MS After School Intervention
Unit: Rational Numbers
Day 7 Lesson
Objective
Students will add, subtract, multiply, and divide with mixed numbers.
Common Core Standards:
7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to
multiply and divide rational numbers.
7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring
that operations continue to satisfy the properties of operations, particularly the distributive
property, leading to products such as (1)(1)  1 and the rules for multiplying signed numbers.
Interpret products of rational numbers by describing real-world contexts.
7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every
quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then
( p / q)  ( p) / q  p / (q) . Interpret quotients of rational numbers by describing real-world
contexts.
7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.
Materials




Concentration Game
Post-it notes
Overhead projector or document camera
Stations Activity
Scenario of the Day (10 min)
Scenario: “Benjamin” is baking cookies for his class party. Here is his list of ingredients: 2
1
cups of
2
1
1
3
2
cups of sugar, 2 teaspoons of baking powder, 3 cups of chocolate chips,
cup of butter,
4
3
4
3
1
3
1 cups of milk, and teaspoon of vanilla.
4
4
flour, 1
His math teacher is an avid baker 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 would change it
5
--- 2 can go into 5 twice which would be 2 wholes, since that is the
2
1
4
1
same as
there is
left over to get 2
2
2
2
to a mixed number. Example:
Have students finish the remaining examples and discuss.
For the first two mixed numbers, ask/guide students to an explanation about how they would change it to an
improper fraction.
Example: 3
11
2
2
9
--- 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)
On the board or overhead, copy 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
10
10
33
3
1
 5  5 hours
3.
6
6
2
1.
Send a Problem (20 minutes)
93
5
 11 tablespoons of dressing
8
8
10 5
1
  2 pizza bagels
4.
4 2
2
2.
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
Answer:
3
 38
 5 
7
7
3
1
2 2
4
8
Answer:
5
 22
 1 
 17 17 
1
2
3 1
3 5
Answer:
8
 50
 2 
21 
 21
3
2
2 2
4
3
Answer:
1
 22
7 

3
 3
1
1
3 2
3
2
Answer:
1
 25
 8 
3
 3
1
1
5 3
3
5
Answer:
2
8
 1 
3 3
7
3
1
1
4
2
Answer:
3
1
5
10
1
1
2
 31
3 2
 5 
6
2
3
6
5
1
 155
 15  15 
Answer: 
10
2
 10
Answer:
2
1
 56
 9 9 
6
3
 6
Closure – Circle of Knowledge (10 minutes)
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.
Answers: 4
1
1
11
cups of flour and sugar, 1
cups of milk and butter, 3
teaspoons
12
4
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.
Answer: He can multiply his recipe by 4.
powder, 13 cups chocolate chips, 2
10 cups of flour, 7 cups of sugar, 9
1
teaspoons baking
3
2
cups of butter, 5 cups of milk, and 3 teaspoons of vanilla.
3
1
10
21
4
7
31
2
17
5
3
7
9
7
2
34
5
2
2
3
4
3
4
Error!
Objects
cannot
be
created
from
editing
field
codes.
1
2
19
4
2
40
3
71
10
13
3
10
7
3
4
31
4
7
1
3
15
8
22
3
10
1
4
37
6
1
3
3
2
5
9
4
1
2
7
11
3
5
3
5
17
7
Error!
Objects
cannot
be
created
from
editing
field
codes.
6
1
6
20
2
6
4
5
23
6
3
5
6
28
5
Concentration
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
6
5
1
4
dressing. How many tablespoons of
dressing will she have?
Station #3
1
1
3
2
Jordan worked 6 hours on Friday and 3
hours on Saturday. How many total hours
did he work?
Station #4
1
30
Michael and his friends ate 2 pizza
28
1
4
bagels last week. They ate
pizza bagels
this week. How many more pizza bagels
were eaten the first week?