Problem solving strategies - Lesson 4 by apteacher

mathematics · @apteacher · May 2 '18

$25.72

Problem solving strategies - Lesson 4

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<h1>Problem solving strategies:</h1>
<p><img src="https://elenikyritsis.files.wordpress.com/2016/04/pss2-1.jpg?w=2000" width="2000" height="1341"/></p>
<p><a href="https://elenikyritsis.files.wordpress.com/2016/04/pss2-1.jpg?w=2000">Image source</a></p>
<ol>
  <li><a href="https://steemit.com/mathematics/@apteacher/problem-solving-using-different-strategies"><strong>Look for a pattern</strong></a></li>
  <li><a href="https://steemit.com/mathematics/@apteacher/problem-solving-using-different-strategies"><strong>Make an organized list</strong></a></li>
  <li><a href="https://steemit.com/mathematics/@apteacher/problem-solving-strategies-lesson-2"><strong>Draw a table</strong></a></li>
  <li><a href="https://steemit.com/mathematics/@apteacher/problem-solving-strategies-lesson-2"><strong>Guess and check (Trial and improvement)</strong></a></li>
  <li><a href="https://steemit.com/mathematics/@apteacher/problem-solving-strategies-lesson-3"><strong>Work backwards</strong></a></li>
  <li><a href="https://steemit.com/mathematics/@apteacher/problem-solving-strategies-lesson-3"><strong>Use logical reasoning</strong></a></li>
  <li><strong>Draw a diagram</strong></li>
  <li><strong>Solve a simpler problem</strong></li>
</ol>
<h3>The second last problem solving strategy we are going to work through is &nbsp;drawing a diagram.</h3>
<p>The last lesson of problem solving strategies will be handled in the next lesson.</p>
<p><br></p>
<h2>7. &nbsp;Draw a diagram</h2>
<p>Mathematical problems may involve objects, positions or spatial relationships.&nbsp;</p>
<p>Drawing a diagram for the given situation can be very useful in solving the mathematical problem.&nbsp;</p>
<p><img src="https://previews.123rf.com/images/svaga/svaga1706/svaga170600003/80835146-vegetable-garden-vector-illustration-with-cabbage-and-radish-agricultural-cultivation-in-the-land-.jpg" width="1300" height="1300"/></p>
<p><a href="https://previews.123rf.com/images/svaga/svaga1706/svaga170600003/80835146-vegetable-garden-vector-illustration-with-cabbage-and-radish-agricultural-cultivation-in-the-land-.jpg">Image source</a></p>
<h3>Example:&nbsp;</h3>
<p>The principal of a school wants to make a vegetable garden on the school grounds. &nbsp;He has a patch where he can plant all different kinds of vegetables. &nbsp;The perimeter of the patch is 40m. &nbsp;He asks the grade 7 learners to find the maximum (the biggest area) of the rectangular garden.&nbsp;</p>
<p>NOTE:&nbsp;</p>
<p>We can draw different rectangles with different length and breadths, as long as the perimeter is equal to 40m every time. &nbsp;We can start with a rectangle with the length 19m and the breadth 1 m.</p>
<p><img src="https://imgoat.com/uploads/f93f983524/109496.png" width="280" height="122"/></p>
<p>The area of this rectangular garden will be 19 x 1 = 19 square meters.</p>
<p>The perimeter of the rectangle = 2 (19 + 1) = 2(20) = 40 m</p>
<p>If we reduce the length of to 18m, the breath will be 2m. &nbsp;</p>
<p>Now we will have the following diagram:</p>
<p><br></p>
<p><img src="https://imgoat.com/uploads/f93f983524/109499.png" width="285" height="128"/></p>
<p>The area of the rectangle now increases to 36 square meters.</p>
<p>The perimeter will still be 2( 18 + 2) = 2 ( 20 ) = 40 m</p>
<p><br></p>
<h3>We can continue to reduce the length and increase the breadth:</h3>
<p>If the length is reduced to 17m the breadth will be 3m. &nbsp;The area will be 17 x 3 = 51 square meters.</p>
<p>If the length is reduced t0 16m the breadth will be 4m. &nbsp;The area will be 16 x 4 = 64 square meters.</p>
<p>We can see every time the length reduces and the breadth increases, the area of the rectangle gets bigger, but the perimeter will stay the same.</p>
<p><img src="https://imgoat.com/uploads/f93f983524/109501.png" width="293" height="127"/></p>
<p>We continue reducing the length and breadth. &nbsp;If the length reduces the breadth increases. &nbsp;This means that the area of the rectangle will be the biggest (largest) if both my length and breadth are the same.</p>
<p>The area of this rectangle will be 10 x 10 = 100 square meters.</p>
<p>The perimeter of the rectangle will be 2 ( 10 + 10) = 2 (20) = 40 meters.&nbsp;</p>
<h3>The maximum area for the vegetable patch will be 100 square meters.</h3>
<p><br></p>
<h2>Activity:</h2>
<p>A tree branch divides into 2 branches. &nbsp;Each of the smaller branches then divides into three branches. &nbsp;Each of the 3 branches, divides into another 4 branches. &nbsp;How many branches of all sizes will there be altogether?</p>
<p><img src="https://annarborbahais.org/public/wp-content/uploads/2016/10/tree-with-leaves-pv.png" width="958" height="719"/></p>
<p><a href="https://annarborbahais.org/public/wp-content/uploads/2016/10/tree-with-leaves-pv.png">Image source</a></p>
<p><img src="https://imgoat.com/uploads/f93f983524/109506.gif" width="414" height="131"/></p>
</html>

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