RENEE LYNETTE WILLEMSEN-GOODE

swarthmore-rutledge school
description of the school
lesson plans and student work
essays and reflections

summerbridge cambridge
description of the program
lesson plans and student work

contact me
by e-mail

Over the course of the summer, I designed and implemented a six-week lesson plan in mathematics. During the course, my two classes studied fractions, decimals, and percentage, but we also covered a unit on negative numbers. Here are six of the lessons I did with the class throughout the summer. (Each lesson was designed for 45 minute block).

 Introduction to Fractions Adding Fractions with Different Denominators Review for the Decimal and Percentage Exam The Amazing Multiple What is a decimal? Negative Numbers

Introduction to Fractions

Objectives:

Students will be able to:

• Write a fraction representing a picture or situation (i.e. fraction of given balloons that are red).
• Identify the numerator and denominator of a fraction
• Explain, in their own words, what a fraction is

Materials:

• M&M challenge sheets
• M&Ms (a mix of peanut and plain)
• Markers
• Pencils
• Napkins

Procedure:

Review the concept of a fraction with the students, introducing the terms numerator and denominator. (Students had seen fractions in their education - so in part this was a review). Explore some common fractions the students might have seen: such as pieces of a pizza or of a candy bar, or the fraction of total students in the room wearing sneakers.

Pass out m&ms and a copy of the M&M challenge worksheet to each student. Explain to students how to make a "fraction wheel" by counting up the total of m&m's and dividing up a circle into that many "equal parts." Have students spend the rest of the period working through the sheets and drawing fraction wheels. Examples of Student Work

Assessment:

Students' ability to make fraction wheels.

Homework:

The Amazing Multiple

Objectives:

Students will be able to:

• Understand what a multiple is and find some multiples of a given number
• Find the lowest common multiple between two numbers
• Identify fractions that are equivalent

Materials:

• "Go Fish" Cards (specially adapted to have equivalent fractions on them)
• A large sheet of paper with the numbers 1-60 pre-written on it.

Procedure:

Ask the students if they know what a multiple is? Either way, discuss with the students what a multiple is.

The Multiple Song:

Have the list of numbers up on the board. Explain to students that they will be making a "multiple song." One student will be assigned to read the numbers one through sixty aloud slowly. Two other students will be assigned to make a noise of their choosing when a multiples of a their number is called. (Each student will have a different numbers) The noise could be clapping, stomping, etc.

As the students are playing the "song," ask students to observe what happens when they reach the lowest common multiple (without using this terminology). When the students say that what happened was that both people made noise, draw out that this number must be a multiple of BOTH numbers. Define this as the lowest common multiple.

Have the students play a few more rounds, this time coming up with predictions for what the LCM will be. Then have the students brainstorm strategies for finding the LCM.

Review of material covered in previous class:

With the remaining time have the students play Equivalent Fraction Go Fish (in each deck are four equivalent fractions, students must make pairs of two equivalent fractions to discard them from their pile).

Assessment:

Observation of kids during multiple activity and go fish game.

Homework:

This was the second time students had seen this concept presented in the classroom.

Objectives:

Students will be able to:

• Add and subtract fractions with different denominators by first converting the fractions to fractions with the same denominator
• Demonstrate visually why you need to convert the fractions to ones with the same denominator

Materials:

• Scissors
• Glue
• Construction Paper with pre-made slots for the activity below (including + and = signs)
• Copies of the packet of circles (see attached) one per group

Procedure:

Activity:

Have the students break up into groups of two or three. Give each group a pair of scissors, glue, some construction paper, and a packet of fraction circles (circles that are broken up into varying numbers of equal pieces). Have the students solve the following addition problems in the following way. First, they should cut out the fraction of the wheel that represents the two addends. In the example to model this (1/2 + 1/4 = 2/4 + 1/4 = 3/4) it is one-half and one-quarter Next they should convert these fractions visually to ones with common denominators by cutting out one-half as two quarters and one quarter as one-quarter. In the last image, they should glue down the answer, which is three-fourths. Model this on the board with an example:

Then have students solve the following two examples by cutting out the appropriate fraction pie pieces, and reassembling them visually to demonstrate the equivalence and addition of the fraction pairs:

1/12 + 5/6 =

3/4 + 1/6 =

Extra Time?

If the students finish early, they can play games of 24.

Assessment:

Look at the products of student work.

Homework:

Students will continue working on a "textbooks" on fractions.

What is a Decimal?

Objectives:

Students will be able to:

• identify the place values in a decimal and say what each place value represents
• understand what place value after the decimal represents and begin to understand the connection between fractions and decimals
• add and subtract numbers in decimal form as pertaining to money

Materials:

• A round object to be used as a decimal point in the human decimal
• Pieces of construction paper with numbers written on them
• Guess Who with numbers boards (one per student)
• Paper receipt paper made from half of an index card (two-three per student)
• Index cards with picture and prices of food items for a classroom supermarket
• Fake paper and coin money

Procedure:

Hook:

Ask students what math skills they need when they are out shopping at a supermarket. List these on the blackboard. Ask students what type of number money is written out as (most of the students should already have learned something about decimals in school).

Activity 1:

Reintroduce the concept of place value by placing a price on the board. Have the students try to label each place value.

Activity 2:

Write out the various place values on the board. Then, have the students stand against the board holding a construction paper number in front of one place value. Hold a decimal point where the decimal point begins. The students are now a human decimal. Have them read the number aloud (4 hundred and thirty and seven and two tenths, for example). Then have the students reorganize themselves and read out the new number a couple of more times.

Activity 3:

Play Guess Who with decimals! Have the students ask questions such as "does your number have a six in the tens place." Each student gets a board and will cross off numbers when they have eliminated them.

Activity 4:

Playing Supermarket: Have the students use prior knowledge to go shopping in the supermarket. Set up index cards with food items and prices on them against the blackboard. Have students get in pairs. One student is given twenty dollars and should pick up a couple of items. They will give these items to their partner who will write up a receipt totaling the item prices and finding the change from twenty dollars. The pairs should then switch roles. Examples of receipts.

Assessment:

Look at the receipts the students have produced.

Homework:

Worksheet and creation of a restaurant menu for use in class tomorrow

Review for the Decimal and Percentage Exam

Objectives:

• Students will review the material for the upcoming exam (adding and subtracting decimals, long division with decimal answers, rounding, percentage)

Materials:

• Student homework from previous night
• Envelopes for each scavenger hunt location containing a clue.
• Copies of each scavenger hunt questions
• Copies of each scavenger hunt reward letter and the final code

Procedure:

Ask the students to take out their homework from the night before (a review sheet in which they had the correct answers given to them). Then ask them which questions they got wrong and go over those problems, taking suggestions from the rest of the class.

Prior to the lesson, the teacher should have set up envelopes with a review problem in them outside in the hallway. Students start off with one problem. When the solve their problem, they should check their answer with the teacher. If they get the problem correct, then they are handed a new clue of a location to look for a problem. On the back of each problem is a letter and number. When the students get all of the clues correct, they will get an answer code, which tells them in what order (based on the number) to put the letters on the back of the clues in. This will spell out a location in the school where they should go to find their "surprise." (This surprise was that we would be eating munchkins after tomorrow's test)

Assessment:

Are the students able to answer the questions?

Homework:

Study for Exam

Introduction to Negative Numbers

Objectives:

Students will be able to:

• understand what a negative number is
• give a couple of real world examples of them
• subtract any two whole numbers to get either a positive or negative number

Materials:

• Guided Note-Taking Sheet on Negative Numbers (see attached).
• Bingo Sheets with positive and negative numbers
• Construction Paper and Markers
• Staircase labeled as a number line with sheets of paper.

Procedure:

Hook:

Tell the class that you are going shopping in a store. Use the following questions
to introduce negative numbers.

Questions for discussion: Imagine I have twenty dollars, do I have enough to pay for a \$15 skirt? Now imagine I have twenty dollars and I want to buy a \$25 dollar skirt. Will I have enough? How much more would I need?Well, let's say my friend was with me and she lent me the \$5 dollars. How much money would I have at the end of the day?

What is a negative number?

Introduce the idea that you really have a debt of \$5. Tell the students that this is a negative number, or less than 0 dollars. Go through the guided note sheet (see attached) and have students write in the definitions of negative and positive numbers as less and greater than zero, respectively. Then have the students give examples of negative and positive numbers, which will be written on the board for students to copy in their note sheet. Then draw a number line on the board and have the students supply answers for what goes in what place on the line. They will copy this onto their sheet.

Subtracting Two Positive Numbers:

Have students create their own number lines on pieces of construction paper and markers. Then have them get up and follow you out of the room into the labeled staircase. Have a landing labeled as 0, and steps going down labeled as negative numbers, stairs going up labeled as positive numbers. Have students move along the stairs to simulate adding and subtracting whole numbers. (i.e. for 2 - 4, have a student stand on the +2 step and move down 4 spaces to get to the answer -2).

Now have students answer the five questions on the back of the guided note-taking sheet. Go over these questions in the large group.

Ask students if they see any pattern to the answers. Hopefully a student will notice that the answers to 5 - 4 and 4 - 5 are the same except for sign. Derive the rules for determining the sign (if the first number is bigger, etc.) with the children.

Practice Time:

Give each child a bingo sheet. Explain the rules of bingo. You will be calling out a subtraction problem and they should cross off the appropriate answer to this problem on their bingo sheet. After each problem is called, have one student relay the answer to the class so that no one crosses of the wrong number and problems in comprehension can be addressed.

List of Possible Bingo Calls:

8-8 = 0
7-8 = -1
9-15 = -6
10-3 = 7
2-9 = -7
15-11 = 4
8-2 = 6
8-10 = -2
5-4 = 1
14-18 = -4
6-3 = 3
3-6 = -3
10-5 = 5
5-14 = -9
3-8 = -5
16-8 = 8
8-16 = -8
11-2 = 9
1-10 = -9
12-2 = 10
1-11 = -10
22-11 = 11
2-13 = -11
24-12 = 12

Evaluation:

Students will be evaluated with respect to their verbal answers during bingo and their written answers during the five questions.