6th grade open ended math practice

Factors and Multiples

1.

Craig is creating gift baskets for the food pantry to give away.  He has 91 canned food items and 52 boxed food items, giving him a total of 143 items. The sum is shown below.

He wants to make sure that every gift basket has an equal amount of canned food items and an equal number of boxed food items, as well as use all of the food items.

Part A: Determine how many gift baskets he will be able to make.

Part B: Then, rewrite the sum to show how these food items will be distributed among the gift baskets.

Part C: Explain why Craig could not make any more gift baskets in this way with the available food items.

After a busy day of orders, a florist has 6 roses, 7 lilies, 3 carnations, 35 chrysanthemums, 27 sunflowers, 18 violets, and 9 tulips left in her inventory. 

Part A: Write a ratio that compares the number of roses to the number of violets.

Part B: Describe what three other comparisons have the same ratio.

Part C: Provide reasoning why more than one comparison can be made with the same ratio.

Consider the calculation below.

"the product of n and 6"

Part A: Write an expression that is equivalent to the calculation above. If it is possible, write another equivalent expression using the same variables and numbers. If it is not possible, explain why not.

Consider the calculation below.

"the difference of x and 8"

Part B: Write an expression that is equivalent to the calculation above. If it is possible, write another equivalent expression using the same variables and numbers. If it is not possible, explain why not.

Consider the calculation below.

"the product of n and 6"

Part A: Write an expression that is equivalent to the calculation above. If it is possible, write another equivalent expression using the same variables and numbers. If it is not possible, explain why not.

Consider the calculation below.

"the difference of x and 8"

Part B: Write an expression that is equivalent to the calculation above. If it is possible, write another equivalent expression using the same variables and numbers. If it is not possible, explain why not.

Mr. Howard wrote the following expressions on the board in order to determine which expressions are equivalent and how they are equivalent.

Explain which of these expressions are equivalent using properties of operations, and then determine how other equivalent expressions could be created using the same properties. Provide at least two examples.

Part A: Consider the equation x + 7 = 16. Which number from the set {5, 7, 9, 11} makes the equation true?

Part B: If the equation above was changed to the inequality x + 7 < 16, would the same number make the inequality true? Explain why or why not.

Do any numbers from the set given in Part A satisfy the inequality? If so, which ones?

Matt and Andrew are soccer players. Throughout the last soccer season, Andrew scored three times as many goals as Matt did.

The expression 3m could represent the number of goals that Andrew scored throughout the last soccer season, with m representing the number of goals that Matt scored.

Write another expression that could be used to represent the number of goals that Matt scored throughout the last soccer season, and explain what the variable represents.

In a long jump competition, Janet jumped 1.75 meters further than Areli. If Janet's jump was a distance of 6.57 meters, how many meters long was Areli's jump?

Michael set up an equation to find the distance Areli jumped. His work is shown below.

Let a = distance in meters of Areli's jump.

Let j = distance in meters of Janet's jump.

Areli jumped a distance of 8.32 meters.

Did Michael correctly determine Areli's distance? Explain why or why not. If he was not correct, determine Areli's actual distance.

Emile's mom told him he could not have any dessert unless he ate more than 7 pieces of broccoli. The graphs below incorrectly represent the pieces of broccoli Emile must eat before he can have dessert. 

Part A: Explain why each of the two graphs incorrectly represent the pieces of broccoli Emile must eat.

Part B: Draw the graph that correctly represents the situation.

Type your response in the box. On a piece of paper, show part B. Turn in your paper to your teacher.

Mr. O'Riley visited a local fair with some students. He determined that the price of a souvenir cup was $4.69. He used this information to determine the total cost, t, based on the number of souvenir cups, c, that he bought.

Part A: Given this information, copy the table below on a separate piece of paper and complete the table by filling in the missing values.

Part B: Create an equation that represents the relationship between the total cost and the number of souvenir cups.

Part C: Mr. O'Riley intended to buy one souvenir cup per student that he brought to the fair. Determine the total cost that Mr. O'Riley would pay if he brought 16 students to the fair, and verify the reasonableness of the total cost using the table.