The sum of the whole is this: walk and be happy; walk and be healthy. The best way to lengthen out our days is to walk steadily and with a purpose.
 - Charles Dickens (1812-1870)

Grade 6

Theory:

Finding the Third Angle of a Triangle

The sum of the interior angles of a triangle is equal to 180^o. To find the third angle of a triangle when the other two angles are known, subtract the number of degrees in the other two angles from 180^o.

Example: How many degrees are in the third angle of a triangle whose other two angles are 40^o and 65^o? Answer: 180^o - 40^o - 65^o = 75^o

Finding the Fourth Angle of a Quadrilateral

The sum of the interior angles of a quadrilateral is equal to 360^o. To find the fourth angle of a quadrilateral when the other three angles are known, subtract the number of degrees in the other three angles from 360^o.

Example: How many degrees are in the fourth angle of a quadrilateral whose other three angles are 80^o , 110^o and 95^o? Answer: 360^o - 80^o - 110^o - 95^o = 75^o

Solutions from the Previous Issue:

1. A class of sixty voted for class president.  30% voted for Albert and 70% voted for Jane.   How many votes did the winner receive?

Solution:

60 x 70% = 42 votes  

2. A town had a population of 50,000 five years ago.  Since then, the population has increased 23%.   How many people currently live in the town?

Solution:

50,000 x ( 100% + 23% ) = 61500 people.

3. Greg wants to buy a radio that costs $90.  It is on sale for 25% off.   If Greg has to pay tax of 4% after the discount, what is the total amount to pay for the radio?

Solution:

The discount is $90 x 25% = $22.5

The radio cost $90 - $22.5 = $67.5

We add the taxes: $67.5 +$67.5 x4% = $67.5 +$2.7= $70.2

4. A sofa costs $955 plus tax.   If the sales tax rate is 7.75%, what is the final price?

Solution:

$955 + $955 x 7.75% = $955 + $74.01 = $1029.01

Proposed Exercises:

1. A firefighter is standing on the middle rung of a ladder. She moved up 9 rungs. The smoke got worse, so she moved back down 13 rungs. When the smoke cleared, she went up 19 rungs to the top. How many rungs does the Ladder have? 

2. A gardener has 36 poinsettia plants to ship to local florists. He ships them in boxes of 4 plants, or boxes of 3 plants. How might he ship all 36 plants if all boxes shipped must be full?  Find as many solutions as you can. 

3. A multiple-choice test contains 40 items.  A correct response earns 5 points, but 2 points are deducted for every incorrect response. Nothing is given nor deducted if the question is unanswered.  Michelle scored 96.  How might she have gotten this score?  Find as many solutions as you can. 

4. In a bowling tournament, Elton scored 188, 212, 214, 196, and 200 in the first five games. In order to quality for the semi-final round, he must average at least 205 for the six games. What is the least he can bowl in his final game to qualify?