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Christmas Problem Solving

Lesson Plans > Mathematics > Algebra > Word Problems
 

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Lauren, Martha, Jake and Judah all decide to buy Christmas gifts for each other.

Lauren spends $5 more than Martha. Martha spends twice as much as Jake, Jake spends $17 less than Judah, and Judah spends $15 less than Lauren and Martha combined.

How much money did they spend altogether?

Hermie the Elf wants to buy Christmas gifts for the students in his dentistry class. Unfortunately, he only has coins - pennies, nickels, dimes, and quarters. In all, he spends twice as many nickels as quarters, four more dimes than nickels, and the number of pennies was seven less than the total of his nickels, dimes and quarters.

In all, he spent $4.57. How many coins did he spend?

We all know the song "The Twelve Days of Christmas," and how the gift giving works:

Day One: 1 partridge in a pear tree

Day Two: 2 turtle doves and 1 partridge in a pear tree

Day Three: 3 calling birds, 2 turtle doves, and 1 partridge in a pear tree

Thus, after three days, the singer has 1 + 3 + 6 = 10 gifts. [Note that some people interpret the song as 1 gift the first day, 2 the second day, three the third day, etc., but that is not what the song says, so we will go with the literal interpretation of the song!]

After Mrs. Claus heard the elves singing this song one Christmas, she decided that the next year she would take this song to the extreme, and extend it to 20 days of Christmas, giving gifts (in the same pattern as the song) for 20 days.

Santa Claus caught wind of what she was doing and, since he is considered to be the epitome of the spirit of giving at Christmas time, decided he couldn't be out-given, and did the 25 days of Christmas instead.

By how many gifts did Santa "outgive" Mrs. Claus?

 

Each member of my family (myself, my wife, and my non-adult children) gives one present to every other member of the family. Each child in my family has 4 living grandparents, and each adult has 3 living grandparents and no living great grandparents. All grandparents give each of their grandchildren 2 gifts, and the great-grandparents give each of their great-grandchildren three gifts. Every child in the family gives each pet one gift, and there are twice as many pets as their are children in the family. We all pitched in together and bought an extra present in case any strangers came to the door on Christmas day.

As it turns out, there are enough Christmas presents so we could open one every day for a year (not a leap year!).

How many children do I have?

I have some strings of red lights, and some strings of green lights for my Christmas tree. All my strings of red lights have the same number of lights on them, and all my strings of green lights have the same number of lights on them.

All the strings of lights have at least 10 lights, and no more than 50 lights.

If I put all of the red-light strings and all the green-light strings on the tree, I would have a total of 278 lights. If I used all of my red-light strings, and only four of my green-light strings, I would have 159 lights.

How many strings of each do I have, and how many lights are on each string?

This year Mr. Krank spent three times as much money on gifts for family members as he did on gifts for co-workers. The amount of money he spent on Christmas decorations was $150 less than the amount of money he spent on Christmas cards. The amount he spent on Christmas charities exceeded the combination of co-worker gifts and Christmas card expense by 20%. In addition to all of this, a third of the total spent on Christmas was expenses related to their famous Christmas-Eve party. If the Kranks had not purchased any Christmas gifts, they would have spent $1983 on Christmas. If, instead, they had chosen to give gifts but skip the Christmas cards, they would have spent $2673 in all.

If the Kranks skipped Christmas altogether, how much money would they have saved?

Lesson Plan/Article

Christmas Problem Solving

On the last day of school before Christmas vacation, I like to give my students some interesting Christmas-themed math problems to work on (we also sometimes have snacks, and maybe even play a math game or two). The slides here are some of the problems I like to use. Make sure you consider the ability level of your students; you may choose to skip some problems, or not work all the way through the set, depending on the group.

Lesson by Mr. Twitchell

Handouts/Worksheets

Problems

Buying Christmas Gifts

Lauren, Martha, Jake and Judah all decide to buy Christmas gifts for each other.

Lauren spends $5 more than Martha. Martha spends twice as much as Jake, Jake spends $17 less than Judah, and Judah spends $15 less than Lauren and Martha combined.

How much money did they spend altogether?

Hermie goes Christmas Shopping

Hermie the Elf wants to buy Christmas gifts for the students in his dentistry class. Unfortunately, he only has coins - pennies, nickels, dimes, and quarters. In all, he spends twice as many nickels as quarters, four more dimes than nickels, and the number of pennies was seven less than the total of his nickels, dimes and quarters.

In all, he spent $4.57. How many coins did he spend?

Twelve Days of Christmas

We all know the song "The Twelve Days of Christmas," and how the gift giving works:

Day One: 1 partridge in a pear tree

Day Two: 2 turtle doves and 1 partridge in a pear tree

Day Three: 3 calling birds, 2 turtle doves, and 1 partridge in a pear tree

Thus, after three days, the singer has 1 + 3 + 6 = 10 gifts. [Note that some people interpret the song as 1 gift the first day, 2 the second day, three the third day, etc., but that is not what the song says, so we will go with the literal interpretation of the song!]

After Mrs. Claus heard the elves singing this song one Christmas, she decided that the next year she would take this song to the extreme, and extend it to 20 days of Christmas, giving gifts (in the same pattern as the song) for 20 days.

Santa Claus caught wind of what she was doing and, since he is considered to be the epitome of the spirit of giving at Christmas time, decided he couldn't be out-given, and did the 25 days of Christmas instead.

By how many gifts did Santa "outgive" Mrs. Claus?

 

Christmas Tree Puzzle

Each member of my family (myself, my wife, and my non-adult children) gives one present to every other member of the family. Each child in my family has 4 living grandparents, and each adult has 3 living grandparents and no living great grandparents. All grandparents give each of their grandchildren 2 gifts, and the great-grandparents give each of their great-grandchildren three gifts. Every child in the family gives each pet one gift, and there are twice as many pets as their are children in the family. We all pitched in together and bought an extra present in case any strangers came to the door on Christmas day.

As it turns out, there are enough Christmas presents so we could open one every day for a year (not a leap year!).

How many children do I have?

Christmas Tree Lights

I have some strings of red lights, and some strings of green lights for my Christmas tree. All my strings of red lights have the same number of lights on them, and all my strings of green lights have the same number of lights on them.

All the strings of lights have at least 10 lights, and no more than 50 lights.

If I put all of the red-light strings and all the green-light strings on the tree, I would have a total of 278 lights. If I used all of my red-light strings, and only four of my green-light strings, I would have 159 lights.

How many strings of each do I have, and how many lights are on each string?

A Kranky Christmas

This year Mr. Krank spent three times as much money on gifts for family members as he did on gifts for co-workers. The amount of money he spent on Christmas decorations was $150 less than the amount of money he spent on Christmas cards. The amount he spent on Christmas charities exceeded the combination of co-worker gifts and Christmas card expense by 20%. In addition to all of this, a third of the total spent on Christmas was expenses related to their famous Christmas-Eve party. If the Kranks had not purchased any Christmas gifts, they would have spent $1983 on Christmas. If, instead, they had chosen to give gifts but skip the Christmas cards, they would have spent $2673 in all.

If the Kranks skipped Christmas altogether, how much money would they have saved?

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