Math Problems Done in Class
Measurement -Ribbon Mina and Hannah wanted to buy some small bags to put candies in and ribbons to
tie them up. If they bought 14 cm of red ribbon, 0.8 m of blue ribbon and 1200
mm of white ribbon, how much ribbon did they buy?
Measurement - Baking Hana wants to bake some muffins for our class. A 3 kg package of muffin mix
makes 150 muffins. How many grams of muffin mix does Hana need to bake 30
muffins?
Patterning Find the next 5 terms in each pattern.
1. Describe how you found each pattern rule.
2. How would you describe the following patterns?
A) 5, 6, 8, 11, 15, 20, 26, 33, 41, 50 . . .
B) 2, 5, 9, 12, 16 . . .
C) 10, 6, 11, 7, 12 . . .
Area/Perimeter, Multiplication/Division,Conversions - Soccer Field
2900 cm
3300 cm
The soccer field above is to be fertilized in the fall to keep the grass green
for the spring season. A bag of fertilizer covers 8 m2 . In the spring, lines will need to be painted around the field to show the boundary.
a) How many bags of fertilizer should the city buy?
b) If a can of spray paint will make a line 24 m long, how many cans of paint
should they buy?
Area/Perimeter/Multiplication/Division Grass Seed A 1600 cm by 2400 cm rectangular section of the playground is to be reseeded
to grow grass. Each bag of grass seed covers 9 m2 . How many bags of seed do
we need to buy? After the seed is planted, we need to put a fence around it so
students don’‛t play on it. How much fencing is needed? Division / Area / Perimeter Egyptian Area Rug
3500 cm
a) Find the area and perimeter in metres of this Egyptian area rug.
b) If 7 students sit on the rug, how much space will they
each have to sit?
2300 cm
(Most recent at top) Measurement Using dot paper, how many different rectangles can you draw with
a. a perimeter of 12 units?
b. an area of 12 square units?
Label your dimensions! Label the area and perimeter. Multiplication Susan is in charge of fundraising at the office where she works. They are raising money to give to the food bank in her city. She is asking each person she works with to collect $25. There are 37 people working in her office. If each person collects $25, how much money in total will have been collected for the food bank? Division 2 groups of friends go out into the neighbourhood to rake leaves for the elderly. Tulja and her 3 friends earn $ 246.00. Luke and his 2 friends earn $174.00. Luke says he’‛ll have more money than Tulja because he only has to share his money with 2 people. Do you agree? Area and Perimeter Using a ruler, measure the top surface of your desk. Round the dimensions to the nearest cm. Find the area and perimeter (pretend the corners aren't rounded). Remember to show your work! Brodric’‛s shoe laces are 47 cm long. Hannah’‛s laces are 0.6 m long and Leo’‛s are 530 mm long. Who has the longest laces? How long would the three laces be in total if they stretched them all out together? What is the most appropropriate unit to measure the laces? Why? Patterning Draw an Input/Output machine. Choose a number and an operation. Use multiples of any number as the input numbers. Find the output numbers. Make a table to show your results. Write the pattern rules for the input and the output numbers. Division There are 109 students who want to play basketball in the after school league. If you want to make teams of 9 students per team, what would your team organization look like? Multiplication
Ms. Pitkin will be placing an order for school supplies, and she asked me to check the number of markers in the school’‛s supply cupboard. I counted 38 boxes, and I know that there are 16 markers in each box. I haven’‛t had time to figure out the total number of markers yet. Please help me solve this problem. Geometry 3D Geometric Figures With your group, create a chart like the one below and fill in the columns with the correct information or drawing.
Shape Net Sketch Faces Edges Vertices
Cube
Rectangular Prism
Sphere
Cylinder
Square based Pyramid
Tetrahedron
Cone
Pentagonal Prism
Octagonal
Prism
Division
Photo Album - I have 434 photos that I’‛m trying to put into an album. If each
page can hold 6 photos, how many pages will I use?
Geometry
Creating Nets
Using graph paper, neatly create a variety of nets of 3D shapes. Use the squares
to help you keep the size accurate!
Patterning
What is the 7th term of this pattern? Start at 200. Subtract 8 each time.
How could you find the 7th term without writing the first 6 terms?
Measurement
Mme Nagge’‛s new dog needs a new kennel to run around in. She wants the kennel
to be rectangular in shape and have an area of 36 square metres.
a) Find all of the possible rectangular kennels that have an area of 36 square
metres. Record your solutions on the graph paper. Remember to include the
dimensions of your rectangles.
b) How much fencing will she need for each rectangular kennel? Show your work.
c) Choose one of the rectangular kennels that you think would be the best design
for her kennel. Explain why you think this is the best design.
Multiplication SJAM sent 1854 students and 58 teachers to a special performance at the
Centre in the Square. The theatre has 49 rows with 48 seats in each row. Were
there any seats empty? Explain.
Area & Perimeter 1) Find the area of a rectangle that has a width of 7 cm and a length of 8 cm.
Draw the rectangle using a ruler! Find the area and perimeter of the rectangle.
Explain how you got your solution.
2) What happens to the area of the rectangle when the width remains at 7 units
and the length decreases to 4 units? Draw the rectangle using a ruler. Find the
area and perimeter of the new rectangle.
a) Compare and explain the differences between the area from the rectangle in #1 to the area of rectangle in #2 .
b) Compare and explain the differences between the perimeter of the rectangle in #1 to the perimeter of the rectangle in #2. Multiplication Estimate the product of 47 x 29. Will it be closer to 1200 or to 1500? Explain.
Then Solve. Patterning Create growing “L’‛s” using tiles. The 1st L has 3 tiles, the 2nd L has 5 tiles, the
3rd L has 7 tiles and so on. Predict the number of tiles you would need to build
the 10th L in the pattern. Can you come up with a rule for this pattern?
Multiplication If 1 bicycle costs $125, what is the cost of 5 bicycles? How about 15 bicycles?
Solve the problem without using the standard algorithm. How many ways can you
solve it?
Area and Perimeter Find the area of a rectangle that has a width of 17 units and a length of 12
units. Draw the rectangle on graph paper using a ruler and let each square on
the paper represent one unit. Find the area and perimeter of the rectangle.
Explain how you got your solution.
Multiplication Solve 100 x 100.
Prove that your answer is correct and determine a rule for multiplying by 10,
100, 1000
Measurement Conversions How many grams are in one serving if 1.5 kg will serve six people? Multiplication I was helping a friend design her new rectangular patio. It will be made of square
tiles. The long side of her patio will be 25 tiles long, and the short side will be 16
tiles long. How many square tiles should she buy? Show more than one way to
solve this problem.
Elapsed Time Name: ______________
After school, Tristan leaves school at 3:35 and walks home (12 minutes), has a
snack (5 minutes), plays Minecraft (60 minutes) and then does his homework (20
minutes) before dinner is ready.
a. What time does eat dinner?
b. What time is this in 24 hour time?
c. Draw the hands on the clock when it is time for Tristan to eat.
Mean, Median, Mode 5, 7, 3, 6, 10, 7, 3, 9, 8, 3, 5, 11, 3
a) Find the mean, median and mode for the above data set.
b) What is the range?
c) What do you think will happen to the mean if 4 is added to the set of data?
Why?
Elapsed Time Problems Solve and show your work!
1) Rebecca is making brownies. They need to bake for 47 minutes. She put them
in the oven at 6:30 P.M. At what time should she take them out?
2) An airplane left the Region of Waterloo Airport at 9:50 A.M. and arrived in
Thunder Bay at 11:45 A.M. How long did the trip take?
3) How long did Xiwen sleep if he went to bed at 9:40 P.M., and got up at 7:20
A.M.?
4) Five hours and 42 minutes after he started a bike tour, Mohab completed the
tour. If he finished at 2:17 P.M., what time did he start?
5) If Mr. Cummings leaves home at 7:55 A.M. and arrives at school at 8:04 A.M.,
how long did it take him to get here?
6) Ms. Banks set a timer at 9:15 A.M. to ring in 35 minutes for a practice quiz in
her classroom. What time will it be when the timer rings?
7) Sarah took a trip to Georgia from Virginia during Spring Break. She left home
at 6:45 A.M. and arrived at 5:55 P.M. How long did the trip take?
8) Hossam left home at 4:42 P.M. and rode his bike to his friend's house. It took
him 23 minutes. What time did he arrive?
9) Mitraa did her science project in three parts. Part one took her 45 minutes.
Part two took her 36 minutes. Part three took her 14 minutes. What was the
total time it took her to finish her project?
10) Dad began cutting grass on Saturday morning at 9:28 A.M. He finished the
entire yard by 10:33 A.M. How long did it take him?
Area Populations from 1996 to 2011 Name: ___________ 2011 2006 2001 1996
Kitchener 219,153 204,668 190,399 178,420
Cambridge 126,748 120,371 110,372 101,429
Guelph 121,688 114,943 106,170 95,821
Waterloo 98,780 97,475 86,543 77,949
1) Based on population in 2011 , what is the total population of Kitchener, Cambridge, Guelph and
Waterloo? Write this amount in standard form, expanded form and in words.
2) How many more people did Guelph have in 2011 than in 1996? Write an equation to help solve for missing variable.
3) Round the populations for Kitchener in each year to the nearest thousand .
4) Now create an appropriate graph to show the change in population of Kitchener from 1996 to
2011. Explain why you chose this type of graph.
5) What conclusion(s) can you make from the population data above?
Making Triangles 1) Construct triangle QRS
<R = 75 degrees <Q = 30 degrees Side QR = 6 cm a) What should <S equal? b) Measure the other 2 sides. c) What kind of triangle have you created? 2) Construct a right angled isosceles triangle with a side measuring 5 cm. a) What are the other 2 angles? b) Measure the side lengths. Geometry
1) Cut out the shapes on the dotted line.
2) Sort them in a way that is logical to you.
3) Using the ipad, take a picture.
4) Explain why you sorted them the way you did (you may use the voice
recording, text box or write on screen)
5) Can you resort the polygons within their groups based on other properties?
6) Repeat #3 & 4
7) Upload your page from Educreations into your Google Drive
DM Mean, Median and Mode
The scores on a math quiz out of 20 were:
5, 8, 11, 5, 18, 20, 19, 15, 14, 5, 17, 18, 19
a) Find the mean, median and mode of the data. You may use a calculator, but
show your work!
b) Mean, median and mode are all types of averages. Which one best represents this data? Why?
Time Miss Snelgrove leaves home on her bike at 6:45 a.m. and arrives at school at 7:51
a.m.
a) How long did it take her to get to school?
b) Show the time she left her house on the clock. c) After school at 3:45 p.m., when it is time to ride
home, what time is it in 24 hour time?
Show your work!
Algebra Solve for the missing variable:
1) 13 + X = 20 2) X - 8 = 25
3) 14 + 12 = X 4) 11 + X = 35 - 20
5) 25 + 10 = X - 5
Write an equation to help you solve the following problem:
I have 14 Smarties in total. 9 are blue. How many are other colours? Algebra C = 3 x n
C = total cost in dollars
N = number of sandwiches purchased
a) What is the cost of 5 sandwiches?
b) If the total cost is $12, how many sandwiches were purchased? Geometry Triangles
a) Construct a triangle with: ab = 6 cm
<abc = 60˚
<cab = 30˚
b) How long are the other 2 sides?
c) What is the other angle? How do you know?
d) What kind of triangle have you made? How do you know?
Equations Daniel went to visit his grandmother, who gave him $1.50. Then he bought a book
costing $3.20. If he has $2.30 left, how much money did he have before visiting
his grandmother? Write an equation (number sentence) to help you solve this
problem.
Place Value
How Big is 100 000?
1) A population of a town is 25 197. A new family moves into town. What might be the new population?
2) I am thinking of a number. It is between 20 000 and 60 000. Each digit is even. The sum of the digits is 10. Find more than one answer.
3) a) How long would it take to roll to 100 000 pennies? b) How high would a stack of 100 000 pennies be? Explain how you could figure these out.
Algebra
1) There are two numbers whose sum is 72. One number is twice the other. What are the numbers? 2) Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quotient will be 20. What is the number?
Data Management
Allowance
Here are the weekly allowances of 15 grade 5 students: $4, $6, $8, $10, $15, $5, $7, $10, $5, $10, $5, $10, $4, $13, $8 a) What is the mean allowance? b) What is the mode of the allowances? c) What is the median allowance? d) Suppose 2 allowances of $13 and $20 are added to the list. What do you think will happen to the mean?
e) Show you work and explain your thinking!
f) Create an appropriate graph of the data.
Time Freight Train A freight train travels 100 km every hour. It passes over a river at 10:00 a.m. 4
hours later, a passenger train passes over the same river. The passenger train
travels 150 km every hour. When does the passenger train overtake the freight
train? How far are they from the river? What time is this in 24 hr time?
Geometry Polygon Angles A) Using a ruler and sharp pencil, create these irregular (not all angles and side
lengths are the same) polygons:
a quadrilateral (4)
a pentagon (5)
a hexagon (6)
a heptagon (7)
an octagon(8)
a decagon(10)
B) Measure and label all side lengths and angle measurements.
What do you notice about what the angles in each polygon add to?
C) Now that you know what each polygon adds to, choose one of the polygons and
create a regular shape. Geometry
Construct triangle GHK.
<H is 45 0
Side HK is 64 mm.
Side HG is 46 mm.
a) What is <K?
What is side GK?
b) Suppose the length of side HG is 7 cm.
What happens to the measure of <K?
What happens to the length of GK? Algebra Number Trick
- Select any number
- Double it
- Subtract 3
- Double again
- Add 2
- Divide by 4
Now try your end number and work backwards. What number do you
predict you will get? Place Value "Water Tank Problem" At my family’‛s cottage, we have a water basin that fills with rainwater. The
water in this basin is pumped to the cottage and used for cooking, cleaning,
bathing, etc. It holds 13 000 litres of water when full.
We use 2 222 L for cooking, 4 580 L for showering, and 3 626 L for cleaning
each week.
1. What is the total amount of water used in a week? Show this amount in
standard form, in words and in expanded form.
1. If it rains a lot over the weekend and we gather 10 000 more litres of
water, will it fill the tank? (Pretend we have already cooked, showered, and
cleaned for this week!) Show your work! Number Sense Aircraft Carrier An aircraft carrier carrying 2 helicopters has a total mass of 439 824 kg. The
first helicopter has a mass of 128 915 kg. The aircraft carrier has a mass of 247
651 kg. What is the mass of the second helicopter?
When you have solved it one way, try it another way.
Algebra
1) 6 x 4 = 12 x
What number relationships does the above equation show?
2) X + 5 = 8 or + 5 = 8
What does the ‘x’‛ and the box represent?
3) Common Equations or Formulas
V = L x W x H
What do the letters in the above equation represent?
a) Solve for V if:
L= 2
W = 3
H = 4
b) If V = 36
L = 2
W = 3
What is the value of H?
4) 5 x + 2 = 27
Geometry - Triangles a) Construct a triangle with:
DE = 5 cm
DF = 5 cm
<D is a right angle
b) Find the measure of the other 2 angles and side EF.
c) What kind of triangle have you constructed? (2 kinds)
d) How do you know your angle measurements are correct?
Data Management Math Marks Miss Snelgrove has the math marks of 26 students: 54, 55, 58, 61, 63, 65, 66,
67, 68, 71, 72, 73, 73, 74, 75, 76, 77, 78, 79, 81, 83, 86, 87, 88, 91, 95.
There are too many pieces of data to graph each mark separately.
a) First, group the marks into appropriate intervals.
b) Create a bar graph to show the data
c) Use a stem and leaf plot to show the data.
If finished above,
d) find mean, median and mode of the data Measurement - Time Tony and Teena work at the museum. The museum is 18 km away. Tony leaves
home and starts walking to work at 5:30 a.m. He walks 4 km every hour. Teena
leaves home and starts riding her bike to work at 7:30 a.m. She cycles 12 km
every hour.
a) If the museum opens at 9:00 a.m., will Tony and Teena be on time? Explain.
b) When does Teena overtake Tony? How far have they travelled?
Geometry - Triangles
a) Construct a triangle with:
cab = 6 cm
<abc = 60˚
<cab = 30˚
How long are the other 2 sides?
What is the other angle? How do you know?
b) Construct triangle MNP.
The length of MN is 4.5 cm.
The measure of <M is 40 0 . The length of MP is 3.7 cm.
Measurement - Time
Homework!
Allan started his homework at 7:15 p.m. and finished at 8:50 p.m. Natalie started
her homework at 6:50 p.m. and finished at 8:10 p.m.
a) Draw the hands on the clock when Natalie started her homework.
b) Whose homework took longer to complete? By how
much?
c) Using 24 hour time, what time did Allan finish his homework?
Show your work!
Data Management
Shoe Sizes Determine the most common shoe size in our class. Create an appropriate graph for your data. Find the mean, median and mode. How would you determine the most common shoe size in Ontario for your age group? How would you use this information (purpose)? Is this discrete or continuous data? 6, 5, 5, 6.5, 5, 9, 5, 5, 4.5, 6.5, 6, 4, 6.5, 5, 3.5, 7, 6, 4, 5, 5, 3, 5.5, 1.5 Place Value SJAM Election SJAM recently held their student council elections. Four students ran for Prime Minister of SJAM. The vote results were: Clark Kent 528 Selina Kyle 313 Bruce Wayne 225 Lois Lane 499
1. Round each amount to estimate the total number of votes 2. Exactly how many students voted? Write this number in expanded form and in words. 3. SJAM has 1600 students. How many students did not vote? 4. One class with 31 students was away on a field trip and didn’‛t get to vote. Could their
votes have changed the results of the election if they were at school on voting day? Place Value 2011 Provincial Election In the 2011 Provincial Election, the riding of Kitchener-Waterloo had 53 263 ballots cast (made). Here is a list of the ballots cast for the top four parties: Elizabeth Witmer - Conservative 21 356 Eric Davis - Liberal 17 837 Isabel Cisterno - NDP 8 259 J.D. McGuire - Green Party 1 307 a) How many votes were cast for these four candidates? Write this answer in expanded form and in words. b) How many other ballots were cast? c) Out of the remaining ballots, 3 624 were spoiled. If these spoiled ballots had
been marked properly, could this have changed who won the election? Explain your thinking. Geometry Construct and classify as many possible triangles (e.g., acute, right, obtuse) that can be made if you are given 2 side lengths - one is 5 cm and one is 3 cm. Time Getting Ready for School If you wake up at 7:30 a.m., and it takes you 10 minutes to eat your breakfast, 5 minutes to brush your teeth, 25 minutes to wash and get dressed, 5 minutes to get your backpack ready, and 20 minutes to get to school, will you be at school by 9:00 a.m.? Data Management Assignment
1) Considering our discussion and the examples we went over in class, you are to choose something that you would like to chart, track, graph daily or weekly over the next several weeks. 2) The data for the topic you choose will be data that could change over time (continuous data) and will be in the form of some type of number (e.g., money, time, temperature)
3) Before Wednesday, you need to confirm the following with Miss Snelgrove: a) What you will be tracking b) The purpose (What information do YOU hope to learn from collecting your data?) c) How exactly are you going to collect the data (personal experiments, accessing secondary data)?
Part B Each school day you will take a few minutes to collect your data for your chosen
topic and record it in a chart starting on the BACK page of your Everything Book.
It is up to you if you choose to collect data on weekends.
Date Sunrise Sunset
Oct. 7 7:28 18:53
Oct. 8 7:29 18:54
Oct 9
Geometry Construct the following triangles. Be sure to label them.
a) Construct a right angled triangle with:
side ab = 5 cm and ac = 3cm
(from a to b is 5 cm) (from a to c is 3 cm)
b) Construct an acute triangle with:
side ab = 6 cm and <abc = 30˚
Place Value Solve the riddle below, showing your work. Then write a cheque to Miss
Snelgrove for the amount of the answer you found.
My hundred thousand’‛s digit is 3 times my thousand’‛s digit. My hundred’‛s digit is
twice my thousand’‛s digit. My one’‛s, ten’‛s and ten thousand’‛s digits are all the
same. The sum of my digits is 18. What number am I?
Geometry Use a protractor, a ruler, and a pencil to construct a scalene triangle with a 30°
angle and a side measuring 12 cm. Label your triangle and explain the steps you
used. Measurement - Time You are traveling from Toronto to Montreal by train. If the train departs
Toronto at 11:30 a.m. and arrives in Montreal at 4:56 p.m., how long will you be on
the train? Using a 24 hour clock, what time did you arrive in Montreal?
Data Management In the space below, answer the following: You may use the back if needed and the graph paper provided. 1) Write a survey question that you will ask classmates. Explain how you will use
the information you gather from this question.
2) Survey classmates to gather your data.
3) Create an appropriate graph of your data. Explain why you chose this type of
graph.
4) What type of data did you gather (primary or secondary and discrete or
continuous)? How do you know?
5) If you wanted to collect data for your question from grade 5 students in all
of Ontario, how would you go about gathering your data?
6) What conclusions can you draw (make) from the data in your graph? Place Value "Johnson Sports Store" The Johnson Sports Store sells baseball bats to baseball leagues in Canada. The
bats are sold as singles (1), in bundles (10) and in canisters (100). Work with your
partner to fill the orders for the bats. Create an order form for each league
indicating the most efficient amounts to ship the bats. Write your amounts in
standard form (number), expanded form and words.
Dundas League Aurora League Belfield League Tigers 50 bats Bumblebees 6 bats Blue Jays 16 bats
Pandas 64 bats Bears 25 bats Cheetahs 32 bats
Lions 16 bats Cubs 29 bats Taranchulas 14 bats
Cardinals 55 bats Gorillas 50 bats