1.) Students will add today’s lesson to their Table of Contents and head their new entry page. The students will write down three simple problems on their new entry page: (1) 1/16 + 1/4 = ____, (2) 1/8 + 1/4= ___, and (3) 1/8 + 1/16 = ___. If I have 1/16 cup of sugar and add another ¼ cup, how much sugar will I have? (Ask similar questions for problems 2 and 3.)
2.) Review Gallon Man with students. Integrate the following learning styles: (1) Verbal/Linguistic (aural) what we hear, (2) Visual /Spatial (handout, slides) what we see, (3) Bodily/Kinesthetic (produce, reproduce) what we do, (4) Logical/Mathematical what we think, (5) Rhythm/Music (mnemonics, repetition, beat, meter), (6) Naturalistic (observe, experience), (7) Existential (feel, know intuitively), (8) Intrapersonal (internal, self-study/reflection), and (9) Interpersonal (external, group-study/interaction)
Ask the students to stand and point to each part of their gallon: (1) tummy--one gallon, (2) vest- two half-gallons, (3) upper arms and thighs--four quarts, (4) use fingers and point to two bones in the lower arms and lower legs--eight pints, and (5) eight fingers and eight toes (tuck in thumbs and forget big toes)--16 pints. Then, ask them questions, which require them to think about, touch, wiggle, say the name for each relevant part(s) of their bodies. These activities are a good review for all nine classes of learners.
3.) Tell the students that, by the end of the lesson, they will be able to mentally add the fractions they wrote in their journals. Tell them that they will always be able to do this for the fractions: fourths, eighths, and sixteenths, by referring to what they already know about Gallon Man.
4.) Ask the students to be seated. Tell them that today we are going to build Fraction Friend. Tell them that Gallon Man is going to be transformed into another helper: Fraction Friend.
5.) Call the students attention to the pieces of colored paper on their desks. Tell them they will be using this paper to build Fraction Friend, exactly as they have constructed Gallon Man.
Ask the students to touch their gallon, half-gallons, quarts, pints, and cups. Then, ask what would that fraction be for each part? This requires the students to make connections: transfer knowledge about physical things to mathematical ideas. It may take some time and a few extra iterations to bring the whole class to understanding.
As the students identify each colored sheet/body part/liquid metric/fraction, have the students tear their paper into the appropriate number of sections, corresponding to the fractional part.
The responses you are looking for are as follows:
Purple- 1 gallon – 1 whole
Red- ½ gallon- ½ + ½ = 1 whole
Orange- 4 quarts- ¼ + ¼ + ¼ + ¼ = 1 whole
Blue- 8 pints- 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 1 whole
Yellow- 16 cups- 1/16 + 1/16 + 1/16 + 1/16 +1/16 + 1/16 + 1/16+ 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16= 1 whole
This part will be a little time consuming. The teacher can be setting up the ELMO for students to show their work and interact with the class members during this time.
6.) Adding Fractions – Write on the board fraction problems for the students to solve. Ask the students to explain what they are doing as they are changing the fractions into parts that they can work with easily.
Demonstrate by using Fraction Friend parts to solve 2/8 + 1/4 =
(¼ is equal to 2/8, so 2/8 + 2/8 is 4/8. Some will know that they can simplify this into 1/2.)
Formative Assessment: Watch students to make sure they are not using parts of the original problem to solve the equation. Ask them to explain how they are solving their problems. Are the students able to make equivalent fractions? Are the students able to add the fractions?
7. Ask the students to look back at the problems they wrote down at the beginning of the lesson. Tell them that they will be working with a partner to solve them, using both of their Fraction Friend parts.
8. Have students work through the problems they wrote in their journals. The teacher should walk around to each table and make sure that the students understand why and can tell others how they are able to use the smaller fractions to make up the larger fraction.
9. Use equity sticks to call on students to share what they have learned by asking them to solve more Fraction Friend problems, using the ELMO to display their thinking.
10. In the following days, the students will work on solving problems with different unlike denominators not found in Fraction Friend. Please visit the following websites: