Elementary Trail
It must be recycling day!
1. If there are 8 bins of recycling for each house and there are 24 houses on a block, how many bins of recycling are there per block?
Ans. 24 x 8 = 192
2. If your recycling is ⅜ plastic and ⅛ tin, what fraction of your recycling must be paper? Remember to reduce your fractions to lowest terms.
Ans. 3/8 + 1/8 = 4/8 and reduced 4/8 = 1/2
3. If a big poster needs 7 staples, and a small poster only need 4, how many of each can you put up if you only have 27 staples left?
Ans. Four small posters and one large poster
4. The poles circumference is 27inches, how many small posters
can you fit around the pole if each one has a width of 9cm?
Ans. 3posters
5. Take a close look at this apartment building, what kind of shapes
do you see?
Ans. Triangles, Squares, Rectangles, Trapezoid
6. Look at the big triangles, what kind of triangles do you think they are?
Ans. Isosceles Congruent Triangles
7. If each apartment has one window, and there is the same amount
of windows on every side, how many apartments are in this building?
Ans. 9 (don't forget the ones behind the bush) x 4 = 36 apartments
8. Take a close look at these pictures, which familiar shape do you see in the grill of the car? Locate any lines of symmetry, letters have symmetry too! Ans. In stop sign picture shape symmetry is green; letters are done in red and black. The familiar shape is a hexagon (honeycomb) and it is used because
the shape makes efficient use of space and building materials
9. What kind of numbers are these?
Ans. Roman Numerals
10. If you went home right now and it took you 15minutes to get there, 21minutes to eat dinner and 70minutes to do your homework, will you still have time to catch your favorite television show at 6 o'clock?
Ans. Yes.
11. Notice any symmetry in the clock design?
Ans. Line of symmetry is right down the center.
12.
In English we use some letter more than others, let's look at this sign and count each time we see a letter. Take a look at this chart that shows the frequency used of each letter in the English language.
(a=7) (b=0) (c=2) (d=2) (e=12) (f=2) (g=1) (h=3) (i=7) (k=1) (L=4) (m=3) (n=2) (o=11) (p=2) (q=0) (r=6) (s=6) (t=7) (u=1) (v=2) (w=5) (x=2) (y=2) (z=0)
13. If a tree in your yard is 36feet tall and you want to chop it up into 12 pieces, how big must each piece be, use long division.
Ans. 3 Feet
14. For every year of a trees life it leaves a ring like mark, estimate the number of rings on the cross section of the tree chunk, approximately how much older is the tree than you are.
Ans. The tree is approximately 92 years old. How much older answers vary.
15. Can you predict what pattern comes next in the sequence? Ans.
16. If there are 3 rows of 8 spaces, how many cars fit in the parking lot?
Ans. 24
17. If the parking lot is full, and each car showed up with 3 people, how many people are in the restaurant?
Ans. 72 people
18. A typical "small car" parking space is 270 square feet, if the length of your car is 16feet and the width of your car is 13 feet, can you park in the small car space?
(hint: Area=Length x Width)
Ans. Yes, car = 208 square feet
19. If this bird feeder has 240 and each bird eats 4 seeds, how many birds can eat from this feeder before it runs out of seeds, use long division.
Ans. 60birds
20. If Marys butt is 14cm, Jacobs butt is 12cm, Donnas butt is 17cm, and Brads butt is 18cm and the bench is only 49cm long, which kids fit perfectly on the bench and who is left out? Try it out with your teammates
Ans. Jacob gets left out.
21. How old was Carolina when she passed away?
Ans. She was 40 years old
22. What year will it be when you are her age?
Ans. Varies
23. If Mary takes 10steps every 15seconds and the "ok to walk" man flashes red after 45seconds, how many steps can Mary take before she has to run across the road in order to make it safely.
Ans. 30 steps.
24. How many squares can you find in this window?
Ans. 7
25. How many triangles can you find in this window (without overlapping)?
Ans. 14
26. What do you think the angle of each corner is?
Ans 380/4= 95 Degrees
27. How many friends can I invite to my super fun bike party, if you can only have one bike per two bars on each side of the bike rack?
Ans. 18
28. If box "A" has 14 out of 20 newspapers left, box "B" has 18 out of 25 papers left and box "C" has 23 out of 31 newspapers, which newspaper is the most popular? which is the least? List them in ascending order.
Ans. A=6 B=7 C=8
29. If you received 25cents for delivering the total number of papers altogether, how much money would you have made?
Ans. 5.25$
30. What is the success ratio (reduced to lowest terms) of this poster if 3 out of 15 phone number tags were taken?
Ans. 1/5
31. Write an equivalent fraction.
Ans. Lots of possibilities, 6/30, 9/45 etc
32. If the basketball hoop is 12feet high and you are 5feet tall with an arm length that is half your height, how high would you have to jump to slam-dunk the ball.
Ans. 12 - 7.5 = 4.5 feet
33. If there are 12 rectangles across the top of the gate and 10 rectangle along the side how many squares are there in total?
Ans. 12 x 10 = 120
34. If each rectangle has a length of 3 and width of 2 what is the total area of the gate? Don't use a calculator, show your work.
Ans. Width: 2 x 10 = 30 and Length = 12 x 3 = 36 so (A = L x W) A = 1080
35. This building has many many shapes, how many shapes can you find here? Let's look!.
36. If the diameter of the garbage can is 40cm, what is its radius?
Ans. 20cm
To find out the size of garbage bag we need, use the formula Circumference = π(radius)²
(hint: the π button is on your calculator)
Ans.Approximately 1256
37. Which do you think will be more effort, taking the stairs or taking the ramp? Which is faster?
Count how many steps it takes to get up the ramp and how many steps it is from the bottom the ramp to the top of the stairs.
Do the results surprise you?
Ans. Varies, stairs in the end are less effort.
38.
a) What kind of triangle do you think this is? Ans. Isosceles
b) Is it a golden triangle? Ans. No
c) What is the measure of the missing angle? Ans. 120 degrees
d) Why do you think triangles are used for sandwich boards instead of squares?
Ans. Squares have one more corner than a triangle does so it takes less force to bend it, the triangle is more stable
39. Coca-cola advertises a 1 in 6 chance of winning a prize, if you buy 120 bottles of coke and only win 12 times are the odds close to what they advertise?
(hint: Reduce to lowest terms).
Ans. We had a 1 in 10 chance.
40. If this house number is 1151 and the next house over here is 1145, what do you think the next house number will be?
Ans. 1139
41. Return to our math-trail map and using the small distance measure in the bottom left corner and your ruler, estimate how far we walked.
Ans. Varies, approximately 7000feet.
It must be recycling day!
1. If there are 8 bins of recycling for each house and there are 24 houses on a block, how many bins of recycling are there per block?
Ans. 24 x 8 = 192
2. If your recycling is ⅜ plastic and ⅛ tin, what fraction of your recycling must be paper? Remember to reduce your fractions to lowest terms.
Ans. 3/8 + 1/8 = 4/8 and reduced 4/8 = 1/2
3. If a big poster needs 7 staples, and a small poster only need 4, how many of each can you put up if you only have 27 staples left?
Ans. Four small posters and one large poster
4. The poles circumference is 27inches, how many small posters
can you fit around the pole if each one has a width of 9cm?
Ans. 3posters
5. Take a close look at this apartment building, what kind of shapes
do you see?
Ans. Triangles, Squares, Rectangles, Trapezoid
6. Look at the big triangles, what kind of triangles do you think they are?
Ans. Isosceles Congruent Triangles
7. If each apartment has one window, and there is the same amount
of windows on every side, how many apartments are in this building?
Ans. 9 (don't forget the ones behind the bush) x 4 = 36 apartments
8. Take a close look at these pictures, which familiar shape do you see in the grill of the car? Locate any lines of symmetry, letters have symmetry too! Ans. In stop sign picture shape symmetry is green; letters are done in red and black. The familiar shape is a hexagon (honeycomb) and it is used because
the shape makes efficient use of space and building materials
9. What kind of numbers are these?
Ans. Roman Numerals
10. If you went home right now and it took you 15minutes to get there, 21minutes to eat dinner and 70minutes to do your homework, will you still have time to catch your favorite television show at 6 o'clock?
Ans. Yes.
11. Notice any symmetry in the clock design?
Ans. Line of symmetry is right down the center.
12.
In English we use some letter more than others, let's look at this sign and count each time we see a letter. Take a look at this chart that shows the frequency used of each letter in the English language.
(a=7) (b=0) (c=2) (d=2) (e=12) (f=2) (g=1) (h=3) (i=7) (k=1) (L=4) (m=3) (n=2) (o=11) (p=2) (q=0) (r=6) (s=6) (t=7) (u=1) (v=2) (w=5) (x=2) (y=2) (z=0)
13. If a tree in your yard is 36feet tall and you want to chop it up into 12 pieces, how big must each piece be, use long division.
Ans. 3 Feet
14. For every year of a trees life it leaves a ring like mark, estimate the number of rings on the cross section of the tree chunk, approximately how much older is the tree than you are.
Ans. The tree is approximately 92 years old. How much older answers vary.
15. Can you predict what pattern comes next in the sequence? Ans.
16. If there are 3 rows of 8 spaces, how many cars fit in the parking lot?
Ans. 24
17. If the parking lot is full, and each car showed up with 3 people, how many people are in the restaurant?
Ans. 72 people
18. A typical "small car" parking space is 270 square feet, if the length of your car is 16feet and the width of your car is 13 feet, can you park in the small car space?
(hint: Area=Length x Width)
Ans. Yes, car = 208 square feet
19. If this bird feeder has 240 and each bird eats 4 seeds, how many birds can eat from this feeder before it runs out of seeds, use long division.
Ans. 60birds
20. If Marys butt is 14cm, Jacobs butt is 12cm, Donnas butt is 17cm, and Brads butt is 18cm and the bench is only 49cm long, which kids fit perfectly on the bench and who is left out? Try it out with your teammates
Ans. Jacob gets left out.
21. How old was Carolina when she passed away?
Ans. She was 40 years old
22. What year will it be when you are her age?
Ans. Varies
23. If Mary takes 10steps every 15seconds and the "ok to walk" man flashes red after 45seconds, how many steps can Mary take before she has to run across the road in order to make it safely.
Ans. 30 steps.
24. How many squares can you find in this window?
Ans. 7
25. How many triangles can you find in this window (without overlapping)?
Ans. 14
26. What do you think the angle of each corner is?
Ans 380/4= 95 Degrees
27. How many friends can I invite to my super fun bike party, if you can only have one bike per two bars on each side of the bike rack?
Ans. 18
28. If box "A" has 14 out of 20 newspapers left, box "B" has 18 out of 25 papers left and box "C" has 23 out of 31 newspapers, which newspaper is the most popular? which is the least? List them in ascending order.
Ans. A=6 B=7 C=8
29. If you received 25cents for delivering the total number of papers altogether, how much money would you have made?
Ans. 5.25$
30. What is the success ratio (reduced to lowest terms) of this poster if 3 out of 15 phone number tags were taken?
Ans. 1/5
31. Write an equivalent fraction.
Ans. Lots of possibilities, 6/30, 9/45 etc
32. If the basketball hoop is 12feet high and you are 5feet tall with an arm length that is half your height, how high would you have to jump to slam-dunk the ball.
Ans. 12 - 7.5 = 4.5 feet
33. If there are 12 rectangles across the top of the gate and 10 rectangle along the side how many squares are there in total?
Ans. 12 x 10 = 120
34. If each rectangle has a length of 3 and width of 2 what is the total area of the gate? Don't use a calculator, show your work.
Ans. Width: 2 x 10 = 30 and Length = 12 x 3 = 36 so (A = L x W) A = 1080
35. This building has many many shapes, how many shapes can you find here? Let's look!.
36. If the diameter of the garbage can is 40cm, what is its radius?
Ans. 20cm
To find out the size of garbage bag we need, use the formula Circumference = π(radius)²
(hint: the π button is on your calculator)
Ans.Approximately 1256
37. Which do you think will be more effort, taking the stairs or taking the ramp? Which is faster?
Count how many steps it takes to get up the ramp and how many steps it is from the bottom the ramp to the top of the stairs.
Do the results surprise you?
Ans. Varies, stairs in the end are less effort.
38.
a) What kind of triangle do you think this is? Ans. Isosceles
b) Is it a golden triangle? Ans. No
c) What is the measure of the missing angle? Ans. 120 degrees
d) Why do you think triangles are used for sandwich boards instead of squares?
Ans. Squares have one more corner than a triangle does so it takes less force to bend it, the triangle is more stable
39. Coca-cola advertises a 1 in 6 chance of winning a prize, if you buy 120 bottles of coke and only win 12 times are the odds close to what they advertise?
(hint: Reduce to lowest terms).
Ans. We had a 1 in 10 chance.
40. If this house number is 1151 and the next house over here is 1145, what do you think the next house number will be?
Ans. 1139
41. Return to our math-trail map and using the small distance measure in the bottom left corner and your ruler, estimate how far we walked.
Ans. Varies, approximately 7000feet.
Just a few Bloopers I thought I would share with you :)
Scroll down to find to find the answers page.
Scroll down to find to find the answers page.
Miss Lopez, you can't park a bike rack into a bike!
Counting big numbers can be tricky!
Intermediate Trail
1. If we walked 1000ft down Oxford street and 2500ft down Linden Avenue, how much distance would we have saved if we cut across the diagonal?
Ans. 1000² + 2500² = c²
√7250000 = √c²
2692.58 ≈ c
2. A rectangular parking lot is 50meters longer than it is wide. What are the dimensions of the parking lot if it measures 250 meters diagonally.
w²+(w+50)²=250²
2w²+100w+2500=62500
w²+50w-30000=0
w = 150 or w = -250
The parking lot is 150ft by 200ft
3. If each side of the Octagon is 6inches what is the total perimeter?
Ans.P = 6(18)
4. What is the total surface area?
Ans. Area = ( 2 + 2√2 )a²
Area = ( 2 + 2√2 )6²
Area=173.82²Inches
5. What is the measure of each angle?
Ans. Angle measure = 180º - 360º = 135º
n
6. If the base of our triangle is 40inches and the height is 80 inches what is the total area of the triangle?
Ans. ½bh → ½(40)(80) → Area = 1600inches²
7. If each plant needs a space of 6 x 6 how many plants can we fit into our triangular garden
Ans. 1600/36 = 44.4 plants
8.How much dirt would we need to buy to fill our triangular garden?
Ans. Volume = Bh → V = (1600(80) → V=128000³inches of dirt
9. If it takes 36L of gas to drive for 193km and we are taking 885km trip, assuming the gas is used at the same rate, how much fuel will we need?
Ans.(193/36=885/x) =165.1L
10. If your car gets 18miles per gallon in he city driving and 24miles per gallon on the highway and you want to bust your friend for driving your car further than they said and it was driven 465 miles on 23 gallons of gasoline how many miles were driven in the city and how many on the highway?
1) x+y=465
2)x/18 +y/24=23
-18x-18y=-8370
24x+18y=9936
x=261
261+y=464
y=204
261 in the city and 204 on highway
11. If we only have 64yards of fencing, what is the largest rectangular area that we can enclose?
Ans. Step1. 2l + 2w = 64 Step2. A = lw Step3. A = -w² + 32w
2l = 64 - 2w = (32-w)w = -1(w²-32w+256-256)
l = 64 -2w = 32w-w² = -(w-16)² + 256
2 -w²+32w w = 16 and l = 32
l = 32 - w
12. According to safety laws all ramps for the disabled must be in the form of a right triangle where every vertical length of 1 feet has a horizontal length of 12feet. If the ramp measures 12ft horizontally and 1ft vertically, what is the length of the ramp?
Ans. h² = 12² + 1²
h² = √145ft
h² ≈ 12.042ft
13. In a triangular cross section of a roof, the second angle is twice as large as the first, the third angle is 20° greater than the first angle. How large are the angles?
Ans. x + (x+20) +(2x) = 180°
4x = 160°
x = 160/4
x = 40° Three angles = 40° , 80° , 60°
14.Most of us play the lottery with 49 different balls and 6 balls get drawn, what are the chances of winning the lottery? (hint: figure out the number of combinations and how many times combinations are repeated)
Just for fun, according to space.com you are more likely to die in an asteroid collision in the year 2029 than you are to win the lottery
Ans. 49 x 48 x 47 x 46 x 45 x 44 = 10,068,347,520.
6 x 5 x 4 x 3 x 2 x 1 = 720
10,068,347,520/720 = roughly 1 in 13,983,816.
15. If your car travels 14mph faster than the bus and you travel 290mi in the time it takes the bus to travel 230mi what is the speed of each vehicle?
Ans. 230 = 290 → 230(r+14) = 290r
r r + 14 230r + 3220 = 290r
161/3 = r or 53 2/3
Therefore r + 14 = 67 2/3
Your cars speed is 67 2 and the bus is 53 2
3 3
Ans. 1000² + 2500² = c²
√7250000 = √c²
2692.58 ≈ c
2. A rectangular parking lot is 50meters longer than it is wide. What are the dimensions of the parking lot if it measures 250 meters diagonally.
w²+(w+50)²=250²
2w²+100w+2500=62500
w²+50w-30000=0
w = 150 or w = -250
The parking lot is 150ft by 200ft
3. If each side of the Octagon is 6inches what is the total perimeter?
Ans.P = 6(18)
4. What is the total surface area?
Ans. Area = ( 2 + 2√2 )a²
Area = ( 2 + 2√2 )6²
Area=173.82²Inches
5. What is the measure of each angle?
Ans. Angle measure = 180º - 360º = 135º
n
6. If the base of our triangle is 40inches and the height is 80 inches what is the total area of the triangle?
Ans. ½bh → ½(40)(80) → Area = 1600inches²
7. If each plant needs a space of 6 x 6 how many plants can we fit into our triangular garden
Ans. 1600/36 = 44.4 plants
8.How much dirt would we need to buy to fill our triangular garden?
Ans. Volume = Bh → V = (1600(80) → V=128000³inches of dirt
9. If it takes 36L of gas to drive for 193km and we are taking 885km trip, assuming the gas is used at the same rate, how much fuel will we need?
Ans.(193/36=885/x) =165.1L
10. If your car gets 18miles per gallon in he city driving and 24miles per gallon on the highway and you want to bust your friend for driving your car further than they said and it was driven 465 miles on 23 gallons of gasoline how many miles were driven in the city and how many on the highway?
1) x+y=465
2)x/18 +y/24=23
-18x-18y=-8370
24x+18y=9936
x=261
261+y=464
y=204
261 in the city and 204 on highway
11. If we only have 64yards of fencing, what is the largest rectangular area that we can enclose?
Ans. Step1. 2l + 2w = 64 Step2. A = lw Step3. A = -w² + 32w
2l = 64 - 2w = (32-w)w = -1(w²-32w+256-256)
l = 64 -2w = 32w-w² = -(w-16)² + 256
2 -w²+32w w = 16 and l = 32
l = 32 - w
12. According to safety laws all ramps for the disabled must be in the form of a right triangle where every vertical length of 1 feet has a horizontal length of 12feet. If the ramp measures 12ft horizontally and 1ft vertically, what is the length of the ramp?
Ans. h² = 12² + 1²
h² = √145ft
h² ≈ 12.042ft
13. In a triangular cross section of a roof, the second angle is twice as large as the first, the third angle is 20° greater than the first angle. How large are the angles?
Ans. x + (x+20) +(2x) = 180°
4x = 160°
x = 160/4
x = 40° Three angles = 40° , 80° , 60°
14.Most of us play the lottery with 49 different balls and 6 balls get drawn, what are the chances of winning the lottery? (hint: figure out the number of combinations and how many times combinations are repeated)
Just for fun, according to space.com you are more likely to die in an asteroid collision in the year 2029 than you are to win the lottery
Ans. 49 x 48 x 47 x 46 x 45 x 44 = 10,068,347,520.
6 x 5 x 4 x 3 x 2 x 1 = 720
10,068,347,520/720 = roughly 1 in 13,983,816.
15. If your car travels 14mph faster than the bus and you travel 290mi in the time it takes the bus to travel 230mi what is the speed of each vehicle?
Ans. 230 = 290 → 230(r+14) = 290r
r r + 14 230r + 3220 = 290r
161/3 = r or 53 2/3
Therefore r + 14 = 67 2/3
Your cars speed is 67 2 and the bus is 53 2
3 3
| In Inches | Buddha | Enlarged | Average Man |
| Height | 36 | 68.4 | 69 |
| Chest | 18 | 34.2 | 44 |
| Waist | 20 | 38 | 38 |
| Hip | 22 | 41.8 | 42 |
16. If this buddha were a real man, what would his dimensions be? Round all your answers to one decimal place.
Ans. divide 69 by 36 to get 1.9 and multiply Buddhas demensions by 1.9