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CCSS Measurement and Data (MD)
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Unpacking the Standards
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Grade 4
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Standard: 4.MD.1 Cluster (m/s/a)
Math Practices: MP2, MP5, MP6
Related CA Standard
Partial 6.MG.2.1, 7.MG.1.1
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min.,
sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit.
Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in.
Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number
pairs (1, 12), (2, 24), (3, 36),…
Essential Skills/Concepts
Know relative sizes of measurement
units within one system of units—both
metric and standard/customary (see
Math standard language for specific
measurement units).
Be able to convert larger units into
smaller units and vice versa (i.e. 2
meters = 200 centimeters, etc.)
Be able to record measurement
equivalents in a two-column table.
Example:
Feet
Inches
1 foot
12 inches
4 feet
48 inches
8 feet
96 inches
And list the conversions in number pairs
(1, 12), (2, 24), (3,36), etc.
Academic Vocabulary:
Measurement units
Metric measurement
Standard/Customary Measurement
Convert, conversions
Teaching Notes/Strategies
Using measurement tools (see resource
column ), teach/review different
measurement units and note their
relation to each other (i.e., a cup is
smaller than a quart; a foot is larger
than an inch; an ounce is smaller than a
pound).
Use real objects to measure using the
appropriate measuring tool.
Use measurements taken to convert to
smaller/larger units and record on a
table.
Resources
Manipulatives:
Rulers
Weight Scale
Capacity containers
Clocks
Anchor charts for metric and
standard/customary measurements and
their equivalents
Math journals
Making a Kilogram
Estimating Weight
Record 1 unit equivalents on an anchor
chart: 12 inches = 1 foot, 3 feet = 1
yard; 2 cups = 1 pint, 2 pints = 1 quart;
16 ounces = 1 pound, etc.
Measurement Conversion Word Problems
Create Gallon Man to show capacity
equivalents.
All available at http://www.k-
Students record measurement
equivalent charts/tables in their math
journals.
Measurement Concentration
Metric Relationships
Capacity Creature
5mathteachingresources.com
Standard: 4.MD.2 Cluster (m/s/a)
Math Practices: MP1, MP2, MP4, MP5, MP6
Related CA Standard
5.MG.1.4
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of
objects, and money, including problems involving simple fractions or decimals, and problems that require expressing
measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams
such as number line diagrams that feature a measurement scale.
Essential Skills/Concepts
Teaching Notes/Strategies
Resources
Prerequisite: knowledge acquired when
mastery 4.MD.1.
Prerequisite: knowledge of different units
of money and how to convert from smaller
to larger units (i.e., 4 quarters = 1 dollar).
Prerequisite: 4.NF standard mastery
working with fractions and decimals.
Prerequisite: Be able to solve problems
using the 4 operations.
Sample Problem: Susan has 2 feet of
ribbon. She wants 3 of her friends to
get the same amount. How much ribbon
will each friend get? Record in fractions
or decimals.
Solve word problems involving distance,
time, liquid volume, mass, and money.
Draw diagrams or use manipulatives to
solve problems (see Resource column)
Problems should include simple fractions
or decimals.
Use conversion tables/charts to aid in
converting units to solve problems.
Problems should require converting units
from smaller to larger and vice versa.
Partner work/talk about how to solve
problems.
Measurement Word Problems
Represent measurement quantities using
diagrams such as number line diagrams
that feature a measurement scale.
Students write solutions in journals.
Elapsed Time Ruler 2
Academic Vocabulary:
All available at http://www.k5mathteachingresources.com
Use the PUSD Universal Problem Solving
Strategy to attack word problems.
Convert—conversion
Intervals of time
Manipulatives:
Rulers
Number line diagrams with a
measurement scale
Clocks
Capacity containers
Play money
Weight Scale
Math Journals
Conversion Tables
Anchor Charts
Elapsed Time Ruler 1
24 Hour Number Line (4 per page)
Standard: 4.MD.3 Cluster (m/s/a)
Math Practices: MP2,
MP4, MP5, MP6, MP7
Related CA Standard
4.AF.1.4, 4.MG.1.1, 4.MG.1.2, 4.MG.1.3, 4.MG.1.4
Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. For example, find
the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a
multiplication equation with an unknown factor.
Essential Skills/Concepts
rd
Teaching Notes/Strategies
Use prior knowledge acquired in 3
grade which is an understanding of
area/perimeter.
Use graph paper, rulers, pattern blocks,
or any other materials to draw diagrams
and measure the area/perimeter.
Use formulas to calculate area and
perimeter of rectangles.
From these diagrams, the formulas for
area and perimeter should evolve.
Students then need adequate practice
with the formulas and marking them
appropriate (i.e. sq2, ft.)
Be able to communicate their
understanding of why the formulas
work.
Know that the answers for the formulas
will be in square units for area and
linear units for perimeter and mark
appropriately.
Academic Vocabulary:
Area
length
Perimeter
width
Square feet
Linear feet
Formulas
Sample Problem: Sally wants to build a pen
for her dog Callie. Her parents give her
$200 to buy the fencing, but want Sally to
design the pen. Her parents suggest that
she consider different plans. Her parents
also remind her that Callie needs as much
room as possible to run and play and that
the pen can be placed anywhere in the yard
and the wall of the house could be used as
one side of the pen. Sally decides to buy
fencing material that costs $8.50 per foot.
She will also need at least one three foot
wide gate for the pen that costs $15.
--Design a pen for Callie. Experiment with
different pen designs and consider the
advice from Sally’s parents. Sally’s house
can also be any configuration. Show your
various design configurations and explain
why certain designs are better for Callie.
Resources
Manipulatives:
Pattern blocks
Graph paper
Rulers
Anchor chart for formulas
How Many Tables?
Fencing a Garden
Designing a Zoo Enclosure
All available at http://www.k5mathteachingresources.com
Standard: 4.MD.4 Cluster (m/s/a)
Math Practices: MP2, MP4. MP5, MP6, MP7
Related CA Standard
4.SDAP.1.0, 4.SDAP.1.3
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems
involving addition and subtraction of fractions by using information presented in line plots. For example, from a line
plot, find and interpret the difference in length between the longest and shortest specimens in an insect collection.
Essential Skills/Concepts
Prerequisites: Understanding fraction
units and adding/subtracting of
fractions (4.NF standards).
Make a line plot to display a data set of
measurements in fractions of a unit.
Solve problems using addition and
subtraction of fractions by using
information presented in line plots.
Teaching Notes/Strategies
PDIM on how to read a line plot.
PDIM on how to make a line plot using a set
of data.
Have students create line plots using graph
paper. Ask similar questions as those below.
Have students collect authentic data from
classmates and put on a line plot. Have them
compare their line plots and answer
questions as partners.
Have students write in math journals about
how to read/solve problems using line plots.
Academic Vocabulary:
Line plots
Data set
Sample Problem: Ten students measure
objects in their desk to the nearest (1/2, ¼,
1/8) inch. They record their results on the
line plot below (in inches) (show example of
line plot).
--How many objects measures ½, ¼, 1/8
inch?
--If you put the objects end to end, what
would the total length be?
--If five 1/8 inch pencils are placed end to
end, what would be the total length?
Resources
Graph paper to draw line plots
Math journals
Anchor charts
Length of Ants Line Plot
Objects in My Desk Line Plot
Both available at http://www.k5mathteachingresources.com
Standard: 4.MD.5a Cluster (m/s/a)
Math Practices: MP6, MP7
Related CA Standard
4.MG.3.5
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and
understand concepts of angle measurement.
a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by
considering the fraction of the circular arc between the points where the two rays intersect the circle. An
angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
Essential Skills/Concepts
Prerequisites: definition/examples
of endpoints, circles, rays
Understand that angles are
geometric shapes formed by two
rays that share a common endpoint.
Understand that an angle measure
is a portion of a circular arc that is
formed by the angle when a circle is
centered at their shared vertex
and that the ARC is what is
measured, not the size of the “pie
piece” that the angle makes
(because different size circles
making different size “pie pieces”
but the ARC measurement (i.e. 60o)
is the same, no matter the size of
the circle.)
Understand that there are 360
degrees in a circle and that an angle
that turns through 1/360 of a
circle is called a one-degree angle.
Understand that these degrees can
be used to measure angles.
Teaching Notes/Strategies
Math journals (or a Geometry Book) to record
definitions and draw examples of geometric
shapes.
Use a diagram showing an angle as part of a
circle to help students see than an angle is
determined by the arc it creates relative to
the size of the entire circle.
Resources
Rulers to draw angles
Compasses to draw circles
Protractors to measure angles
Graph paper to draw figures
Math journals (or geometry books)
Graph paper to draw figures
Color code the different parts: rays,
endpoints, arc
PDIM on how to use a compass.
Have students draw this diagram with various
sizes of circles and angles to reinforce
concept.
PDIM on using a protractor to measure
angles. Then have students use protractors to
measure angles.
Make your own worksheets to practice angle
measurement.
http://www.worksheetworks.com/math/geometry/m
easuring-angles.html
http://www.math-aids.com/Geometry/Angles/
Academic Vocabulary:
Angles
circular arc
Shapes
rotation
Rays
vertex
Endpoint
protractor
Degrees and its symbol
compass
o
Standard: 4.MD.5b Cluster(m/s/a)
Math Practices: MP6, MP7
Related CA Standard
NEW
An angle that turns through n one-degree angle is said to have an angle measure of n degrees.
Essential Skills/Concepts
Prerequisite: Understand that a 360
rotation makes a complete circle
Teaching Notes/Strategies
o
Understand that if an angle turns
through n one-degree angle, it is said to
have an angle measure of n degrees.
(i.e., An angle turns through 40 onedegree angles, so it has a measurement
of 40 degrees.)
Academic Vocabulary:
Variable
Degrees and its symbol
Angles
Rotation
o
Resources
Use graph paper to draw/show each
one-degree angle in an angle (such as a 5
degree angle).
Graph paper for drawing angles
Mark the ARC of a circle with the onedegree increments to increase
understanding.
Protractor for measuring circles
Compass for drawing circles
Standard: 4.MD.6 Cluster (m/s/a)
Math Practices: MP2, MP5, MP6
Related CA Standard
5.MG.2.1
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
Essential Skills/Concepts
Prerequisite: Understand that a 360
rotation makes a complete circle
Understand benchmark angles of 90
and 180o.
o
Understand benchmark angles of 45
and 30o.
o
Teaching Notes/Strategies
o
Students can use appropriate
terminology of acute, right, and obtuse
to describe angles and rays
(perpendicular).
Academic Vocabulary:
Rotation
Degrees and its symbol
o
Benchmark angles
Acute, right, obtuse, perpendicular
Use angles in context (such as clock
hands) to measure/compare/identify
angles.
Student identify different types of
angles using real-world objects around
them.
Students compare angles to the
benchmark angles identified in the skills
column 
Resources
Protractors
Clocks with 2 hands (to show different
angles in context)
Math Journal (or geometry book)
Predicting and Measuring Angles
Angle Barrier Game
Angles in Triangles
Angles in Quadrilaterals
All available at http://www.k5mathteachingresources.com
Related CA Standard
NEW
Math Practices: MP6, MP7
Standard: 4.MD.7 Cluster (m/s/a)
Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of
the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown
angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a symbol for the
unknown angle measure.
Essential Skills/Concepts
Teaching Notes/Strategies
Prerequisites: Understand concepts of
angle measure, gain experience
measuring angles, and familiarity with
the geometric terms used to define
angles as geometric shapes (4.MD.5 and
4.MD.6).
PDIM on how to solve for an unknown angle.
Recognize that angle measurements can
be added together to form larger
angles.
Given real-world problems, students write
equations to solve problems for unknown
angles.
When an angle is broken into several
parts, the sum of the angles
measurements added together is the
measurement of the whole angle.
Students discuss how they solved problems
and/or write them in math journals (or a
geometry book).
Solve addition/subtraction problems to
find unknown angles on a diagram and in
the real-world.
Use equations with a symbol for the
unknown angle measure.
Academic Vocabulary:
See previous 4.MD standards 5 and
6
Students use pattern blocks to simulate
problems
Given a diagram, students write equations to
solve problems for unknown angles.
Sample Problem:
a. In the roof framework shown, the
measure of one angle is 80o. What is
the unknown angle measure?
n
80o
b. When the clocks hands are on the 12
and 1, the angle is 30o, so what is the
measurement of the angle when the
hands are on the 12 and the 4?
Resources
Protractors
Clocks with hands for solving real-world
problems
Graph paper or tracing paper for
drawing
Pattern blocks for manipulating angles
to solve problems
Math journals
Anchor charts of different types of
angles.
Unknown Angle Word Problems
How Many Degrees?
Angles in a Right Triangle
Pattern Block Angles
All available at http://www.k5mathteachingresources.com