2910
/www/nrich/html/content/id/2910/
1
2011-02-01T00:00:01
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Can you complete the squares?
<br></br>
Use the pencil on the screen to finish the squares.<br></br>
<br></br>
<a href="/content/id/2910/squares.swf">Full Screen Version</a>
<p style="font-style: italic;"></p>
<mdo:flash height="400" width="400"><param name="movie" value="/content/id/2910/squares.swf" ></param><param name="flashplayerversion" value="7" ></param><param name="height" value="400" ></param><param name="width" value="400" ></param></mdo:flash><p style="font-style: italic;"></p>
<p style="font-style: italic;"></p>
<div></div>
<div></div>
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</div>
<div></div>
<div>
</div>
<br></br>
If you are working away from the computer, you might like to print off <a href="/content/id/2910/completesquares.doc">this sheet</a>
of the squares to complete.<br></br>
<p><span style="font-style: italic;">This activity comes from BEAM's </span><a style="font-style: italic;" href="http://www.beam.co.uk/about/MoM/MoM.html">Maths of the Month
</a><span style="font-style: italic;"><br></br></span>
</p>
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<span class="editorial">Jamie from Great Hilton High School sent in
some pictures of his solutions. He says</span> <br></br>
<br></br>
When trying to make a square, there are 2 rules to follow, which
are: <br></br>
1. All the sides need to be the same size. <br></br>
2. There must be 4 perpendicular angles (or right angles). <br></br>
<br></br>
To complete the squares, see how many grid squares 1 line takes up
and rotate the line 90 degrees. Keep doing this until you get a
full square.<br></br>
<br></br>
<mdo:image width="241" height="243" src="sq1sol.gif" alt="Solution for first square"></mdo:image><mdo:image width="241" height="243" src="sq2sol.gif" alt="Solution for second square"></mdo:image><br></br>
<mdo:image width="241" height="243" alt="Solution for third square" src="sq3sol.gif"></mdo:image><mdo:image width="252" height="252" src="sq4sol.gif" alt="Solution for fourth square"></mdo:image><br></br>
<mdo:image width="252" height="252" alt="Solution for fifth square" src="sq5sol.gif"></mdo:image><br></br>
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<h2>Complete the Square</h2>
<br></br>
Can you complete the squares?<br></br>
Use the pencil on the screen to finish the squares.<br></br>
<br></br>
<a href="/content/id/2910/squares.swf">Full Screen Version</a>
<p style="font-style: italic;"> </p>
<mdo:flash height="400" id="/content/id/2910/squares.swf" width="400"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/2910/squares.swf"></param>
<param name="flashplayerversion" value="7"></param>
<param name="height" value="400"></param>
<param name="width" value="400"></param>
</mdo:flash>
<p style="font-style: italic;"> </p>
<p style="font-style: italic;"> </p>
<div> </div>
<div> </div>
<div> </div>
<div> </div>
<div> </div>
<br></br>
If you are working away from the computer, you might like to print off <a href="/content/id/2910/completesquares.doc">this sheet</a> of the squares to complete.<br></br>
<p><span style="font-style: italic;">This activity comes from BEAM's</span> <a href="http://www.beam.co.uk/about/MoM/MoM.html" style="font-style: italic;">Maths of the Month</a></p>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div><a href="http://nrich.maths.org/public/viewer.php?obj_id=2910&part=index">This problem</a> is excellent for helping to reinforce the properties of squares and in particular for highlighting the fact that a square is a square no matter what orientation it is in.</div>
<br></br>
<h3>Possible approach</h3>
<div>You could introduce this activity by showing the children a square piece of paper. Put the square on the board so that its sides are parallel to the sides of the board and ask the class what shape it is. How do they know? Then, invite one pupil to come up and pin the square on the board in a different way. Is the shape still a square? You might find that an interesting discussion ensues! It
is common for children to call a tilted a "diamond" but the earlier we can encourage them to avoid this, the better.</div>
<br></br>
<div>Once pupils have tried the problem (whether on paper or using the interactivity), they could show each other their completed squares and discuss the drawings before sharing them with you and/or the whole class. Playing the game <a href="http://nrich.maths.org/public/viewer.php?obj_id=2526&part=index">Square It</a> would be a good way to end this lesson.</div>
<br></br>
<h3>Key questions</h3>
<div>What do you know about squares?</div>
<div>What do you need to add to this to make it a square?</div>
<br></br>
<h3>Possible extension</h3>
<div>You could give some learners a grid (for example $3$ by $3$ small squares) and challenge them to draw all possible squares on it, if all corners have to be on the grid.</div>
<br></br>
<h3>Possible support</h3>
<div>Children may need rulers to convince themselves that the sides of the shape they have drawn are (or are not!) the same. Turning the page also helps!</div>
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What do you know about squares? Can this help you finish the
diagrams?<br></br>
It might be easier to <a href="/content/id/2910/completesquares.doc">print off</a> the question
and then use a pencil and ruler to complete the squares.<br></br></mdoxml>
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Complete the Square
Complete the squares - but be warned some are trickier than they
look!
2D Geometry, Shape and Space
Squares
Information and Communications Technology
Interactivities
Admin
Lower primary mapping document