A Story of Units
A Story of Units
Grade 4 – Module 7
Exploring Measurement with Multiplication
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A Story of Units
Session Objectives
– Examination and overview of the development of
mathematical understanding across the module
with a focus on the standards within the lessons.
– Introduction to mathematical models and
instructional strategies to support implementation
of A Story of Units.
– Consideration of scaffolding to provide multiple
entry points for students at all levels.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
A Story of Units
Scaffolding Mathematics Instruction
Key Points
– Amplify Language
– Move from Concrete to Representation to Abstract
– Give Specific Guidelines for Speaking, Reading,
Writing, or Listening
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A Story of Units
Agenda
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•
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Introduction to the Module
Concept Development
Module Review
Year in Review
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A Story of Units
Curriculum Overview of A Story of Units
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A Story of Units
Module Overview
• Narrative
• Focus and foundational
standards
• Mathematical practices
• Overview of Topics and
Lesson Objectives
• Terminology
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A Story of Units
New Terminology
• Metric system of measurement
• Customary system of measurement
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cup
pint
quart
gallon
ounce
pound
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Suggested Tools and Representation
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Centimeter ruler, Meter stick
12 inch ruler, Yard stick
Digital scale (metric and customary units)
Balance scale with mass weights
Gallon, quart, pint, and cup containers
Beaker marked with liters and milliliters
Analog clock with second hand
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Agenda
•
•
•
•
Introduction to the Module
Concept Development
Module Review
Year in Review
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Core Fluency Differentiated Practice Sets
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Opportunity for review and mastery of
the addition and subtraction algorithm.
4 Practice Sets
– A: Multi-digit addition
– B: Multi-digit subtraction
– C: Multi-digit subtraction with zeros
in the minuend
– D: Multi-digit addition and
subtraction
Differentiated Practice
– Part 1
– Part 2: fewer regroupings
– Both parts have same solutions.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Core Fluency Differentiated Practice Sets
• 120 seconds to complete.
– Correct Sets move on.
– Incorrect Sets used as
remedial practice. Repeat
until mastery.
• Keep record of progress.
– Share with caring adults.
– Celebrate improvement
and advancement.
• Found in G4-M7-L2. Used
throughout Module 7.
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A Story of Units
Topic A: Measurement Conversion Tables
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5 lessons to discover conversion from larger to smaller measurement units
– focus on customary units of length, weight, and capacity
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New terms
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customary units
metric units
customary system of measurement
metric system of measurement
Tools/Representations
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multiplicative comparison
2-column table
number line
tape diagrams
4.OA.1, 4.OA.2, 4.MD.1
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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pound
ounce
cup
pint
quart
gallon
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balance scale
1 lb and 1 oz weights
yardstick, inch ruler
capacity containers
water
analog clock, stopwatch
A Story of Units
Convert Pounds to Ounces
• Use a balance scale to:
– discover 1 pound is
heavier than 1 ounce.
– determine how many
ounces equal 1 pound.
• Use multiplication to:
– convert pounds to ounces.
– apply the distributive property to convert number of
pounds not found in 2-column table to ounces.
Lesson 1
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A Story of Units
Convert Pounds to Ounces
Pounds
Ounces
1
16
2
32
3
48
4
64
5
80
6
96
7
112
8
128
9
144
10
160
Lesson 1
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rule for converting pounds to ounces:
Multiply the number of pounds by 16 ounces.
15 pounds = ____ ounces
10 lb + 5 lb = (10×16 oz) + (5×16 oz)
= 160 oz + 80 oz
= 240 oz
12 lb 10 oz = ___ oz
= (12×16 oz) + 10 oz
= 192 oz + 10 oz
= 202 oz
A Story of Units
Convert Yards to Feet & Feet to Inches
Lesson 1
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A Story of Units
Turn and Talk
How does this task align with the
Universal Design for Learning (UDL)
in providing multiple options for:
•
•
•
Representation: the “what of learning”
Action/Expression: the “how” of learning
Engagement: the “why” of learning
G4–M7–Lesson 1
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A Story of Units
Convert Gallons to Quarts
• In groups, students discover the rule for
converting gallons to quarts.
– Multiply the number of gallons by 4 quarts.
• How many quarts are in 13 gallons?
– 13×4 qt = 52 qt
– (10×4 qt) + (3×4qt) = 40 qt + 12 qt = 52 qt
• How many quarts are in 18 gallons 3
quarts?
– 18×4 qt = 72 qt
– 72 qt + 3 qt = 75 qt
Lesson 2
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A Story of Units
Convert Quarts to Pints & Pints to Cups
• Continue interactive experiment
of determining conversion rules
for quarts to pints and pints to
cups.
• Relate pints to gallons.
• Relate cups to quarts and gallons.
• Discuss relationships and record
on Practice Sheet.
Lesson 2
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A Story of Units
Conversion of Days, Hours, Minutes, and Seconds
Lesson 3
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A Story of Units
Complete Problems #1-4.
• Use RDW process to solve.
• Be prepared to share your strategies with peers.
Lesson 4
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A Story of Units
Problem 1:
Beth is allowed 2 hours of TV time each week.
Her sister is allowed 2 times as much TV as her.
How many minutes of TV can Beth’s sister watch?
Lesson 4
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A Story of Units
Problem 2:
Clay weighs 9 times as much as his baby sister.
Clay weighs 63 pounds.
How much does his baby sister weigh in ounces?
Lesson 4
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A Story of Units
Problem 3:
Helen has 4 yards of rope.
Daniel has 4 times as much rope as Helen.
How many more feet of rope does Daniel have than Helen?
Lesson 4
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A Story of Units
Problem 4:
A dishwasher uses 11 liters of water for each cycle.
A washing machine uses 5 times as much water as a
dishwasher uses for each load.
Combined, how many milliliters of water are used for 1
cycle of each machine?
Lesson 4
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A Story of Units
Share and Critique Peer Strategies
Mathematical Practice 3
Construct viable arguments and critique the reasoning of others.
xx
Lesson 5
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A Story of Units
Topic B: Problem Solving with Measurement
• 6 lessons to develop strategies for adding and
subtracting mixed units of measurement and solve
word problems including multiplicative comparison
problems.
• Tools/Representations:
– Number bonds
– Arrow way
– Tape diagrams
4.OA.2, 4.OA.3, 4.MD.1, 4.MD.2
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Teaching Sequence for Addition and
Subtraction for Mixed Units of Measurement
Addition
• single unit + single unit
• mixed unit + single unit
• mixed unit + mixed unit
Topic B
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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Subtraction
• single unit – single unit
• mixed unit – single unit
• mixed unit – mixed unit
Lesson 6: Capacity
Lesson 7: Length
Lesson 8: Weight
Lesson 9: Time
A Story of Units
Composing Units
2 fourths + 3 fourths = 5 fourths = 1 one 1 fourth
4 fourths 1 fourth
2 quarts + 3 quarts = 5 quarts = 1 gallon 1 quart
1
4 quarts
Topic Opener B
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1 quart
1
A Story of Units
Adding Mixed Units
2 quarts + 3 quarts
Lesson 6
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3 pints + 4 pints
A Story of Units
Adding Mixed Units
5 gallons 2 quarts + 3 quarts
Lesson 6
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5 quarts 3 cups + 3 cups
A Story of Units
Adding Mixed Units
5 gallons 2 quarts + 4 gallons 3 quarts
Lesson 6
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7 quarts 3 cups + 2 quarts 3 cups
A Story of Units
Decomposing Units
4 fourths − 3 fourths = 1 fourth
1 − 3 fourths = 4 fourths − 3 fourths = 1 fourth
1 quart − 3 cups = 4 cups − 3 cups = 1 cup
8 quarts − 3 cups = 7 quarts 1 cup
7 quarts
4 cups
Topic Opener B
© 2012 Common Core, Inc. All rights reserved. commoncore.org
1
A Story of Units
Subtracting Mixed Units
1 gallon – 1 pint
1 quart – 2 cups
8 gallons – 1 pint
6 quarts – 2 cups
Lesson 6
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A Story of Units
Subtracting Mixed Units
8 quarts 1 cup – 3 cups
8 quarts 1 cup – 6 quarts 3 cups
Lesson 6
© 2012 Common Core, Inc. All rights reserved. commoncore.org
9 gallons 2 quarts – 3 quarts
9 gallons 2 quarts – 4 gallons 3 quarts
A Story of Units
Turn and Talk
How does this task align with the
Universal Design for Learning (UDL)
in providing multiple options for:
• Representation: the “what of learning”
• Action/Expression: the “how” of learning
• Engagement: the “why” of learning
G4–M7–Lessons 6 and 7
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A Story of Units
Try Problems #6-11.
• Practice different addition and subtraction strategies
for length, weight and time.
Lessons 7-9
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A Story of Units
Solving Multi-Step Measurement Word Problems
Patti went swimming for 1 hour 15 minutes on Monday.
On Tuesday, she swam twice as long as she swam on Monday.
On Wednesday, she swam 50 minutes less than the time she swam on Tuesday.
How much time did she spend swimming during these three days?
Lesson 10 – Problem Set #12
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A Story of Units
Topic C: Investigation of Measurements
Expressed as Mixed Numbers
• 3 lessons to convert mixed number measurement units to
smaller units and solve word problems.
• Tools/Representations:
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Tape diagrams
Number line
Number bond
Yardstick
12 inch ruler
1 qt container
1 gal container
4.OA.3, 4.MD.1, 4.MD.2
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Convert Mixed Number Measurements to
Smaller Units
• length
• capacity
Lesson 12
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A Story of Units
Convert Mixed Number Measurements to
Smaller Units
• weight
• time
Lesson 13
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A Story of Units
Try Problems #13-16.
• Sample questions from the Exit Tickets for Lessons 12
and 13.
• Consider how a student may solve pictorially or
abstractly.
Try Problems #19-20.
• Sample questions from the
Problem Set of Lesson 14.
• Use RDW to solve.
Lessons 12-14
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Turn and Talk
• What difficulties would you
anticipate with student
understanding of the
mathematics in this section?
• What scaffolds would be
effective for addressing those
difficulties?
G4–M7–Lesson 14
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Agenda
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•
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Introduction to the Module
Concept Development
Module Review
Year in Review
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Review the End-of-Module Assessment
• Complete #6 of the assessment.
• Compare your responses to the sample student work.
• Discuss your results with a peer.
– What may students struggle with?
– What may teachers struggle with?
• Complete the remaining problems.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Agenda
•
•
•
•
Introduction to the Module
Concept Development
Module Review
Year in Review
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Year in Review
• Lessons 15-16: Create and determine the area of
composite figures
• Lesson 17: Practice and solidify Grade 4 fluency
• Lesson 18: Practice and solidify Grade 4 vocabulary
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Determine the Area for Composite Figures
Emma’s rectangular bedroom is 11 feet long and 12 feet
wide with an attached closet that is 4 feet by 5 feet.
How
many square feet of carpet does Emma need to cover both
the bedroom and closet?
Lesson 15
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A Story of Units
Mini-Personal Boards
Materials: plastic page protector, manila folder, tape
Steps:
1. Cut page protector in half horizontally.
2. Tape to top half of folder with the opening at the
top.
3. Slip Problem Set into page protector. Fold back top
half of Problem Set.
4. Complete. Check answers by unfolding top half of
Problem Set.
Special Note: Do NOT copy Homework back-to-back in
Topic D.
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A Story of Units
Practice and Solidify Grade 4 Fluency
Lesson 17
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A Story of Units
Practice and Solidify Grade 4 Vocabulary
Lesson 18
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A Story of Units
Module 7 Key Points
• Students develop an understanding of the two
measurement systems.
• Students convert from larger to smaller units of
measurements.
• Students apply knowledge of the four
operations to solve real world problems.
• Students connect the practice of solving
with mixed units to mixed measurement
units.
© 2012 Common Core, Inc. All rights reserved. commoncore.org