Algebra Readiness Intervention
Unit: Operations with Fractions
Day 5 Lesson
Objective
Students will add, subtract, multiply, and divide with mixed numbers.
Materials
•
•
•
•
“Concentration” resource sheets
Post-it notes
Overhead projector or document camera
“Stations” resource sheets
Scenario of the Day (10 min)
Scenario: “Benjamin” is baking cookies for his class party. Here is his list of
1
3
1
ingredients: 2 cups of flour, 1 cups of sugar, 2 teaspoons of baking powder,
2
4
3
1
2
1
3
3 cups of chocolate chips, cup of butter, 1 cups of milk, and teaspoon of vanilla.
4
3
4
4
His math teacher loves to bake and wants to know the following information when he
brings in the cookies. How much flour and sugar were used? How much milk and butter
were used? What was the total number of teaspoons used?
DO NOT SOLVE. Discuss this scenario with students. Have students brainstorm and
share ideas on how to solve the problem. List ideas on board. What information is
needed? What operations could be used… etc. Lead students to the use of operations
with mixed numbers.
Introductory Activity (15 minutes)
Post three headings on the board/overhead.
Proper Fraction
Improper Fraction
Mixed Number
Ask for volunteers to write examples on the board of each type of number. Try to get
about five examples for each column. Be sure to explain the properties of each type of
number.
For the first two improper fractions, ask/guide students to an explanation about how they
5
would change it to a mixed number. Example:
--- 2 can go into 5 twice which would
2
4
1
1
there is left over to get 2
2
2
2
Have students finish the remaining examples and discuss.
be 2 wholes, since that is the same as
For the first two mixed numbers, ask/guide students to an explanation about how they
would change it to an improper fraction.
Example: 3
2
9
2
11
--- 3 would be and more would give you
3
3
3
3
Have students finish the remaining examples and discuss.
(Note: Avoid using the rule of multiplying and adding, rather focusing on number sense
and understanding, not just another rule to remember.)
Concentration (20 minutes)
Using the overhead or document camera, display a copy of the Concentration game.
Each square should be covered with a sticky note. Label each column with a letter (A, B,
C…) and each row with a number (1, 2, 3…).
Students may play individually or with a partner. Each turn consists of students choosing
two squares to determine if the numbers are a match. Students may take notes on the
locations to help speed along the game. Make sure that each student or pair gets a turn to
choose.
This activity reinforces the skill of converting between improper fractions and mixed
numbers.
Mixed Number Stations (15 minutes)
Place students in groups of three or four. Each group should be given 2-3 minutes to
complete a station. Call time and have students rotate to the next station. Continue until
students have completed all problems or time runs out.
The problems in this activity will require students to add and subtract with mixed
numbers. These problems should be solved by changing to improper fractions, then
adding or subtracting. Solutions should be converted to mixed numbers.
Answers:
43
3
= 4 inches of yarn
1.
10
10
33
3
1
= 5 = 5 hours
3.
6
6
2
93
5
= 11 tablespoons of dressing
8
8
10 5
1
= = 2 pizza bagels
4.
4 2
2
2.
Send a Problem (20 minutes)
Divide students into groups of three. Assign/choose roles.
Role 1 – Improper Fraction Converter
Role 2 – Multiplier/Divider
Role 3 – Mixed Number Converter
Post a problem for the groups to solve using the roles selected. After three problems,
rotate roles so that each person takes a turn at each role.
Problems:
5
1
1 !3
7
6
3#
& 38
Answer: $ = 5 !
7"
% 7
2
3
1
÷2
4
8
5#
& 22
Answer: $ = 1 !
17 "
% 17
1
2
3 ÷1
3
5
8#
& 50
Answer: $ = 2 !
21 "
% 21
3
2
2 !2
4
3
1#
& 22
=7 !
Answer: $
3"
% 3
1
1
3 !2
3
2
1#
& 25
Answer: $ = 8 !
3"
% 3
1
1
5 ÷3
3
5
2#
&8
Answer: $ = 1 !
3"
%3
1#
3
1
1
2
& 31
÷1
3 !2
Answer: $ = 5 !
6"
4
2
2
3
%6
5
1#
1
& 155
= 15 = 15 !
3 !5
Answer: $
10
2"
10
% 10
Closure – Circle of Knowledge (10 minutes)
7
2
1#
& 56
Answer: $ = 9 = 9 !
6
3"
% 6
Revisit the Scenario of the Day. Place students in groups of three. Each student should
answer one of the three posed questions. Students then rotate their solutions to have their
circle members check their work.
1
11
1
Answers: 4 cups of flour and sugar, 1 cups of milk and butter, 3
teaspoons
4
12
12
Extension Question: Suppose the cookies were a huge success and four other teachers
wanted cookies for their classrooms. What could Benjamin do? How much of each
ingredient would he need to buy? Have students complete this in their groups, each
person finding two or three answers.
1
Answer: He can multiply his recipe by 4. 10 cups of flour, 7 cups of sugar, 9
3
2
teaspoons baking powder, 13 cups chocolate chips, 2 cups of butter, 5 cups of milk,
3
and 3 teaspoons of vanilla.
Concentration
21
4
7
31
2
17
5
3
7
9
7
2
34
5
1
10
4
1
2
19
4
2
40
3
71
10
13
3
10
7
3
4
3
4
31
4
7
15
8
1
4
37
6
1
3
3
2
5
9
4
1
2
7
1
3
11
3
5
3
5
5
1
4
2
2
3
83
10
22
3
10
17
7
6
1
6
20
2
6
4
5
23
6
3
5
6
28
5
Station #1
Kelly has
10
2
5
inches of yarn to make
6
1
10
friendship bracelets. She uses
inches
over the weekend. How much yarn
remains?
Station #2
3
8
Maggie needs tablespoons of oil and
tablespoons of vinegar for her salad
dressing. How many tablespoons of
dressing will she have?
6
5
1
4
Station #3
1
1
3
Jordan worked 6 hours on Friday and 2 3
hours on Saturday. How many total hours
did he work?
Station #4
1
Michael and his friends ate 30 2 pizza
1
28
4
bagels last week. They ate
pizza bagels
this week. How many more pizza bagels
were eaten the first week?