Grade 6 Tasks Index

Grade 6 Tasks Index

Task / Standard / Unit
Baking Cookies / 6NS1
Drinking Hot Cocoa / 6NS1
Drinking Juice / 6NS1
Setting Goals / 6NS2
Gifts from Grandma / 6NS3
Movie Tickets / 6NS3
The Florist Shop / 6NS4
Mile High / 6NS5
Jumping Fleas / 6NS7
Games at Recess / 6RP1
Voting for two / 6RP1
Mangos for sale / 6RP2
Price per pound / 6RP2
Walk-a-thon / 6RP3
Friends meeting on bicycles / 6RP3
Running / 6RP3
Overlapping Squares / 6RP3
Shirt Sale / 6RP3
The Djinni’s Offer / 6EE1
Rectangle Perimeter / 6EE4
Log Ride / 6EE5
Firefighter Allocation / 6EE6,7
Morning Walk / 6EE7
Fruit Salad / 6EE7
Fishing Adventures / 6EE8
Chocolate bar sales / 6EE9
Areas of Polygons / 6G1
Banana Bread / 6G2
Candle Box / 6G4
Smoothie Box / 6G4
Puppy Weights / 6SP2
Electoral College / 6SP2,5
Candy Bars / 6SP4,5
Puzzle Time / 6SP4,5
Suzi’s Company / 6SP5

Grade 6 Tasks

Baking Cookies (6NS 1)

Alice, Raul, and Maria are baking cookies together. They need3/4cup of flour and1/3cup of butter to make a dozen cookies. They each brought the ingredients they had at home.

Alice brought2cups of flour and1/4cup of butter, Raul brought1cup of flour and1/2cup of butter, and Maria brought1/14cups of flour and3/4cup of butter. If the students have plenty of the other ingredients they need (sugar, salt, baking soda, etc.), how many whole batches of a dozen cookies can they make?

Solution

The children brought2+1+1/14=41/4cups of flour and1/4+/1/2+3/4=11/2cups of butter. They have enough flour for41/4÷3/4=52/3batches and they have enough butter for11/2÷1/3=41/2batches , so the butter is the limiting factor. Thus, they can make 4 whole batches of a dozen cookies each.

Drinking Hot Cocoa (6NS 1)

One mug of hot chocolate uses2/3cup of cocoa powder. How many mugs can Nelli make with 3 cups of cocoa powder?

a.Solve the problem by drawing a picture.

b.Explain how you can see the answer to the problem in your picture.

c.Which of the following multiplication or divisions equations represents this situation? Explain your reasoning.

3×2/3=? 3÷2/ 3=? 2/3÷3=?

d.Solve the arithmetic problem you chose in part (c) and verify that you get the same answer as you did with your picture.

Solution

1. Below is a picture that can be used to solve the problem.

1. The picture shows three rectangles that each represent 1 cup of cocoa powder. Each cup is divided into thirds. Since one mug requires2/3cup, 2 thirds are shaded to show a single mug of cocoa. There are four whole groups of2/3cups of cocoa and1/2of a group of2/3cups of cocoa shown in the picture.

Nelli can make41/2mugs of cocoa.

1. We have divided the 3 cups of cocoa powder into groups of size2/3, so we are finding out how many groups of2/3there are in 3. So the correct equation is:

3÷2/3=?

1. Solve the arithmetic problem you chose in part (c) and verify that you get the same answer as you did with your picture.

3÷2/ 3 = 3/1×3/ 2 = 9/2 = 41/2

So the computation gives the same answer as we see in the picture.

Drinking Juice (6NS1)

Alisa had1/2liter of juice in a bottle. She drank3/8liters of juice. What fraction of the juice in the bottle did Alisa drink?

Solution

First, draw a rectangle that represents12liter.

We know that Alisa has1/2liter of juice in a bottle. Now we break the rectangle that represents1/2liter into four smaller rectangles. Each small rectangle represents1/4of1/2, which is

1/4×1/2=1/8liter.

Alisa drank3/8of a liter of juice so 3 of the small rectangles are shaded. We can now see that 3 of the 4 rectangles that make up the juice in the bottle are shaded.

Alisa drank3/4of the juice that was in the bottle.

Setting Goals (6NS2)

a.Seth wants to buy a new skateboard that costs$169. He has$88 in the bank. If he earns$7.25 an hour pulling weeds, how many hours will Seth have to work to earn the rest of the money needed to buy the skateboard?

b.Seth wants to buy a helmet as well. A new helmet costs$46.50. Seth thinks he can work 6 hours on Saturday to earn enough money to buy the helmet. Is he correct?

c.Seth’s third goal is to join some friends on a trip to see a skateboarding show. The cost of the trip is about$350. How many hours will Seth need to work to afford the trip?

Solution

1. 167 - 88 = 79, so Seth needs to make$79. Since

79÷7.25≈10.9

Seth will have to work about 11 hours to make enough money to buy the skateboard.

1. No, Seth is not correct. 6 x 7.25 = 43.5 which is not enough to buy the helmet; he needs$3 more which will require a bit less than a half an hour more work.

1. Since350÷7.25≈48.3Seth will have to work about 50 hours.

Gifts from Grandma (6NS3)

a.Juanita spent$24.50 on each of her 6 grandchildren at the fair. How much money did Juanita spend?

b.Nita bought some games for her grandchildren for$42.50 each. If she spent a total of$340, how many games did Nita buy?

c.Helen spent an equal amount of money on each of her 7 grandchildren at the fair. If she spent a total of$227.50, how much did each grandchild get?

Solution

a.Juanita spent 6 groups of$24.50, which is6×24.5=147dollars all together.

b.Since the number of games represents the number of groups, but we don’t know how many games were purchased, this is a “How many groups?” division problem. We can represent it as

?×42.5=340

or

340÷42.5=?

So Nita must have purchased 8 games.

c.Here we know how many grandchildren there are (so we know the number of groups), but we don’t know how much money each one gets (the number of dollars in each group). So this is a “How many in each group?” division problem. We can represent it as

7×?=227.5

or

227.5÷7=?

So Helen must have spent$32.50 on each grandchild.

Movie Tickets (6NS3)

Hallie is in 6th grade and she can buy movie tickets for$8.25. Hallie's father was in 6th grade in 1987 when movie tickets cost$3.75.

a.When he turned 12, Hallie's father was given$20.00 so he could take some friends to the movies. How many movie tickets could he buy with this money?

b.How many movie tickets can Hallie buy for$20.00?

c.On Hallie's 12th birthday, her father said,

When I turned 12, my dad gave me$20 so I could go with three of my friends to the movies and buy a large popcorn. I'm going to give you some money so you can take three of your friends to the movies and buy a large popcorn.

How much money do you think her father should give her?

Solution

1. To find out how many tickets he could buy with$20, we divide 20 by the price of a single ticket:

20÷3.75=5.3¯

Since it's not possible to purchase a part of of a ticket, this means that he could buy 5 tickets and will have some money left over. Since

5×3.75=18.75

and

20−18.75=1.25

her father could buy 5 movie tickets in 1987 with$20, and he would have$1.25 left over.

1. As before, to find out how many tickets she could buy with$20, we divide 20 by the price of a single ticket:

20÷8.25=2.42

As before, she can't buy part of a ticket. Furthermore,

2×8.25=16.50

and

20−16.50=3.50

So Hallie can buy 2 movie tickets if she has$20, and she will have$3.50 left over.

1. Sincec. ×3.75=15, a large popcorn had to cost$5.00 or less if her father bought it with the change from buying the tickets. Hallie's movie tickets cost8.25÷3.75=2.2times as much as movie tickets cost in 1987. Assuming the price of popcorn increased at the same rate, and since2.2×5=11, she should be able to buy a large popcorn for$11.00. Four tickets cost4×8.25=33dollars. With these assumptions, Hallie's father should give her at least$44.00.

The Florist Shop (6NS4)

The florist can order roses in bunches of one dozen and lilies in bunches of 8. Last month she ordered the same number of roses as lilies. If she ordered no more than 100 roses, how many bunches of each could she have ordered? What is the smallest number of bunches of each that she could have ordered? Explain your reasoning.

Solution

The florist could have ordered any multiple of 12 roses that is less than 100:

12, 24, 36, 48, 60, 72, 84, or 96.

The florist could have ordered any multiple of 8 lilies that is less than 100:

8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

If she ordered the same number of each kind of flower, she must have ordered a common multiple of 8 and 12, shown in the table below:

Number of each kind of flower / 24 / 48 / 72 / 96
Number of bunches of roses / 2 / 4 / 6 / 8
Number of bunches of lilies / 3 / 6 / 9 / 12

The number of bunches of each are shown in the second and third rows. We can find the number of bunches of roses by dividing the number of flowers by 12, and we can find the number of bunches of lilies by dividing the number of flowers by 8.

The smallest number of each she could have ordered was 2 bunches of roses and 3 bunches of lilies.

Mile High (6NS5)

Denver, Colorado is called “The Mile High City” because its elevation is5280feet above sea level. Someone tells you that the elevation of Death Valley, California is−282feet.

a.Is Death Valley located above or below sea level? Explain.

b.How many feet higher is Denver than Death Valley?

c.What would your elevation be if you were standing near the ocean?

Solution

a.Death Valley is located below sea level. We know this because its elevation is negative. Sea level is the base for measuring elevation. Sea level elevation is defined as 0 ft. All other elevations are measured from sea level. Those places on Earth that are above sea level have positive elevations, and those places on Earth that are below sea level have negative elevations. Thus, Death Valley, with an elevation of -282 feet, is located below sea level.

b.To find out how much higher Denver is than Death Valley, we can reason as follows:

Death Valley is 282 feet below sea level. Denver is 5280 above sea level. So to go from Death Valley to Denver, you would go up 282 feet to get to sea level and then go up another 5280 feet to get to Denver for a total of

282+5280=5562 feet.

Thus, Denver, Colorado is 5562 feet higher than Death Valley, California.

c.If you were standing near the ocean, your elevation would be close to zero. Depending on how high or low the tide is and where exactly you are standing, your elevation could be as low as -50 feet (or as high as 50 feet) if you are at the edge of a very low tide (or a very high tide, respectively) at the Bay of Fundy.

Jumping Fleas (6NS7)

A flea is jumping around on the number line.

a.If he starts at 1 and jumps 3 units to the right, then where is he on the number line? How far away from zero is he?

b.If he starts at 1 and jumps 3 units to the left, then where is he on the number line? How far away from zero is he?

c.If the flea starts at 0 and jumps 5 units away, where might he have landed?

d.If the flea jumps 2 units and lands at zero, where might he have started?

e.The absolute value of a number is the distance it is from zero. The absolute value of the flea’s location is 4 and he is to the left of zero. Where is he on the number line?

Solution

It would be a good idea to use a number line to illustrate these solutions.

a.If he starts at1and jumps3units to the right, then the flea is at4. He is4units away from zero.

b.If he starts at1and jumps3units to the left, then the flea is at−2. He is|−2|=2units away from zero.

c.If the flea starts at0and jumps five units away, then he is either at−5or5.

d.If the flea lands on0and jumped2units, then he started at either−2or2.

e.If the absolute value of the flea’s location is4, then he is either at−4or4. Since he is to the left of zero, the flea is at−4.

Games at Recess (6RP 1)

The students in Mr. Hill’s class played games at recess.
6 boys played soccer
4 girls played soccer
2 boys jumped rope
8 girls jumped rope
Afterward, Mr. Hill asked the students to compare the boys and girls playing different games.
Mika said,

“Four more girls jumped rope than played soccer.”

Chaska said,

“For every girl that played soccer, two girls jumped rope.”

Mr. Hill said, “Mika compared the girls by looking at the difference and Chaska compared the girls using a ratio.”

1. Compare the number of boys who played soccer and jumped rope using the difference. Write your answer as a sentence as Mika did.
2. Compare the number of boys who played soccer and jumped rope using a ratio. Write your answer as a sentence as Chaska did.
3. Compare the number of girls who played soccer to the number of boys who played soccer using a ratio. Write your answer as a sentence as Chaska did.

Solution

1. Four more boys played soccer than jumped rope.
2. For every three boys that played soccer, one boy jumped rope. Therefore the ratio of the number of boys that played soccer to the number of boys that jumped rope is 3:1 (or "three to one").
3. For every two girls that played soccer, three boys played soccer. Therefore the ratio of the number of girls that played soccer to the number of boys that played soccer is 2:3 (or "two to three").

Mangos for sale (6RP2)

A store was selling 8 mangos for$10 at the farmers market.
Keisha said,

“That means we can write the ratio 10 : 8, or$1.25 per mango.”

Luis said,

“I thought we had to write the ratio the other way, 8 : 10, or 0.8 mangos per dollar."

Can we write different ratios for this situation? Explain why or why not.

Solution

Yes, this context can be modeled by both of these ratios and their associated unit rates. The context itself doesn’t determine the order of the quantities in the ratio; we choose the order depending on what we want to know.

Price per pound (6RP 2)

The grocery store sells beans in bulk. The grocer's sign above the beans says,

5pounds for$4.

At this store, you can buy any number of pounds of beans at this same rate, and all prices include tax.

Alberto said,

“The ratio of the number of dollars to the number of pounds is 4:5. That's$0.80 per pound.”

Beth said,

"The sign says the ratio of the number of pounds to the number of dollars is 5:4. That's 1.25 pounds per dollar."

a.Are Alberto and Beth both correct? Explain.

b.Claude needs two pounds of beans to make soup. Show Claude how much money he will need.

c.Dora has$10 and wants to stock up on beans. Show Dora how many pounds of beans she can buy.

d.Do you prefer to answer parts (b) and (c) using Alberto's rate of$0.80 per pound, using Beth's rate of 1.25 pounds per dollar, or using another strategy? Explain.

Solutions

Alberto and Beth are both correct. Their rates could be illustrated with a double number line or a ratio table like the following:

Pounds / Dollars
1 / .80
1.25 / 1
2.5 / 2
5 / 4

(b) Double the quantities in Alberto's rate to find the price of two pounds:

Pounds / Dollars
1 / .80
2 / 1.60

(c) Starting from Beth's rate and multiplying both quantities by ten shows the number of pounds that can be purchased for 10 dollars:

Pounds / Dollars
1.25 / 1
12.50 / 10

(d) Answers may vary. We can efficiently answer part (b) using Alberto's rate and part (c) using Beth's rate.

Walk-a-thon (6RP 3)

Julianna participated in a walk-a-thon to raise money for cancer research. She recorded the total distance she walked at several different points in time, but a few of the entries got smudged and can no longer be read. The times and distances that can still be read are listed in the table below.

a.Assume Julianna walked at a constant speed. Complete the table and plot Julianna’s progress in the coordinate plane.

b.How fast was Julianna walking in miles per hour? How long did it take Julianna to walk one mile?

c.Next year Julianna is planning to walk for seven hours. If she walks at the same speed next year, how many miles will she walk?

Time in hrs / Miles walked
1
2 / 6
12
5

Solution

1. We see that the only complete time-distance pair indicates that Julianna walked 6 miles in 2 hours. If she walked at a constant speed, we can conclude that Julianna walked 3 miles in 1 hour. Using this speed, we can find the remaining values in the table by multiplying the hours she walked by 3 (or, alternatively, by entering 3 in row next to 1 and then adding 3 for every hour walked). We get the following table.

Time in hrs / Miles walked
1 / 3
2 / 6
3 / 9
4 / 12
5 / 15

Let's plot her progress in the coordinate plane by having her time, in hours, be represented on the horizontal axis, and the number of miles she walked be represented on the vertical axis. Using the rows in the table above as our coordinate points, we get the following graph.

1. We found in part (a) that Julianna walks 3 miles in 1 hour.

Looking at the picture above, we can see that if she walks 3 miles in one hour, and she is walking at a constant speed, then it will take her13of an hour to walk 1 mile.

We can also look at a double number line.

We can see on the double number line that 1 hour corresponds to three miles and13hour corresponds to 1 mile.

So, we find that it took Julianna13hours, or 20 minutes, to walk 1 mile.

1. We found in parts (a) and (b) that Julianna’s rate of travel was 3 miles per hour. If this stayed constant, we can find how many miles she would walk in 7 hours by extending our table.

Time in hrs / Miles walked
1 / 3
2 / 6
3 / 9
4 / 12
5 / 15
6 / 18
7 / 21

1. Thus, we see that in 7 hours, Julianna will walk 21 miles at that rate.

Friends meeting on bicycles (6RP 3)

Taylor and Anya live 63 miles apart. Sometimes on a Saturday, they ride their bikes toward each other's houses and meet somewhere in between. Taylor is a very consistent rider - she finds that her speed is always very close to 12.5 miles per hour. Anya rides more slowly than Taylor, but she is working out and so she is becoming a faster rider as the weeks go by.

a.On a Saturday in July, the two friends set out on their bikes at 8 am. Taylor rides at 12.5 miles per hour, and Anya rides at 5.5 miles per hour. After one hour, how far apart are they?

b.Make a table showing how far apart the two friends are after zero hours, one hour, two hours, and three hours.