3rd Grade - Divide Total Cost To Find Cost Of One

Multiplication and Division
Divide Total Cost to Find Cost of One
Determine the unit cost when given the total cost and number of units
Number Sense: division with money The ability to solve a problem and come up with the unit cost (price per item) when the total cost of a group of items is given and the number of units purchased is given.

Sample Problems


What operation is used to solve a problem in which you want to know the cost of each object if you know the total cost of a group of objects and you know how many objects were purchased? (division)


Is estimation valuable in problems such as these? (yes, estimation can help us know if the answer is reasonable) For example, if the total cost is about $24 and 6 units were sold, the answer should be about $4 per unit.


The market is a great place to practice division with money concept. If a child buys 3 organic apples for $.40 each, how many can be bought for $3.00? (7) Will it always come out exactly when spending money? (No, sometimes you may spend less than you have, but always make sure to round up, so you don’t get stuck having to pay more than you have.)


Children can learn how to count back money as if the child was a cashier at a store. Start with the amount the customer paid and count back up to the dollar amount that was given. For example, if the customer bought items that cost $4.25 and paid with a ten-dollar bill, the child can start counting by saying $4.25. Then the child can add three quarters and say $4.50, $4.75, $5.00 and then add another $5 or five ones and count back up to $10.00.


Understand that division of money is used in every day life: If the child is not sure about how to solve a problem, draw a picture. For example, Janet must pay $20.00 for each of 4 tickets to a concert. She wants to know how much cash to bring to the ticket booth. The child may want to draw 4 tickets (rectangles) and label each one with a 20. The child can then skip count by 20s as they count the 4 tickets. 20, 40, 60, 80 or the child may write the number 20 in each ticket and use it like an equation 20 + 20 + 20 + 20 = 80.

Learning Tips


Allow children to create a pretend store that sells multiples of certain items. A child and the computer can take turns buying multiple items and figuring out what the unit cost is once the total is given at the cash register. One will know the unit price and have to figure out the total and the other will hear the total and have to figure out the unit price. Switch turns. A single child can ask a parent to play the game, too! You might introduce the game as the “Mystery Price Game.” You may choose what item in our store you would like to “buy” and you may decide how many to buy. Our “cashier” will add up the total on the computer and tell you what the cost will be for your purchases. Your job is to figure out how much it would have cost if you only bought one of the items. You may buy three times and then we’ll switch places so (the other player) will have a chance to be shopper and you’ll have a chance to be the cashier.


To play the game Gnome Share you will need to find some household items that you can use as “jewels” (perhaps you have some old beads or you might buy some inexpensive ones at a craft store. Small gems are also available at many craft stores—often used for the bottom of vases or fish tanks). When you’re ready, tell your child the Gnome Share story: “In the Land of Numbers is a great jeweled forest, where gems and riches are hidden everywhere. Two children have stumbled through a magical door and down a rainbow path where they met a plump little gnome, named Gnome Share. Gnome Share showed them all the piles of jewels (bring them out for the child to see) and he (or she) told the children that it was his/her job to divide the riches equally among all the people that lived in the Land of Numbers. The gnome then handed the two children a bag of 8 gems. The children worried that they wouldn’t know how to share them, but Gnome Share showed them how to make sure they each get the same number. The children asked to help Gnome Share with his work and he readily agreed but he wanted to know, first, if the children could figure out a way to divide them equally.”

Hand your child a bag of 8 gems and ask the child to show the gnome that they can divide them equally. Encourage your child to talk about the method they’ve devised: you can make the next round of the game harder or easier, depending on their success. Encourage them to devise new strategies when the ones they’ve used aren’t practical. For example, “one for you and one for me” works well for perhaps 8 gems, but when the bag contains, perhaps, 100 gems, that method is cumbersome. How else could you do it?

While this game isn’t technically about “money” most children understand that “gems” are another expression of value that can be quantified by naming what each piece is worth, even if you are making up the value as part of a story. To make this activity more money-specific, you can modify the instructions so that the bag contains a dollar-value of gems; i.e., this bag of gems is worth 10 gnome dollars. In our town today are 5 gnomes that must share it. How much will each gnome get? How many gems will each get so the value is the same for each?


Children can use food manipulatives, such as grapes at their kitchen table to act out the work of Gnome Share after they decide how much each item is worth. They can then use manipulatives to act out other simiilar division scenarios moving the child from the world of fantasy to the real world of, for example, shopping.


Use base ten blocks to have children practice dividing into equal groups. Have children write down a division sentence based on the model with the cubes. For example, if children divide six into three groups, the number sentence would read 6/3=2.


Make this concept come to life by acting out mini stories with your child. Allow them to handle real money to figure out dollar and change amounts. When you go shopping, talk through the process with your child and allow them to help you figure out if you have enough cash to buy your desired items and also if you received the correct change. For example, if you want to buy items that cost $5 each, how many can you buy with $50? ($50 divided by 5 = 10) or to figure unit cost. You spend $50 total and buy 10 items. How much did each one cost? ($5)

Extra Help Problems


$48.00 total was collected and 6 neckties were purchased. How much did they each cost?


Su spent $9 for each t-shirt she purchased for the baseball team. How much would it cost to dress the team of 20?


Ed wants to spend about $80 for a gift for his mother for Mother’s Day. He finds a set of ceramic figures that his mother would love. Each figure costs $6. How many can he buy? (13)


Total cost: $4.50

Number of units: 90

Cost per unit = ______ ($4.5 divided by 90=$.05 Each unit costs five cents.)


Total cost: $24.00

Number of units: 80

Cost per unit = ______ ($24.00 divided by 80 = 30 cents. Each unit costs $.30)


Total cost: ________

Number of units: 100

Cost per unit: $.55 ($.55 x 100 = $55.00. The total cost for 100 units is $55.00)


Advanced problem:

Cost per unit: $1.50

Number of units: ________

Total cost: $27.00 ($27.00 divided by $1.50 = 18. Eighteen units were sold.)

If children are not yet comfortable with division, they may use actual coins and dollars to figure out the above problems.


Each candy costs $.50 and you purchase 10 of them. How much do you spend? ($5.00)


You buy a bunch of bananas at the market. The cost $.40 each. You pay $2.80. How many did you purchase? (7)


You win a shopping spree at the toy store worth $1,000. You want to buy a flying airplane that costs $270. How much do you have left to spend? ($730) If you spend the rest equally on five different toys, how much did each toy cost? ($146)


$280/7= ($4)


$1,200/40 = ($30)


$890/5 = ($178)


4 x $186 = ($744)


3 x $12 = ($36)


$144 divided by _____ = 12 (12)


$110 divided by _____ = 11 ($10)


45 units are bought at a cost of $.20 each. How much is paid? ($9.00)


800 units are purchased at a total cost of $1,600. How much did each unit cost? ($2.00)


You buy yourself and a friend an ice cream for $3.00. How much did each one cost? ($1.50)


You go to the store and buy bread and milk for your mom. Each of them costs the same amount and you spend $2.60. How much did each one cost? ($1.30)


Write a story problem to go with the equation: 2 x $1.00 = $2.00


Write a story problem to go with the equation: $80 = $40 + $40 or $40 x 2 = $80 or $80/2 = $40.


Your mother signs you and a friend up for a basketball league. She pays $200 total. How much did it cost for each of you? ($100)


Your mom sells cookies at the bake sale for $.50 each. You bring $5.00 to school. How many can you buy? (10)



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