# The Craft of Word Problems

## CONTENTS OF CURRICULUM UNIT 04.05.03

## Solving Word Problems Using Subtraction

Your feedback is important to us!

After viewing our curriculum units, please take a few minutes to help us understand how the units, which were created by public school teachers, may be useful to others.

## Lesson Plans

I would like to offer three lesson plans that I feel carrying out the goals of this unit. I thought it would be foolish to try and recreate what Saxon Math already covers and does quite well. What I decided to do was to share a few lessons that would be supplemental or projects done by the whole class. In some cases they would extend over a few days or could become favorite activities students could do on their own or in the math center. The three lessons used are tried and true kinds of activities that students will enjoy. The New Haven Public Schools have been using the Saxon program for over five years. Teachers have now been encouraged to move beyond the basic program and make it our own by incorporating activities and projects that create excitement and motivation in our students.

I see the first lesson plan:
*
How much is your name worth?
*
as a lesson that could be easily done in the first few days of school as a kind of ice-breaker. In the lesson each letter has a corresponding dollar value from $1 to $26. Students have to add up the total worth of the letters in their names. This lesson is an interesting one because at the beginning of the year it allows the teacher to see how students tackle a problem? Do they list the value of all the letters in their names and add them at once. Do they add a letter at a time? Do they put one and two digit numbers in the correct place?

Once students do this activity with their names they can at a later time look for the most valuable 3 letter word they can think of or the 4 letter word with the greatest value. Students might also figure out the values of specific words. By doing this teachers can manipulate the type of addition problems students will be doing. As the process goes along this lesson can also lead to students writing about math. What do they notice about the words that have higher values or lower values? Given two words like
*
act
*
and
*
wet
*
which one would they guess to be the most valuable? Why?

In the second lesson:
*
How many seeds does this pumpkin have?
*
Students are going to review their understanding of place value, which the research says is an important concept for students to understand. Again this lesson is linked to a holiday related theme that is going to get students actively involved and working in groups. Another reason I believe these are valuable lessons is because students of all abilities can do them.

By counting up the pumpkin seeds students are again dealing with counting, grouping into tens, having more than ten and less than ten. They need to be able to add to 10, figure out how many more they need to make ten and they need to be able to go from ones to tens to hundreds to possibly thousands as they count the number. By gluing the seeds onto paper strips and building a place value chart to illustrate the number of seeds students are once again reviewing their knowledge of place value. This activity is also informative for the teacher as a way to see what problems still exist in the understanding of this basic concept.

The third and final suggested activity is called:
*
How many calories in your favorite MacDonald’s meal?
*
This is a more generic type of lesson that can be used in a variety of ways depending on your objective. Students are given copies of MacDonald menus with the caloric values listed by each food item. The menu is available on the web. The lesson has three tasks. First students are asked to calculate the number of calories in their choice of a drink and sandwich. Once again students are dealing with setting up the problem, adding with regrouping and place value. Second, they will be required to find the meals with the highest and lowest caloric value. In this task students must understand the construction and deconstruction of numbers to ten as they try to with their knowledge of the addends to ten look for reasonable pairs to add. What numbers will most likely add to a higher number? What numbers will likely add to a lower total. Again, this is valuable information for the teacher to see what aspects of the “knowledge package” are missing. In the third task, students are told that a student has a meal worth a given number of calories. They are given two of the items chosen and must figure out the third. Here students must be able to successfully add and possibly regroup large numbers but they must also find a missing part.

These lessons are merely templates and can be used and expanded in various ways. There are numerous menus available and so this activity could be expanded to compare the results from MacDonald’s compared to Wendy’s or Burger King. Prices could also be used to expand this activity into money amounts. The whole concept of shopping; whether for clothes, or toys, or a class party can be used to initiate math activities that students will relate to and enjoy. Activities like these will be fun and still allow the teacher to review a variety of math topics relevant to subtraction with renaming.

### Lesson Plan #1

How much is your name worth?Objective: Students will calculate the value of their names given a chart assigning a dollar value to each letter.

Materials:

A list of dollar values for each letter: A=$1, B=$2, c=$3, etc.

paper

pencils

Procedure:

- 1. Students are asked to write down their first names across the top of the paper.
- 2. Under each letter the student is told to put down the value of each letter in their name.
- 3. The students then are asked to write a number sentence that will help them figure out the dollar value of their name.
- 4. Students would be asked to predict who they would expect to have the highest valued name, and why, the lowest, etc.

Extension Activities:

The teacher should collect the papers and hang them up, or put them into a book form to be kept for the class to look at. Students might also do their last names. There is a similar activity that is often used called Dollar Words in which students are challenged to find a word whose letters add up to $1.00.

### Lesson Plan #2

How many seeds does this pumpkin have?Objective: Students will estimate, count and order pumpkin seeds into groups of ones, tens, hundreds, and thousands if necessary in order to visualize how place value works with large numbers.

Materials:

1 large pumpkin

4 different colors of construction paper glue

Procedure:

- 1. Display the pumpkin so that students can guess the number of seeds it contains. Record their guesses on a chart.
- 2. Cut the pumpkin and remove the seeds. Separate the seeds from the pulp and let them dry.
- 3. Have small groups of children count out the seeds into groups of ten and glue them to a piece of the same colored paper cut into strips similar to the rods in the base ten blocks.
- 4. Those tens should be bundled together and stuck onto a square of another color that represents the flat or 100 block.
- 5. As groups work together any left over seeds that cannot be made into a ten should be glued to individual square that would represent the ones.
- 6. After the seeds are all counted they should be displayed on a bulletin board showing the hundreds (or thousands if necessary) from left to right.
- 7. Check the actual number of seeds with the children’s guesses. Discuss the reasonableness of the guesses.
- 8. Write the number of seeds with expanded notation with words and numerals and as a compact number. For example:
- 5 hundreds + 3 tens + 6 ones
- 500 + 30 +6
- 536

### Lesson Plan #3

How many calories in your favorite MacDonald’s meal (Based on a lesson described in*Making Sense: Teaching and Learning Mathematics with Understanding*by James Hiebert et al.)

Objective: To give students a chance to practice addition and subtraction with renaming in a real world situation.

Materials:

Nutritional Menus from a fast food restaurant -- MacDonaldd’s, Burger

King and others are available on the web. Since many of the items are rounded to the nearest ten the teacher may have to adjust a few numbers in order to necessitate regrouping when adding or subtracting.

paper

pencils

Procedure:

- 1. The teacher asks the students to suggest what they would choose for lunch if they could have a sandwich and a drink.
- 2. In the first task, after taking down a couple of suggestions the teacher asks the students to find the number of calories in the meal.
- 3. In the second task, students then are asked to ask which sandwich has the highest calorie count and what the difference is between the highest and lowest caloried sandwiches on the menu.
- 4. The third task in this lesson would be to turn it into a multi-step problem, for example: Tommy has chosen a meal worth 824 calories. He had a Big Mac, milk and one other item. What is the other item?