204 kB Grade 4 Math-Unit 3 Curriculum

Commercial Township Public Schools
Common Core Curriculum
Content Area:
EnVision Math
Grade:
4
Unit Plan Title:
Unit 3
Unit Summary:This unit will cover pattern concepts including multiplication fact
patterns, repeating patterns, number sequences, extending pattern tables, writing
pattern rules, geometric patterns;fraction concepts including
comparing/ordering fractions, adding fractions with like denominators, improper
fractions and mixed numbers, adding/subtracting mixed numbers; measurement
concepts including customary units of length, capacity, weight, changing
customary units, metric units of length, capacity, mass, changing metric units,
units of time; and problem solving strategies including acting it out, using
reasoning, writing to explain, and working backward.
Unit Rationale:
 Students will apply prior knowledge needed for using multiplication and
division problems within 100 to solve word problems with a symbol for the
unknown number to represent the number. Students will need to use this
understanding to identify the rule in number and shape patterns. This
understanding will be essential in determining factors of numbers ranging
1-100. Pattern understanding will also be needed for Place Value and
Fractional equivalence.
 Students will need a prior understanding that a fraction 1/b is the quantity
formed by 1 part when a whole is portioned into “b” equal parts; also
understanding a fraction as “a/b” as the quantity formed by “a” parts of
size 1/b. Students will understand and be able to explain equivalence of
fractions in special cases and compare fractions by reasoning about there
size.
 In this topic students will make connections between numerators,
denominators, and one whole. Students will have the ability to add and
subtract simple fractions to build upon their understanding of mixed
numbers and ready themselves for topic 13. Students will know how to
read a tape measure and follow fractions on a number line for real world
situations.
 In this topic students will connect fractions with measuring on a tape
measure for customary and metric units. This will give students a base
understanding for measuring and estimating in measurement with more
difficult problems in topic 15.
In this unit plan the following 21st Century themes and skills are addressed
Indicate whether these skills are EEncouraged, T-Taught, or ACheck all that apply.
Assessed in this unit by marking E, T,
21st
X
Century Themes
A on the line before the appropriate
skill.
21st Century Skills
Global Awareness
E,T
Environmental Literacy
E,T,A Critical Thinking and
Problem Solving
E,T
Communication
Health Literacy
Civic Literacy
Financial, Economic, Business,
and Entrepreneurial Literacy
E,T
Creativity and Innovation
Collaboration
Primary Interdisciplinary Connections:
Students will need a good reading comprehension strategy to use in Math.
Students will use context clues in order to determine meanings of unfamiliar
words. Students will make connections to real-world problem solving and
mathematical problems.
Anchor Standards, Domains, ContentStandard (s)
 Operations and Algebraic Thinking (Domain)
o Gain familiarity with factors and multiples (Cluster)
 4.OA.4-Find all factor pairs for a whole number in the range 1-100.
Recognize that a whole number is a multiple of each of its factors.
Determine whether a given whole number in the rage 1-100 is a
multiple of a given one-digit number. Determine whether a given
whole number in the range 1-100 is prime or composite. (Standard)
o Generate and analyze patterns (Cluster)
 4.OA.5-Generate a number or shape pattern that follows a
given rule. Identify apparent features of the pattern that were
not explicit in the rule itself. (Standard)
 Numbers and Operations—Fractions (Domain)
o Extend understanding of fraction equivalence and ordering (Cluster)
 4.NF.1-Explain why a fraction a/b is equivalent to a fraction (n x
a)/(n x b) by using visual fraction models, with attention to how
the number and size of the parts differ even though the two
fractions themselves are the same size. Use this principle to
recognize and generate equivalent fractions. (Standard)
 4.NF.2-Compare two fractions with different numerators and
different denominators, e.g., by creating common dominators or
numerators, or by comparing to a benchmark fraction such as
½. Recognize that comparisons are valid only when the two
fractions refer to the same whole. Record the results of
comparisons with symbols >, =, or <, and justify the conclusions,
e.g., by using a visual fraction model. (Standard)
o Build fractions from unit fractions by applying and extending previous
understandings of operations on whole numbers (Cluster)
 4.NF.3-Understand a fraction a/b with a>1 as a sum of fractions
1/b.(Standard)
 4.NF.3a-Understand addition and subtraction of fractions as
joining and separating parts referring to the same whole.
(Standard)
 4.NF.3b-Decompose a fraction into a sum of fractions with the
same denominator in more than one way, recording each
decomposition by an equation. Justify decompositions, e.g., by
using a visual fraction model. Example: 3/8=1/8 + 1/8 + 1/8;
3/8= 1/8 + 2/8. (Standard)
 4.NF.3c-Add and subtract mixed numbers with like
denominators, e.g., by replacing each mixed number with an
equivalent fraction, and/or by using properties of operations and
the relationship between addition and subtraction. (Standard)
 4.NF.3d-Solve word problems involving addition and subtraction
of fractions referring to the same whole and having like
denominators, e.g., by using visual fraction models and
equations to represent the problem. (Standard)
 Measurement and Data (Domain)
o Solve problems involving measurement and conversion of
measurements from a larger unit to a smaller unit. (Cluster)
 4.MD.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
measurements equivalents in a two-column table. (Standard)
 4.MD.2-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.
(Standard)
Technology Standards
8.1.4.A.1: Demonstrate effective input of text and data using an input device
8.1.4.E.2: Evaluate the accuracy of, relevance to, and appropriateness of using
print and non-print electronic information sources to complete a variety of tasks
8.1.4.F.1: Select and apply digital tools to collect, organize, and analyze data that
support a scientific finding.
Essential Questions
Enduring Understandings
 1-2 How can patterns be used to find
 1-2: There are patterns in the
products with factors of 2,5, and 9?
products for multiplication facts
with factors of 2, 5, and 9.
 1-5 How can students recognize
patterns and be able to continue the
 1-5: Some problems can be solved
pattern?
 2-1 How can students identify and
extend repeating geometric or
repeating number patterns?
 2-2 How will students identify and
extend whole-number patterns
involving addition and subtraction?
 2-3How will students extend tables of
ordered pairs for situations involving
multiplication, addition, or subtraction?
 2-4How can students find a rule and
extend the table, given a table of
number pairs?
 2-5 How can students extend patterns
of cubes or tiles?
 2-6 How will students use Act It Out
and Reasoning to solve problems?
 11-6 How can benchmark fractions be
used to compare fractions with unlike
denominators?
 11-7 How can common denominators
and equivalent fractions be used to
order fractions with unlike
denominators?
 12-1 How can students use models to
add fractions with like denominators?
 12-2 How can students use
computational procedures to add
fractions with like denominators and
solve problems?
 12-6 How will students identify and
write mixed numbers as improper
fractions and improper fractions as
mixed numbers?
by identifying elements that repeat
in a predictable way.
 2-1: Some patterns consist of
shapes or numbers arranged in a
unit that repeats.
 2-2: Some numerical sequences
have a rule that tells how to
generate more numbers in the
sequence.
 2-3: Some real-world quantities
have a mathematical relationship;
the value of one quantity can be
found if you know the value of the
other quantity.
 2-4: Some real-world quantities
have a mathematical relationship;
the value of one quantity can be
found if the value of the other
quantity is known.Patterns can be
used to identify some relationship.
 2-5: Some sequence of geometric
objects change in predictable ways
that can be described using a
mathematical rule.
 2-6: Some problems can be solved
by using objects to act out the
actions in the problem.
Some problems can be solved by
reasoning about the conditions in
the problem.
 11-6: If two fractions have the
same denominator, the fraction
with the greater numerator is the
greater fraction. If the two fractions
have the same numerator, the
fraction with the lesser
denominator is the greater fraction.
 11-7: Ordering 3 or more numbers
is similar to comparing 2 numbers
because each number must be
compared to each other number.
 12-1: A model can be used to add
two or more fractions.
 12-2: When adding fractions with
like denominators, you are adding
 12-7 How can models be used to add
and subtract mixed numbers?

 12-8 How can models and
computational procedures be used to
add mixed numbers?
 12-9 How will models and
computational procedures be used to
subtract mixed numbers?
 11-8 How can students decide and
write to explain whether an answer is
correct or not?



 14-1 How can students estimate and
measure length by choosing the most
appropriate unit of length?
 14-2 How can students fluently
estimate and compare customary
capacity units (cups, pints, quarts, and
gallons)?
 14-3 How can students estimate
fluently estimate and measure with
units of weight?


 14-4 How can students convert
between customary units?

 14-5 How can students solve and
explain the answers to each problem
in writing?

portions of the same size. So, you
can add the numerators without
changing the denominator.
12-6: Fractional amounts greater
than 1 can be represented using a
whole number and a fraction.
Whole number amounts can be
represented as fractions. When
the numerator and denominator
are equal, the fraction equals 1.
12-7: Models can be used to show
different ways of adding and
subtracting mixed numbers.
12-8: One way to subtract mixed
numbers is to subtract the
fractional parts and then subtract
the whole number parts.
Sometimes whole numbers or
fractions need to be renamed.
12-9: One way to subtract mixed
numbers is to subtract the
fractional parts and then subtract
the whole number parts.
Sometimes whole numbers or
fractions need to be removed.
11-8: Mathematical explanations
can be given using words,
pictures, numbers or symbols. A
good explanation should be
correct, simple, complete, and
easy to understand.
14-1: Length can be estimated and
measured in different systems
(customary, metric) using different
units in each system that are
related to each other. Length can
also be estimated in different
systems.
14-2: Capacity is a measure of the
amount of liquid a container can
hold. Capacity can be measured
in different systems (customary,
metric) and using different units in
each system that are related to
each other.
14-3: The weight of an object is a
 14-6 How can students estimate and
measure length to the nearest
centimeter, and choose the most
appropriate metric unit for measuring
length?
 14-7 How can students estimate
fluently measure capacity with
milliliters and liters?
 14-8 How can units of mass- grams
and kilograms be used to estimate
and measure?
 14-9 How can metric units be used to
convert measurements?
 14-10 How can students compare
several units of time and convert from
one unit of time to another?
 14-11 How can students solve
problems that require finding the
original times, measurements, or
quantities that led to a result that is
given?
measure of how heavy an object
is.
 14-4: Relationships between
customary measurement units can
be expressed as a function (e.g.
12 inches to 1 ft. or 12 in. = 1ft).
Relationships exist that enable you
to convert between customary
units of the same attribute by
multiplying or dividing.
 14-5: Mathematical explanations
can be given using words,
pictures, numbers or symbols. A
good explanation should be
correct, simple, complete, and
easy to understand.
 14-6: Length can be estimated and
measured in different systems
(customary, metric) using different
units in each system that are
related to each other. Length can
also be estimated in different
measurement systems.
 14-7: Capacity is a measure of the
amount of liquid a container can
hold. Capacity can be measured
in different systems (customary,
metric) and using different units in
each system that are related to
each other.
 14-8: Mass is the measure of the
quantity of matter in an object.
Weight and mass are different
measures.
 14-9: Relationships between
metric units can be expressed as a
function (e.g., 10mm to 1 cm or
10mm = 1cm). Relationships exist
that enable you to convert
between metric units of the same
attribute by multiplying or dividing.
 14-10: Time can be expressed
using different units that are
related to each other.
 14-11: Some problems with the
initial data point unknown can be
solved by starting with the end
result and by reversing the steps
and processes to work backward
to find the initial data point.
Learning Targets/Objectives
1-2:Students will use patterns to find products with factors of 2, 5, and 9.
1-5:Students will recognize patterns and be able to continue the pattern.
2-1: Students will identify and extend repeating geometric or repeating number
patterns.
2-2: Students will identify and extend whole-number patterns involving addition
andsubtraction.
2-3: Students will extend tables of ordered pairs for situations involving
multiplication, addition, and subtraction
2-4: Students will find a rule and extend the table, given a table of number pairs.
2-5: Students will extend patterns of cubes or tiles.
2-6: Students will use the strategies Act It Out and Use Reasoning to solve
problems.
11-6: Students will use benchmark fractions to compare fractions with unlike
denominators.
11-7:Students will use common denominator and equivalent fractions to order
fractions with unlike denominators.
11-8:Students will write to explain whether an answer is correct or not.
12-1:Students will use models to add fractions with like denominators.
12-2 :Students will use computational procedures to add fractions with like
denominators and solve problems.
12-6 :Students will identify and write mixed numbers as improper fractions and
improper fractions as mixed numbers.
12-7 :Students will use models to add and subtract mixed numbers.
12-8 :Students will use models and computational procedures to add mixed
numbers.
12-9 :Students will use models and computational procedures to subtract mixed
numbers.
14-1 : Students will estimate and measure length by choosing the most
appropriate unit of length.
14-2 : Students will estimate fluently with customary capacity units (cups, pints,
quarts, and gallons). They will compare the relative sizes of capacity
measurements.
14-3 : Students will estimate fluently and measure with units of weight.
14-4 : Students will be able to convert between customary units.
14-5 : Students will solve and explain the answers to each problem in writing.
14-6 : Students will estimate and measure length to the nearest centimeter, and
choose the most appropriate metric unit for measuring length.
14-7 : Students will estimate fluently with milliliters and liters. They will measure
capacity using these metric units.
14-8 : Students will estimate and measure with units of mass—grams and
kilograms.
14-9 : Students will be able to convert between metric units.
14-10: Time can be expressed using different units that are related to each other.
14-11 : Students will solve problems that require finding the original times,
measurements, or quantities that led to a result that is given.
Evidence of learning
Summative Assessment:
 Topic 2 Test
 Topic 11/12 Test
 Topic 14 Test
 RAC Unit 3 Math Assessment
Formative Assessments:
*Any or all of these may be used to informally assess students.
 Daily Common Core Review (www.pearsonsuccessnet.com)
 Quick Check (www.pearsonsuccessnet.com)
 enVision Practice Workbooks
 Teacher Observation
 Multiplication Timed Tests
 Teacher Created Materials
 Center Activities
 Sweep Scores
 Index Card with Summaries
 Hand Signals
 Student Conference
 3-minute pause
 Self-Assessment
 Exit Card
 Portfolio Check
 Choral Response
 Debriefing
 One Sentence Summary
 Think-Pair-Share
 Turn to Your Partner
 Oral Questioning
Lesson Plans
Lesson
Lesson 1-2 and 1-5
Lesson 2-1
Lesson 2-2
Lesson 2-3
Lesson 2-4
Lesson 2-5 and 2-6
Timeframe
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
Topic 2 Test and Review RAC #’s 1-3
Lesson 11-6
Lesson 11-7
Lesson 12-1
Lesson 12-2
Lesson 12-6
Lesson 12-7
Lesson 12-8
Lesson 12-9
Lesson 11-8
RAC Review 4-16
Topic Test 11/12
Review Patterns/Fractions
Review Patterns/Fractions
Lesson 14-1
Lesson 14-2
Lesson 14-3
Lesson 14-4
Lesson 14-5
Lesson 14-6
Lesson 14-7
Lesson 14-8
Lesson 14-9
Lesson 14-10 and RAC Review 17-20
Lesson 14-11 and Review of Variables
and Word Problems
Lesson 14-11 and Review of Variables
and Word Problems
Review Day- Topic 14 skills
Topic 14 Test
Unit 3 RAC Assessment
Resources
 enVision Materials
 SmartBoard Measurement Tools
 Rulers
 Length, Weight, Capacity Manipulatives
 (www.pearsonsuccessnet.com)
 Unit 3 RAC Assessment
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson

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