes first. Order duration of events in daily life e.g. brushing teeth, lunch time
Appreciating the passing and sequence of time perceived through changes in natural occurrences e.g. start of with morning, afternoon, evening and then night – division of days and weeks – months of the year. Use timelines, plotting major events – cross over into HASS. Divisions in kids' lives using broad daily partitions (morn, arvo). Order of days in the week. Activity - use visual clues to assist with und of time by categorising pics of common daily events - use cr poster to illustrate school-based activities occur on reg days.
- Determining a give point in time through the reading of a clock face (p. 471). A logical step. Teachers put this above other elements which is a mistake. Visible movement of clock hands or changing numerals on dig clock. After broad divisions of morn, afternoon and night grasped, idea day can be divided further introduced. Invest std units of second, min and hour to dev und of how long units are. Activity - draw own clock face to divide circle into 12 relatively equal parts. Kids can still be in base 10 mode.
Time estimation
How long until recess? Using other activities they are familiar with and answering about the same time it takes you to brush your teeth
How many mins they have been in class since the morning break or since the school began
How long would it take to run through an egg timer, what other things may take that long?
CRA
Concrete materials
Representational
Abstract
A (the triangle) = 1/2 (base x height) which is based on halving the rectangle
Represent time in different ways
Can't manipulate and pick up and handle
Understanding time in our lives - not easy for kids as not in control of own time often
Calendars
Schedules
Clocks - match time on dig and analog clocks
Years 4 to 8 have incomplete understanding of area (Blume, Galindo & Walcott, 2007) because area differs from length in we don't measure area directly. We measure a combo of lengths and use a formula to calc area. Sts need to first understand attribute of area before measuring & calc it.
Area learning sequence
Years 2 & 3 - begins by making direct physical comparisons of the areas of diff objects
Years 3 & 4 - followed by exploring concept of area as a measure of covering - meaning of mm as the number of units needed to cover region is developed
Years 4 & 5 - use non-std and std units in covering activities to determine area of reg and non-reg figures and regions
Years 6 to 9 - once mastered above stages, progress to dev and apply various formulae used to calc area
Comparing areas more complex than comparisons of length - must take into account L, W and shape.
Area activities
Investigating conservation of area - cutting A4 sheet of paper in half diagonally and then rearranging into other shapes e.g. what other shapes could be made using the two triangles? Sts consider and discuss what might be an approp tessellating unit of area to investigate area of each arrangement. Record what they have noticed and give reasons,
Move from non-std units to std units - use 1cm squares for covering activities - reg and irregular. Use cm square gird paper to trace outline of hand - explain strats used to count full and part squares on grid.
Considered one of the most difficult mm concepts for child to understand (text)
Time in daily lives and measure of time should be included in classroom mm explorations
hurrying to get to school
staying up late