TRENTON PUBLIC SCHOOLS
Department of Curriculum and Instruction
108 NORTH CLINTON AVENUE
TRENTON, NEW JERSEY 08609
Grade 1 Mathematics
CURRICULUM GUIDE AND INSTRUCTIONAL ALIGNMENT
Trenton BOE Approved August 26, 2013- Revised June 16, 2014
Page 1
Grade 1 Units at Glance
(per NJDOE Model Curriculum)
Overview
The unit design was created in line with the areas of focus for first grade mathematics as identified by the Common Core State Standards. Each
unit is comprised of standards that are considered major content along with supporting content.
Unit 1 begins with two benchmarked standards “Add and subtract within 20 (fluently within 10)” [1.OA.6] -- repeated in units 4 and 5 – and
“Count to 120” [1.NBT.2]. In unit 2, students are introduced to word problems and symbols for unknowns in equations – another benchmarked
standard [1.OA.1]. Students see addition and subtraction as counting (adding two is the same as “counting on” two) and solve simple arithmetic
problems involving the place value concept, properties of the operations, making 10s, and decomposing. Place value with “tens and ones” and
“multiples of tens” begins in unit 3 and extends into unit 2 as measurement. Geometric shapes and their attributes are treated in unit 5.
Unit 1: Add and subtract within 20
Cluster
Add and subtract
within 20.
Prerequisites
Standard
Description
K.OA.1
Create addition and
subtraction events with
objects (or make
drawings) to represent a
sum (putting together) or
a difference (taking from)
up to 10.
1.OA.5
Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
1.OA.6
Add and subtract within 20, demonstrating fluency for addition and subtraction
within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 +
4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 –
3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction
(e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent
but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent
6 + 6 + 1 = 12 + 1 = 13).
K.OA.2
Use objects or drawings
to represent and solve
addition and subtraction
word problems (within
10)
K.OA.3
Decompose numbers
less than or equal to ten
into pairs of numbers in
more than one way and
record with a drawing or
Trenton BOE Approved August 26, 2013- Revised June 16, 2014
Page 2
equations (e.g., write 7
as 2 + 5 and 6 + 1).
Understand and apply
properties of
operations and
the relationship
between addition and
subtraction.
Extend the counting
sequence.
Understand place
value.
K.OA.4
Given a number less
than 10, find a number
that makes 10 (e.g., 1 +
9, 2 + 8, 3 + 7, 4 + 6, 5
+ 5, etc.).
1.OA.3
Apply properties of operations as strategies to add and subtract. Examples: If 8
+ 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of
addition.) To add 2 + 6 + 4, the second two numbers can be added to make a
ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
K.OA.5
Fluently add and
subtract within 5
1.OA.4
Understand subtraction as an unknown-addend problem. For example, subtract
10 – 8 by finding the number that makes 10 when added to 8.
1.NBT.1
Count to 120, starting at any number less than 120. In this range, read and
write numerals and represent a number of objects with a written numeral.
1.NBT.2
Understand that the two digits of a two-digit number represent amounts of tens
and ones. Understand the following as special cases: 10 can be thought of as a
bundle of ten ones — called a “ten.” a. The numbers from 11 to 19 are
composed of a ten and one, two, three, four, five, six, seven, eight, or nine
ones.
K.NBT.1
Compose and
decompose numbers
from 11 to 19 into a
group of ten and one(s)
with or without
manipulatives. Record
each composition or
decomposition through a
drawing or equation.
Unit 2: Represent and solve problems involving addition and subtraction
Cluster
Prerequisites
Represent and solve
problems involving
addition and subtraction.
K.OA.1
Create addition and
subtraction events with
objects (or make drawings)
to represent a sum (putting
together) or a difference
Standard
1.OA.1
Trenton BOE Approved August 26, 2013- Revised June 16, 2014
Description
Use addition and subtraction within 20 to solve word problems involving
situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using objects,
drawings, and equations with a symbol for the unknown number to
represent the problem.
Page 3
(taking from) up to 10.
K.OA.2
Use objects or drawings to
represent and solve
addition and subtraction
word problems (within 10)
1.OA.2
Solve word problems that call for addition of three whole numbers
whose sum is less
than or equal to 20, e.g., by using objects, drawings, and equations with
a symbol for the unknown number to represent the problem.
K.OA.5
Fluently add and subtract
within 5
Work with addition and
subtraction equations.
K.OA.3
Decompose numbers less
than or equal to ten into
pairs of numbers in more
than one way and record
with a drawing or equations
1.OA.7
(e.g., write 7 as 2 + 5 and 6 + 1).
K.OA.5
Fluently add and subtract
within
1.OA.8
Understand the meaning of the equal sign, and determine if equations
involving
addition and subtraction are true or false. For example, which of the
following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 =
2 + 5, 4 + 1 = 5 + 2.
Determine the unknown whole number in an addition or subtraction
equation relating
three whole numbers. For example, determine the unknown number
that makes the equation true in each of the equations 8 + ? = 11, 5 = �–
3, 6 + 6 = �.
K.CC.1
Count to 100 by ones and by
tens.
Extend the counting
sequence.
K.CC.A.2
Count forward beginning
from a given number within
the known sequence (instead
of having to begin at 1).
1.NBT.1
K.CC.A.3
Write numbers from 0 to 20.
Represent a number of
objects with a written
numeral 0-20 (with 0
representing a count of no
Trenton BOE Approved August 26, 2013- Revised June 16, 2014
Count to 120, starting at any number less than 120. In this range, read
and write
numerals and represent a number of objects with a written numeral.
Page 4
objects).
Unit 3 Understanding Place Value
Cluster
Prerequisites
Understand place value.
K.NBT.1
Compose and decompose
numbers from 11 to 19 into a
group of ten and one(s) with
or without manipulatives.
Record each composition or
decomposition through a
drawing or equation.
Use place
valueunderstanding and
properties of operations to
add and subtract.
K.NBT.1
Compose and decompose
numbers from 11 to 19 into a
group of ten and one(s) with
or without manipulatives.
Record each composition or
decomposition through a
drawing or equation.
Standard
Description
1.NBT.2
Understand that the two digits of a two-digit number represent
amounts of tens and ones. Understand the following as special cases:
c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two,
three, four, five, six, seven, eight, or nine tens (and 0 ones).
1.NBT.3
Compare two two-digit numbers based on meanings of the tens and
ones digits, recording the results of comparisons with the symbols >,
=, and <.
1.NBT.4
Add within 100, including adding a two-digit number and a one-digit
number, and adding a two-digit number and a multiple of 10, using
concrete models or drawings and strategies based on place value,
properties of operations, and/or the relationship between addition
and subtraction; relate the strategy to a written method and explain
the reasoning used. Understand that in adding two-digit numbers, one
adds tens and tens, ones and ones; and sometimes it is necessary to
compose a ten.
1.NBT.5
Given a two-digit number, mentally find 10 more or 10 less than the
number, without having to count; explain the reasoning used.
Trenton BOE Approved August 26, 2013- Revised June 16, 2014
Page 5
1.NBT.6
Subtract multiples of 10 in the range 10-90 from multiples of 10 in
the range 10-90 (positive or zero differences), using concrete models
or drawings and strategies based on place value, properties of
operations, and/or the relationship between addition and subtraction;
relate the strategy to a written method and explain the reasoning
used.
Unit 4: Measure lengths indirectly and by iterating length units
Cluster
Prerequisites
Standard
Description
1.MD.1
Order three objects by length; compare the lengths of two objects
indirectly by using a third object.
K.MD.2
Directly compare and
describe two objects with a
measurable attribute in
common using “more
of”/”less of” the attribute.
For example, directly
compare the heights of two
children and describe one
child as taller/shorter.
1.MD.2
Express the length of an object as a whole number of length units, by
laying multiple copies of a shorter object (the length unit) end to end;
understand that the length of an object is the number of same-size
length units that span it with no gaps or overlaps. Limit to contexts
where the object being measured is spanned by a whole number of
length units with no gaps or overlaps.
N/A
1.MD.3
Tell and write time in hours and half-hours using analog and digital
clocks.
K.G.2
Correctly name shapes
regardless of their
orientations or overall size.
1.G.1
Distinguish between defining attributes (e.g., triangles are closed and
three-sided) versus non-defining attributes (e.g., color, orientation,
overall size); build and draw shapes to possess defining attributes.
K.MD.1
Describe measurable
attributes of objects, e.g.,
length and weight.
Measure lengths indirectly
and by iterating length
units.
Tell and write time.
Reason with shapes and
their attributes.
Trenton BOE Approved August 26, 2013- Revised June 16, 2014
Page 6
K.G.5
Model shapes in the world by
building shapes from
components (e.g., sticks and
clay balls) and drawing
shapes.
K.G.6
Compose simple shapes to
form larger shapes For
example, “Can you join these
two triangles with full sides
touching to make a
rectangle?”
K.OA.1
Create addition and
subtraction events with
objects (or make drawings)
to represent a sum (putting
together) or a difference
(taking from) up to 10.
Represent and solve
problems involving
addition and subtraction
K.OA.2
Use objects or drawings to
represent and solve
addition and subtraction
word problems (within 10)
1.OA.1
Use addition and subtraction within 20 to solve word problems
involving situations of adding to, taking from, putting together, taking
apart, and comparing, with unknowns in all positions, e.g., by using
objects, drawings, and equations with a symbol for the unknown
number to represent the problem.
1.OA.6
Add and subtract within 20, demonstrating fluency for addition and
subtraction within 10. Use strategies such as counting on; making ten
(e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number
leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the
relationship between addition and subtraction (e.g., knowing that 8 +
4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or
known sums (e.g., adding 6 + 7 by creating the known equivalent 6 +
K.OA.5
Fluently add and subtract
within 5
Add and subtract within 20.
K.OA.5
Fluently add and subtract
within 5
Trenton BOE Approved August 26, 2013- Revised June 16, 2014
Page 7
6 + 1 = 12 + 1 = 13).
Extend the counting
sequence.
K.NBT.1
Compose and decompose
numbers from 11 to 19 into a
group of ten and one(s) with
or without manipulatives.
Record each composition or
decomposition through a
drawing or equation.
1.NBT.1
Count to 120, starting at any number less than 120. In this range,
read and write numerals and represent a number of objects with a
written numeral.
Unit 5: Reason with shapes and their attributes
Cluster
Prerequisites
Standard
Represent and interpret
data
N/A
1.MD.4
Reason with shapes and
their attributes.
K.G.2
Correctly name shapes
regardless of their
orientations or overall size.
K.G.3
Analyze and compare twoand three-dimensional
shapes in different sizes and
Description
Organize, represent, and interpret data with up to three categories;
ask and answer questions about the total number of data points, how
many in each category, and how many more or less are in one
category than in another.
1.G.2
Compose two-dimensional shapes (rectangles, squares, trapezoids,
triangles, half-circles, and quarter-circles) or three-dimensional
shapes (cubes, right rectangular prisms, right circular cones, and right
circular cylinders) to create a composite shape, and compose new
shapes from the composite shape.
1.G.3
Partition circles and rectangles into two and four equal shares,
describe the shares using the words halves, fourths, and quarters,
and use the phrases half of, fourth of, and quarter of. Describe the
whole as two of, or four of the shares. Understand for these examples
Trenton BOE Approved August 26, 2013- Revised June 16, 2014
Page 8
that decomposing into more equal shares creates smaller shares.
orientations by counting
sides or vertices (“corners”)
or comparing attributes such
as side lengths.
K.G.4
Analyze and compare twoand three-dimensional
shapes in different sizes and
orientations by counting
sides or vertices (“corners”)
or comparing attributes such
as side lengths.
K.G.5
Model shapes in the world by
building shapes from
components (e.g., sticks and
clay balls) and drawing
shapes.
K.G.6
Compose simple shapes to
form larger shapes For
example, “Can you join these
two triangles with full sides
touching to make a
rectangle?”
Represent and solve
problems involving
addition and subtraction.
K.OA.1
Create addition and
subtraction events with
objects (or make drawings)
to represent a sum (putting
together) or a difference
1.OA.1
Trenton BOE Approved August 26, 2013- Revised June 16, 2014
Use addition and subtraction within 20 to solve word problems
involving situations ofadding to, taking from, putting together, taking
apart, and comparing, with unknowns in all positions, e.g., by using
objects, drawings, and equations with a symbol for the unknown
number to represent the problem.
Page 9
(taking from) up to 10.
K.OA.2
Use objects or drawings to
represent and solve
addition and subtraction
word problems (within 10)
K.OA.5
Fluently add and subtract
within 5
Add and subtract within 20.
K.OA.5
Fluently add and subtract
within 5
1.OA.6
Add and subtract within 20, demonstrating fluency for addition and
subtraction within 10. Use strategies such as counting on; making ten
(e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 =14); decomposing a number leading
to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the
relationship between addition and subtraction (e.g., knowing that 8 +
4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or
known sums (e.g., adding 6 + 7 by creating the known equivalent 6 +
6 + 1 = 12 + 1 = 13).
Extend the counting
sequence.
K.NBT.1
Compose and decompose
numbers from 11 to 19 into a
group of ten and one(s) with
or without manipulatives.
Record each composition or
decomposition through a
drawing or equation.
1.NBT.1
Count to 120, starting at any number less than 120. In this range,
read and write numerals and represent a number of objects with a
written numeral.
Trenton BOE Approved August 26, 2013- Revised June 16, 2014
Page 10
UNIT NAME: Add and Subtract within 20
Grade level:
1
District-Approved Text: My Math, McGraw-Hill
Unit 1:
Stage 1 – Desired Results
Enduring Understandings/Goals:
 I can add and subtract up to 20 to solve problems by using objects, drawings, and equations.
 I can use commutative and associative properties as a strategy to add or subtract.
 Subtraction is an unknown addend.
 Counting is related to addition and subtraction.
 I can determine unknown numbers by using equations with equal signs.
Essential Questions:
 How do you add numbers?
 How do you subtract numbers?
 How do I use strategies to add numbers?
 What strategies can I use to subtract?
 How can I use place value?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Standard:
1.OA.3
Apply properties
of operations as
strategies to add
and subtract.
Student
Learning
Objectives
Apply properties of
operations to add
or subtract whole
numbers within 20
(commutative and
Assessment/ Evidence
Students will write different addition and subtraction with zero
number sentences. They will utilize counters, and dominoes to
depict the problems. They will create drawings of their own
depicting zero.
Trenton BOE Approved August 26, 2013-revised June 2014
My Math Resources
Lesson 1.4 (29-34)
Lesson 2.4 (127-132)
Lesson 3.8 (255-260)
Other Resources
K-5 Math Teaching
Resources:
http://www.k5mathteachingresou
11
(Students need
not use formal
terms for these
properties.)
Students will compare and contrast the operations of addition and
subtraction utilizing key vocabulary from previous chapters and
reviewing learned strategies.
rces.com/1st-gradenumberactivities.html
Examples: If 8 +
3 = 11 is known,
then 3 + 8 = 11
is also known.
(Commutative
property of
addition.)
To add 2 + 6 +
4, the second
two numbers
can be added to
make a ten, so 2
+6+4=2+
10 = 12.
(Associative
property of
addition.)
Students will write a number sentence to represent the problem of
the day.
www.quantiles.com
Prerequisite
Skills:
Model the Math: using assorted manipulatives and materials TE
K.OA.1
K.OA.2
K.OA.3
K.OA.4
K.OA.5
See unit
overview above
for full
description of
standard(s).
associative
properties of
addition). (5)
Students investigate ways to model with math. They will come
together to discuss their results to look for and make use of
structure.
Students will utilize two-color counters to create addition number
sentences.
Students will play Simon Says to practice subtracting a number
from the same number.
My Math Words and
My Vocabulary Cards
Foldable: TE
5 Activities:
Apply properties of
operations to add or
subtract whole
numbers within 20
(Commutative &
Associative properties
of addition).
http://www.readten
nessee.org/math/tea
chers/k3_common_c
ore_math_standards
/first_grade/operatio
ns_algebraic_thinkin
g/1oab4/1oab4_acti
vity.aspx
Literature Connection: Specified trade titles can be read to prepare
students for the lessons.
Real-World Problem Solving Library:
Math and Science-Healthful Snacks
Math and Science-What Do They Eat?
Math and Science-Double the Number
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Formative Assessments
Journal Writing: Explain the process of adding 0 in a short written
response.
Trenton BOE Approved August 26, 2013-revised June 2014
12
Exit Slips: Problem solving with zero.
Line-Up: Students will demonstrate ways to make 8.
Skill-Based Task: How can you use cubes to show that 12-5 is the
same as 12-7?
Problem-Based Task: Have children work in pairs. The first child
tosses two number cubes and writes an addition fact. The second
child switches the addends and writes the new fact. Repeat the
process.
Questions:
•There are 4 boys and 5 girls on Laticia’s soccer team. There are 5
boys and 4 girls on her brother’s team. Laticia says that she knows
that there is the same number of players on both teams because
she knows that 4+5 and 5+4 are the same amount. Do you agree
with Laticia? Explain. You may use objects or drawings to help you
solve this problem.
•On Monday, 3 girls and 2 boys sat at the round table. 4 boys sat
at the square table. Use objects or drawings to represent this
situation. On Tuesday, only the 3 girls sat at the round table. Two
boys sat with the other 4 boys at the square table. Use objects or
drawings to represent this situation. Regina says that there were
more children seated at the tables on Monday than on Tuesday.
Do you agree? Explain.
1.OA.4
Understand
subtraction as
an unknownaddend problem.
For example,
subtract 10 – 8
by finding the
number that
makes 10 when
added to 8.
Solve subtraction
problems using
unknown addends
(within 20). (6)
Students will model subtraction with different sets of connected
cubes.
Have various items available for exploration such as rulers, pencils,
staplers, and books. Students will model the subtraction process.
Write related addition and subtraction facts on separate sentence
strips. Explain related facts and invite students to write their
related facts on board.
Have students work in small groups to utilize connecting cubes to
investigate how you can subtract to find missing addends.
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson 2.2 (115-120)
Lesson 4.6 (313-318)
Lesson 4.8 (325-330)
K-5 Math Teaching
Resources:
http://www.k5mathteachingresou
rces.com/1st-gradenumberactivities.html
www.quantiles.com
13
Prerequisite
Skills:
My Math Words and
My Vocabulary Cards
K.OA.1
K.OA.2
K.OA.3
K.OA.4
K.OA.5
Foldable: TE
See unit
overview above
for full
description of
standard(s).
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare
students for the lessons.
Real-World Problem Solving Library:
Math and Science-What Do They Eat?
Math and Science-Rock Collections
1.OA.4
Solve subtraction
problems using
unknown addends
(within 20).
5 Activities:
•http://www.readte
nnessee.org/math/t
eachers/k3_commo
n_core_math_stand
ards/first_grade/op
erations_algebraic_t
hinking/1oab4/1oab
4_activity.aspx
Differentiated Instruction: Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
 My Homework SE
Formative Assessments
Think-Pair-Share: Students will use work mats to show a partner
how they would model a problem.
Quick Draw:
Students have 3 minutes to draw an example of related facts.
Interviews:
Students will work in pairs to explain the strategy they used to find
the missing addend in a addition sentence.
Skill -Based Task: Can you subtract 20 -6 by finding the number
that makes 20 when added to 6?
Problem-Based Task: Student starts at 15 and has 7 items left.
How many items does she need to arrive back at 15.
Our class was given 20 cupcakes. 18 children came to school that
day. How many cupcakes are left?
Questions
•Abby is decorating for her birthday party. She has red, yellow,
blue, and green balloons. Each color of balloons is in a separate
Trenton BOE Approved August 26, 2013-revised June 2014
14
bag. She counts 8 red balloons, 3 yellow, 2 blue, and 5 green ones.
Abby knows that she can add these numbers to find out how many
balloons she has altogether. Abby writes: 8 + 3 + 2 + 5 =? Abby
notices that there are two ways that she can make a 10 to make
these numbers easier to add. Task: Show two ways that Abby
could arrange these numbers to make them easier to add. •Isabella
has 17 coins. 8 are pennies and the rest are quarters. How many
quarters does Isabella have? Write a number sentence that
matches this story. Use a symbol for the unknown number. Solve
the problem. Show your thinking with pictures, numbers, or words.
1.OA.5
Relate counting
to addition and
subtraction
(e.g., by
counting on 2 to
add 2).
Prerequisite
Skills:
K.OA.1
K.OA.2
K.OA.3
K.OA.4
K.OA.5
See unit
overview above
for full
description of
standard(s).
Count forwards or
backwards from
any number within
20 to solve
addition or
subtraction
problems. (2)
Students will model counting on to find the sum. Students will
be given counting cubes and other manipulatives to explore
counting on and different number combinations.
Discuss how a number line is helpful when you are subtracting. Use
a number line and connecting cubes to model counting back.
Create a class Venn diagram that compares and contrasts using a
number line to add and subtract.
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare
students for the lessons.
Real-World Problem Solving Library:
Math and Science-Double the Number
Math and Science-Rock Collections
Differentiated Instruction: Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson
Lesson
Lesson
Lesson
Lesson
3.1
3.2
3.3
4.1
4.2
(211-216)
(217-222)
(223-228)
(281-286)
(287-292)
4 Possible
Activities
http://www.k5mathteachingresou
rces.com/1st-gradenumberactivities.html
Games & Activities
http://www.louisiana
believes.com/docs/d
efaultsource/teachertoolboxresources/2014math-k-2curriculumguidebook.pdf?sfvrs
n=4
6 Games/ Activities
http://www.internet
4classrooms.com/co
mmon_core/relate_c
ounting_addition_su
btraction_counting_
on_operations_algeb
raic_thinking_first_1
st_grade_math_mat
hematics.htm
15
Formative Assessments
Virtual
Manipulatives:
http://www.connect
ED.mcgraw-hill.com
Think-Pair-Share:
Group students in pairs, have them think about how to use cubes
to count on. They think about it first, then share with a partner,
then share with the class.
K-5 Math Teaching
Resources:
http://www.k5mathteachingresou
rces.com/1st-gradenumberactivities.html
Exit Slips:
Students roll a number cube to write how many pennies they would
have if they were given three more.
Write and solve age related (two years ago) number sentences.
Thumb It: Students will choose a number and utilize the number
line to add on 3. When sharing answers, thumbs up or thumbs
down to show approval.
www.quantiles.com
Response Cards: Students will utilize a flash card with an addition
fact using adding on to write the sum.
Skill -Based Task:
Given 16+2, can you show two more ways to show 18 using the
Associative property of addition?)
Problem-Based Task: Knowing that 8+6=14 and 14-6=8, use this
relationship between addition and subtraction for 7+6.
•Questions:
1. Write each number that matches the clue. 1 more than
37______, 1 less than 80 ____, 2 more than 49 ____, 2 less than
95 ____.
2. Provide the child with two dot dice. Roll the dot dice and count
all to obtain the total value of the two dice.
(For benchmark 1 the total number used should be less than or
equal to 12.)
Have students write the symbol =. Discuss that this symbol shows
that the two sides of the sentence are equal to each other. Remind
them to say equals when they see the symbol in a math problem.
Add or subtract
1.OA.6
Add and subtract whole numbers
within 20 using
within 20,
strategies
demonstrating
including making a Students will work in pairs to make connecting cube trains and
fluency for
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson
Lesson
Lesson
Lesson
Lesson
1.5 (37-42)
1.7 (49-54)
1.8 (55-60)
1.9 (61-66)
1.10 (69-74)
Virtual
Manipulatives:
http://www.connect
ED.mcgraw-hill.com
16
addition and
subtraction
within 10. Use
strategies such
as counting on;
making ten
(e.g., 8 + 6 = 8
+ 2 + 4 = 10 +
4 = 14);
decomposing a
number leading
to a ten (e.g., 13
– 4 = 13 – 3 – 1
= 10 – 1 = 9);
using the
relationship
between
addition and
subtraction
(e.g., knowing
that 8 + 4 = 12,
one knows 12 –
8 = 4); and
creating
equivalent but
easier or known
sums (e.g.,
adding 6 + 7 by
creating the
known
equivalent 6 + 6
+ 1 = 12 + 1 =
13).
Prerequisite
Skills:
K.OA.1
K.OA.2
K.OA.3
K.OA.4
K.OA.5
10 or
decomposing a
number leading to
a 20. (4)
write addition and subtraction number sentences. They will
manipulate them vertically and horizontally to explore how you can
write a number sentence in a different way.
They will explore various ways to make 4, 5, 6, 7, 8, 9 and 10
using assorted two-color counters and other manipulatives. They
will practice subtracting from 4, 5, 6, 7, 8, 9, and 10.
Students will define new vocabulary: related facts and identify the
similarities between addition and subtraction number sentences.
Have students model the doubles facts using connecting cubes and
writing the corresponding addition number sentence.
Problem Solving:
Purposely present an incorrect answer and ask students to find the
error.
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare
students for the lessons.
Real-World Problem Solving Library:
Math and Science-Healthful Snacks
Math and Science-What Do They Eat?
Math and Science-Double the Number
Math and Science-Rock Collections
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
1.11 (75-80)
2.5 (133-138)
2.8 (153-158)
2.9 (159-164)
2.10 (167-172)
2.11 (173-178)
2.12 (179-184)
2.13 (185-190)
3.4 (229-234)
3.5 (235-240)
3.7 (249-254)
4.3 (293-298)
4.5 (307-312)
4.7 (319-324)
K-5 Math Teaching
Resources:
http://www.k5mathteachingresou
rces.com/1st-gradenumberactivities.html
www.quantiles.com
18 Activities &
Centers
http://www.readten
nessee.org/math/tea
chers/k3_common_c
ore_math_standards
/first_grade/operatio
ns_algebraic_thinkin
g/1oac6/1oac6_activ
ity.aspx
22 Games and
Activities
http://www.internet
4classrooms.com/co
mmon_core/add_su
btract_within_20_de
monstrating_fluency
_operations_algebrai
c_thinking_first_1st_
grade_math_mathe
matics.htm
Differentiated Instruction: Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Formative Assessments:
See unit
Trenton BOE Approved August 26, 2013-revised June 2014
17
overview above
for full
description of
standard(s).
Exit Slips:
Students will write and solve addition problems both horizontally
and vertically.
Students will write two ways of making a sum of 5.
Quick Draw:
Have students draw pictures to represent all of the ways to make 6
on one side of the paper. Then have them draw all of the ways to
make 7 on the other side.
Response Cards:
Students will write two number sentences that have a sum of 8.
Skill-Based Task:
For which sum of 20 can the addends not be switched? (10
+10=20)
Problem-Based Task: Using 13 red counters and 5 yellow counters,
have students fill two ten-frames. Do the counters fill the tenframes? Are there too many or too few counters?
•Three cats are drinking milk. Some more cats come to drink
milk. Then there were nine cats drinking milk. How many
cats came to drink milk with the first three? Write a number
sentence that matches this story. Use a symbol for the
unknown number. Solve the problem. Show your thinking
with pictures, numbers, or words.
•http://www.doe.k12.de.us/assessment/files/Math_Grade_1.
pdf
•http://ccssmath.org/?page_id=179
Count utilizing
Students will count forward to 120 by counting on from any
1. NBT.1
written or verbal
number less than 100.
Count to 120,
numerals starting
starting at any
at any number
Utilize counting strategies to enhance understanding of how the
number less
numbers in the counting sequence are related—each number is one
than 120. In this less than 100. (1)
more (or one less) than the number before (or after). Students also
range, read and
read and write numerals to represent a given amount.
write numerals
and represent a
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson
364)
Lesson
402)
Lesson
422)
Lesson
428)
5.3 (3595.9 (3975.12 (4175.13 (423-
Virtual
Manipulatives:
http://www.connect
ED.mcgraw-hill.com
K-5 Math Teaching
Resources:
18
number of
objects with a
written numeral.
Prerequisite
Skills:
K.NBT.1
See unit
overview above
for full
description of
standard(s).
Display a set of manipulative coins (pennies and dimes) and explain
that using one dime would equal ten pennies. Explain that counting
dimes is like counting by tens. Students will count by fives using
nickels.
 Students will practice counting back by 1s by singing the song
“One Hundred Twenty Cartons of Juice on the Wall”.
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare
students for the lessons.
Real-World Problem Solving Library:
Math and Science-Look Again
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Formative Assessments:
Quick Draw: Students will be asked to draw their answer to a
specified problem within a 3-5 minute timeframe.
Response Cards: Students will use manipulative coins to count by
fives.
Ask students to write the missing numbers in a sequence up to
120.
Example/Non-Example: Students will be asked to model one
example and one non-example of a specified number with base ten
blocks.
Lesson 5.14 (429434)
http://www.k5mathteachingresou
rces.com/1st-gradenumberactivities.html
www.quantiles.com
•Book: From One to
One Hundred
Author: Teri Sloat
•Concentration
Game:
https://www.illustrat
ivemathematics.org/i
llustrations/405
•Teacher creates a
spinner with
numbers less than
100. The student
spins the spinner,
write down that
number, and write
next 6 numbers to
follow
Counting to 100
Game:
http://www.learnwith-mathgames.com/counting
-to-100.html
•Missing number
worksheet:
http://firstgradecom
moncore.weebly.co
m/uploads/1/6/8/9/1
6891474/train_50__worksheet_1.pdf
•Show clear jars
Trenton BOE Approved August 26, 2013-revised June 2014
19
Modeling: Ask students to use base-ten blocks to show a number
that has a specified hundreds, tens, and ones.
with different
amount of objects
(i.e. a jar of linking
cubes, jelly beans,
paper clips, etc).
Have students
identify which jars
they think have the
most objects. Have
students share their
reasoning. Have
groups/partners
count the objects in
each jar, write the
number, and write
the amount on a
sticky note that can
be placed on a
number line. Have
the class share their
findings.
Think-Pair-Share:
Askt students to think about the difference between certain
numbers and turn to a partner to name the differences.
Skill-Based Task:
Can you find the missing numbers (23, 24,__,__, 27, __)
Problem-Based Task: Have students fill in the missing numbers on
the hundred chart.
•Fill in the blanks. Count on from 26.
26, ____, ____, ____, ____, ____, ____
•Read the problem to the student: Mrs. Scrinzi is counting students
as they enter the classroom. She has just counted the 8th student.
What numbers will Mrs. Scrinzi say for the next 5 students?
8, __, ___, ___, ___, ___.
Compose and
Students will actively be introduced to the idea that a bundle of ten
1.NBT.2
decompose
ones is called “a ten”. (unitizing) Students will unitize a group of
Understand that
numbers
to
20
to
ten ones as a whole unit (“a ten”), then they are able to count
the two digits of
identify
the
value
groups as though they were individual objects.
a two-digit
of
the
number
in
number
the tens and ones
Example: 4 trains of ten cubes each have a value of 10. They
represent
place.
(3)
would be counted as 40 rather than as 4.
amounts of tens
and ones.
Note:
Understand the
This can often be challenging for young students to consider a
following as
group of something as “one” when all previous experiences have
special cases:
been counting single objects.
a. 10 can be
(This is the foundation of the place value system.)
thought of as a
bundle of ten
This will require time and numerous rich experiences with concrete
ones — called a
“ten.”
b.The numbers
from 11 to 19
are composed of
manipulatives to develop.
a ten and one,
two, three, four,
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
5.1
5.2
5.4
5.5
5.6
5.7
(347-352)
(353-358)
(365-370)
(371-376)
(379-384)
(385-390)
Virtual
Manipulatives:
http://www.connect
ED.mcgraw-hill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingresou
rces.com/1st-gradenumberactivities.html
www.quantiles.com
13 Activities &
Centers
http://www.readten
nessee.org/math/tea
20
five, six, seven,
eight, or nine
ones.
c.The numbers
10, 20, 30, 40,
50, 60, 70, 80,
90 refer to one,
two, three, four,
five, six, seven,
eight, or nine
tens (and 0
ones).
Show fourteen by writing the number as 10 and some left over (14
is 10 and 4).
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare
students for the lessons.
Real-World Problem Solving Library:
Math and Science-Look Again
Prerequisite
Skills:
K.NBT.1
See unit
overview above
for full
description of
standard(s).
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
 My Homework SE
chers/k3_common_c
ore_math_standards
/first_grade/number
_operations_in_base
_ten/1nbtb2/1nbtb2
_activity.aspx
10 Activities
http://www.k5mathteachingresou
rces.com/1st-gradenumberactivities.html
Lesson and activities
http://www.oakland.
edu/upload/docs/SE
HS/ERL/GLCEs/1.NB
T.2.abc_hickey.pdf
Formative Assessments:
Exit Slip: Ask students to write how many…10 and 6 more, etc.
Example/Non-Examples: Have students draw one example on the
front side of their paper to match the description on the board and
one non-example on the back side.
Give each student pair a pile of connecting cubes and ask them to
model one example of a certain number as tens and ones. Ask
them to model one non-example.
Response Cards:
Provide students with a handful of bears, buttons, counters, or
other small classroom object. Ask students to record how manytens
and ones they have of each object.
Skill-Based Task:
Can you write sixteen using two ten frames and showing the
number as 10 (one full ten frame), and 6 in the second ten frame?
Trenton BOE Approved August 26, 2013-revised June 2014
21
(Sixteen is 10 and 6).
Question
•Place 19 cubes on the table in a scattered arrangement. Say: I
have a pile cubes. How many do you think there are? Count and
see After the student counts, ask: “How many cubes are in the
pile? Say: Write that number on this piece of paper. Then, circle
the digit in the ones place (9). Say: Show me with your cubes this
amount. After the student shows the cubes, point to the digit in the
tens place (1) and say:
Stage 2 – Assessment Evidence
Other Evidence:
 Classwork
 Exit slips
 Homework
 Individual and group tests
 Open-ended questions
 Portfolio
 Quizzes
Suggested Performance Tasks:
 Exemplars
 Extended projects
 Math Webquests
 Writing in Math/Journal
Stage 3 – Learning Plan
Lesson Plan Template
Suggested Pacing for Required 80 Minute Math Block
Lesson
Objective
Using 3-part
objective in
student-friendly
language
For example,
“I will solve 10
addition word
problems with
Opening/Do Now
Homework Review
(10-15 minutes)
(5-10 minutes)
Do Now may include:
 spiral review of
prerequisite skills for
day’s lesson
 pretest to assess skills
and to see where
students are regarding
today’s objective
 a writing in math type
May choose to review a
few specific problems
from previous nights’
homework to assess for
understanding.
Students may also selfassess by identifying
specific problems or
Trenton BOE Approved August 26, 2013-revised June 2014
Instructional Components
Mini Lesson
I DO/ WE DO
(15-20 minutes)
Whole group minilesson with a
built-in check for
understanding
upon completion.
Independent/Partner/Group
Work YOU DO
(20-30 minutes)
Lesson activity including at least
one check for understanding.
Math centers should be
implemented during this time.
Suggestions:
 Technology
 Problem-based/Skill-based
Task
Summary and
Exit Slip
(10 minutes)
As a class, teacher should
facilitate a summary of
the day’s targeted
objective then provide an
exit question (last check
for understanding) that
allows students to
individually prove their
understanding of the
22
80% accuracy.”
of prompt/question for
students to
explain/expand upon
their thinking



areas that they had
difficulty with and
topics in which they
may require additional
support.
Vocabulary Work
Writing in Math
Art/Music Connections
objective. √
UNIT NAME: Word problems Involving Addition and Subtraction
Grade level:
1
District-Approved Text: My Math, McGraw-Hill
Unit 2:
Stage 1 – Desired Results
Enduring Understandings/Goals:
 I can add and subtract up to 20 to solve problems by using objects, drawings, and equations.
 I can use commutative and associative properties as a strategy to add or subtract.
 Subtraction is an unknown addend.
 Counting is related to addition and subtraction.
 I can determine unknown numbers by using equations with equal signs.
Essential Questions:
 How do you add numbers?
 How do you subtract numbers?
 How do I use strategies to add numbers?
 What strategies can I use to subtract?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
Trenton BOE Approved August 26, 2013-revised June 2014
23
8.
Look for and express regularity in repeated reasoning.
Standard:
1.OA.1
Use addition
and
subtraction
within 20 to
solve word
problems
involving
situations of
adding to,
taking from,
putting
together,
taking apart,
and
comparing,
with
unknowns in
all positions;
e.g. by using
objects,
drawings,
and
equations
with a
symbol for
the unknown
number to
represent the
problem.
Prerequisite
Skills:
K.OA.1
K.OA.2
K.OA.5
Student
Learning
Objectives
Use addition and
subtraction
within 20 to
solve word
problems
involving
situations or
adding to, taking
from, putting
together, taking
apart, and
comparing with
unknowns in all
positions. (1)
Assessment/ Evidence
My Math Resources
Explore numbers to 20 to solve comparison problems. (Two amounts are
compared to find “How many more” or “How many less”.)
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Students will read and use equations to represent their thinking. They
should have need extensive experiences with
addition and subtraction situations in order to connect the experiences
with symbols (+, -, =) and equations (5 = 3+ 2).
My Math Words and
My Vocabulary Cards
Foldable: TE
1.1 (11-16)
1.2 (17-22)
1.3 (23-28)
1.6 (43-48)
2.1 (109-114)
2.2 (115-120)
2.3 (121-126)
2.6(141-146)
2.7 (147-152)
3.6 (243-248)
3.8 (255-260)
4.4 (299-304)
Other Resources
Virtual Manipulatives:
http://www.connectE
D.mcgraw-hill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingresour
ces.com/1st-gradenumberactivities.html
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare
students for the lessons.
www.illuminations.nct
m.org
www.quantiles.com
Real-World Problem Solving Library:
Math and Science-Healthful Snacks
Math and Science-What Do They Eat?
Math and Science-Double the Number
Math and Science-Rock Collections
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Example: Have five students stand in front of the class. Show a variety of
item such as 3 pencils, 7 erasers, and 4 books. Ask the students how
many more or fewer items are needed if giving each student one.
Formative Assessments:
Exit Slip: Tell students an addition number story that relates to their daily
Trenton BOE Approved August 26, 2013-revised June 2014
24
classroom experience. How many…?
Have students write a number sentence to match the problem.
See unit
overview
above for full
description of
standard(s).
Response Cards: Tell the addition story…how did you solve the problem?
Describe a take away situation in your classroom...how many?
Quick Draw: Have students draw pictures to represent and explain the
meaning of the vocabulary words add, parts, and whole.
Think-Pair-Share: Students answer questions on their own, then tell their
answer to a partner, and then share with the class.
Students use a work mat to show their partner how they would model a
problem.
Journal Writing: Write a journal response to explain how to write a
subtraction number sentence.
Skill-Based Task:
Using dominos, can you show different ways to make 12?
Problem-Based Task:
Form two large squares with tape on the floor. Ask ten students to walk
around the large squares. Play then stop music and have children jump
into a square. Record the number of students in each square. Repeat
showing different combinations for ten.
1.OA.2
Solve word
problems that
call for
addition of
three whole
numbers
whose sum is
less than or
equal to 20.
E.g. by using
objects,
drawings,
and
Solve addition
word problems
with three whole
numbers with
sums less than
or equal to 20.
(2)
Students will solve multi-step word problems by adding and subtracting,
using a variety of mathematical representations.
Example: Mrs. Smith has 4 oatmeal raisin cookies, 5 chocolate chip
cookies, and 6 gingerbread cookies. How many
cookies does Mrs. Smith have?
I wrote:
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson 3.9 (261-266)
Virtual Manipulatives:
http://www.connectE
D.mcgraw-hill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingresour
ces.com/1st-gradenumberactivities.html
www.illuminations.nct
25
equations
with a
symbol for
the unknown
number to
represent the
problem.
Prerequisite
Skills:
K.OA.1
K.OA.2
K.OA.5
See unit
overview
above for full
description of
standard(s).
m.org
I know that 4 and 6 equals 10, so the oatmeal raisin and gingerbread
equals 10 cookies. Then I added the 5 chocolate chip cookies. 10 and 5 is
15. So, Mrs. Smith has 15 cookies.
www.quantiles.com
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare
students for the lessons.
Real-World Problem Solving Library:
Math and ScienceDouble the Number
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Example: Draw a graphic organizer with 19 in the center. Display two
numbers on each branch. Students must find the missing number to add
up to 19 (ep. 6+4+__ as one branch, etc.).
Formative Assessments:
Response Cards: Have students solve for the sum of three addends.
Think-Pair-Share: Group students in pairs and ask them questions about
the sum and the strategy they used to find the sum. Invite pairs to
present their thinking and explanations to the class.
Skill-Based Task:
Can you use counters to solve problems with three addends with sums no
greater than 20?
Problem-Based Task:
Trenton BOE Approved August 26, 2013-revised June 2014
26
Write numbers 1-5 on three sets of ping pong balls. Put the balls in a bag
and have each student take three. Students then arrange balls into the
order in which they will add the numbers. Next have students switch the
same balls around and add again.
1.OA.7
Understand
the meaning
of the equal
sign, and
determine if
equations
involving
addition and
subtraction
are true or
false. For
example,
which of the
following
equations are
true and
which are
false? 6 = 6,
7 = 8-1, 5+2
= 2+5, 4+1
= 5+2.
Demonstrate
understanding of
the equal sign
by determining if
an equation is
true or false. (3)
Students will develop their understanding of the equal sign by solving
numerous problems with mathematical tools, rather than symbols.
An equation needs to “balance”, with equal quantities on both sides of the
equal sign.
Examples:
• an operation on the left side of the equal sign and the answer on the
right side
(5 + 8 = 13)
• an operation on the right side of the equal sign and the answer on the
left side
(13 = 5 + 8)
• numbers on both sides of the equal sign (6 = 6)
Lesson 1.13 (87-92)
Lesson 2.14 (191-196)
Virtual Manipulatives:
http://www.connectE
D.mcgraw-hill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingresour
ces.com/1st-gradenumberactivities.html
www.illuminations.nct
m.org
www.quantiles.com
• operations on both sides of the equal sign (5 + 2 = 4 + 3).
My Math Words and
My Vocabulary Cards
Foldable: TE
Prerequisite
Skills:
Model the Math: using assorted manipulatives and materials TE
K.OA.3
K.OA.5
Literature Connection: Specified trade titles can be read to prepare
students for the lessons.
See unit
overview
above for full
description of
standard(s).
Real-World Problem Solving Library:
Math and Science-Healthful Snacks
Math and Science-What Do They Eat?
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Trenton BOE Approved August 26, 2013-revised June 2014
27
Wrap It Up
My Homework SE
Example: Having students use bingo chips, ask them to show different
number sentences that equal 11. Emphasize how these number sentences
are equivalent.




Formative Assessments:
Response Cards: Write several statements on the board and have students
show the appropriate side of their card; true or false.
Have students identify whether given statements are true or false.
Exit Slips: Students twill answer whether a statement is true or false.
Skill-Based Task:
Can you show three different ways to get to fifteen using counters?
Problem-Based Task:
Using two colors of teddy bear counters, partners will work together to
reach sums less than twenty.
1.OA.8
Determine
the unknown
whole
number in an
addition or
subtraction
equation
relating to
Solve addition or
subtraction
equations by
finding the
missing whole
number in any
position. (4)
Students will use their understanding of addition and subtraction to solve
equations with an unknown (boxes or pictures).
Example: Determine the unknown number that makes the equation true.
5-
=2
5 minus something is the same amount as 2. Hmmm. 2 and what makes
5? 3! So, 5 minus 3 equals 2. Now it’s true!
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson 1.12 (81-86)
Lesson 4.6 (313-318)
Lesson 4.8 (325-330)
Virtual Manipulatives:
http://www.connectE
D.mcgraw-hill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingresour
28
three whole
numbers. For
example,
determine
the unknown
number that
makes the
equation true
in each of the
equations 8
+? = 11, 5
= □ -3, 6 + 6
= □.
Prerequisite
Skills:
K.OA.3
K.OA.5
See unit
overview
above for full
description of
standard(s).
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
ces.com/1st-gradenumberactivities.html
www.illuminations.nct
m.org
www.quantiles.com
Literature Connection: Specified trade titles can be read to prepare
students for the lessons.
Real-World Problem Solving Library:
Math and Science-Healthful Snacks
Math and Science-Rock Collections
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Example:
Using number cards, make number sentences with missing sums such as
(6+3=__). Students can also make sentences with missing addends such
as 7+__=15.
Formative Assessments:
Exit Slip: Have students utilize work mats to solve for the missing part of
10.
Modeling: Using a work mat and counters, present students with a
scenario to model.
Quick Draw: Allow students 3 minutes to draw an example of related
facts.
Self-Assessment: Ask students how they can check the answer to a
subtraction fact. Have them use counters to explain their thinking.
Interviews: Invite students to work in pairs, with one being the interviewer
and the other being the interviewee. Have students explain the strategy
Trenton BOE Approved August 26, 2013-revised June 2014
29
they used to find the missing addend in an addition sentence.
Response Cards: Have students identify the missing addend in a number
sentence. Extend the activity by asking students to write the remaining
facts in the fact family.
Skill-Based Task:
Given several dominoes, can you write an addition sentence for each one?
Problem-Based Task:
Show students between ten and twenty counters. Then have them close
their eyes and cover some of the counters with your hand. How many are
left? How many are covered up? Then write a number sentence to
represent the action.
1.NBT.1
Count to 120,
starting at
any number
less than
120. In this
range, read
and write
numerals and
represent a
number of
objects with
a written
numeral.
Prerequisite
Skills:
K.NBT.1
See unit
overview
above for full
description of
standard(s).
Count to 120,
starting at any
number less
than 120. (5)
Read and write
numerals to 120
including
representing a
number of
objects with a
written numeral.
(6)
Students will count forward to 120 by counting on from any number less
than 120.
Students will read and write numerals to represent a given amount in
order to develop accurate counting strategies that build on the
understanding of how the numbers in the counting sequence
are related.
Example: Have children count from one to one hundred on a number chart
pointing to each number as they say it. Next have them start at thirty-four
and have them count to sixty-four. Repeat for other intervals.
Formative Assessment:
Quick Draw: Allow students 3-5 minutes to draw their answer to a related
question.
Lesson 5.3 (359364)
Lesson 5.9
(397-402)
Lesson 5.12 (417422) Lesson 5.13
(423-428) Lesson
5.14 (429-434)

Virtual Manipulatives:
http://www.connectE
D.mcgraw-hill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingresour
ces.com/1st-gradenumberactivities.html
www.illuminations.nct
m.org
www.quantiles.com
Line Up: Invite students to skip-count by tens to 100 chorally as a class.
Challenge all students to be lined up by the time 100 is reached.
Call on students to use a number chart to count from 86 to 117. As
Trenton BOE Approved August 26, 2013-revised June 2014
30
students take turns, allow them to line up.
Response Cards: Have students place 9 manipulative nickels in a row on
their desks. Ask students to count the nickels by fives to find out how
many there are in all.
Ask students to write the missing numbers on a half sheet of scrap paper.
Example/Non-Example: Write 117 on the board and ask students to model
one example and one non-example of 117 with base-ten blocks.
Self-Assessment: Have students line up the cards in order than remove 2
cards. Have each student pair join another to find the missing numbers.
Skill-Based Task: Can you fill in the missing the missing numbers on the
hundred chart?
Problem-Based Task:
Ask children to write the sequence of numbers from 65-88 in their math
journal.
Stage 2 – Assessment Evidence
Other Evidence:
 Classwork
 Exit slips
 Homework
 Individual and group tests
 Open-ended questions
 Portfolio
 Quizzes
Suggested Performance Tasks:
 Exemplars
 Extended projects
 Math Webquests
 Writing in Math/Journal
Stage 3 – Learning Plan
Lesson Plan Template
Suggested Pacing for Required 80 Minute Math Block
Lesson
Objective
Opening/Do Now
(10-15 minutes)
Homework
Review
Trenton BOE Approved August 26, 2013-revised June 2014
Instructional Components
Mini Lesson
I DO/ WE DO
Independent/Partner/Group
Work
Summary and
Exit Slip
31
(5-10 minutes)
Using 3-part
objective in
student-friendly
language
For example,
“I will solve 10
addition word
problems with
80% accuracy.”
Do Now may
include:
 spiral review of
prerequisite
skills for day’s
lesson
 pretest to
assess skills and
to see where
students are
regarding
today’s objective
 a writing in
math type of
prompt/question
for students to
explain/expand
upon their
thinking
May choose to
review a few
specific problems
from previous
nights’
homework to
assess for
understanding.
Students may
also self-assess
by identifying
specific problems
or areas that
they had
difficulty with
and topics in
which they may
require
additional
support.
Trenton BOE Approved August 26, 2013-revised June 2014
(15-20 minutes)
Whole group mini-lesson
with a built-in check for
understanding upon
completion. √
YOU DO
(20-30 minutes)
Lesson activity including at least
one check for understanding. √
Math centers should be
implemented during this time.
Suggestions:
 Technology
 Problem-based/Skillbased Task
 Vocabulary Work
 Writing in Math
 Art/Music Connections
(10 minutes)
As a class, teacher
should facilitate a
summary of the
day’s targeted
objective then
provide an exit
question (last check
for understanding)
that allows students
to individually prove
their understanding
of the objective. √
32
UNIT NAME: Understand Place Value
Grade level:
1
District-Approved Text: My Math, McGraw-Hill
Unit 3:
Stage 1 – Desired Results
Enduring Understandings/Goals:
 Understanding place value can lead to number sense and efficient strategies for computing with numbers.
Essential Questions:
 How does a digit’s position affect its value?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Standard:
1.NBT.2c
Understand
that the two
digits of a
two-digit
number
represent
amounts of
tens and
ones.
Understand
the following
as special
cases: the
Student
Learning
Objectives
Decompose
two-digit
numbers as
the sum of
tens and
ones for
numbers less
than 100. (1)
Assessment/ Evidence
Students will work with objects that can be grouped, while focusing on a
specific amount of groups of tens with none left-over.
5 tens =50
7 tens = 70
They will practice the counting and writing the decade numbers.
10, 20, 30, 40, 50, 60, 70…
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Trenton BOE Approved August 26, 2013-revised June 2014
My Math
Resources
Lesson 5.2 (353358)
Lesson 5.4 (365370)
Lesson 5.6 (379384)
Lesson 5.7 (385390)
Other Resources
Virtual
Manipulatives:
http://www.connec
tED.mcgrawhill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingreso
urces.com/1stgrade-number-
33
numbers 10,
20, 30, 40,
50, 60, 70,
80, 90 refer
to one, two,
three, four,
five, six,
seven, eight,
or nine tens
(and 0 ones).
Literature Connection: Specified trade titles can be read to prepare students
for the lessons.
Real-World Problem Solving Library:
Math and Science-Look Again
www.illuminations.
nctm.org
www.quantiles.com
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Prerequisite
Skills:
Wrap It Up
My Homework SE
K.NBT.1
Examples: Students need beans, cups, place value mats and a die. Students
take turns rolling the die and adding that amount of beans to a place value
mat. Each time a ten is made, the beans are transferred to a cup and moved
to the tens place. Play alternates until one student passes one hundred and
wins the game.
See unit
overview
above for full
description of
standard(s).
activities.html
Using number cards 10-99 and snap cubes and a place value mat, model how
to represent a 2-digit number.
Formative Assessments:
Line Up: Ask one student to name a number that ends in a zero and then line
up. Students will count by tens from that number up to 100.
Example/Non-Example: Invite students to work in pairs to use connecting
cubes to model one example of 34 as tens and some more. Also ask them to
model one non-example.
Debriefing: Invite students to reflect on the various strategies they can use
when solving word problems.
Modeling: Invite students to model numbers using base-ten blocks.
Skill-Based Task: Using base-10 blocks, 47. Tell the number of tens and ones
in the number.
Problem-Based Task: Maya has three number cards.
Trenton BOE Approved August 26, 2013-revised June 2014
2
7
4
34
What is the largest 2-digit number Maya can make using these cards?
Using base 10 blocks, show the number Maya made. Then tell the total
number of tens and ones in Maya’s number.
1.NBT.3
Compare two
two-digit
numbers
based on
meanings of
the tens and
ones digits,
recording the
results of
comparisons
with the
symbols >,
=, and <.
Compare two
digit numbers
using <, >,
and =
symbols. (2)
Students will use their understanding of groups and order of digits to
compare two numbers by examining the amount of tens and ones in each
number. They will connect the vocabulary to the symbols: greater than (>),
less than (<), and equal to (=).
Example: Compare these two numbers. 42 __ 45
42 has 4 tens and 2 ones. 45 has 4 tens and 5 ones. They have the same
number of tens, but 45 has more ones than 42. So, 42 is less than 45. 42 <
45
42 is less than 45. I know this because when I count up I say 42 before I say
45.
42 < 45
This says 42 is less than 45.
My Math Words and
My Vocabulary Cards
Lesson 5.10 (403408
Lesson 5.11 (409414)
Virtual
Manipulatives:
http://www.connec
tED.mcgrawhill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingreso
urces.com/1stgrade-numberactivities.html
www.illuminations.
nctm.org
www.quantiles.com
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare students
for the lessons.
Real-World Problem Solving Library:
Math and Science-Look Again
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Trenton BOE Approved August 26, 2013-revised June 2014
35
Wrap It Up
My Homework SE
Examples: Students will work in partners. Partner one will make a two-digit
number with snap cubes. Partner two will draw a symbol card with >, <, =
and then make a number that is >, <, = to partner one’s number.
Display a number card on the board. Using dry erase student boards, each
student will write a number that is <, >, or = to depending on instructions.
Students will then explain reasoning to each other.
Formative Assessments:
Line Up: Have boys line up in one line and girls in another. Ask students to
compare the number of boys to girls. Then have students form lines on
different characteristics such as shirt colors or birth months. Ask students to
compare the lines.
Modeling: Challenge students to create models with base-ten blocks to
determine which number is greater.
3-2-1 Strategy Form: Ask students what they learned today about comparing
numbers. Have them share with a partner 3 things that they learned, 2 things
that they want to know more about, and 1 question they have.
Exit Slip: Give each student a number between 1 and 99 and ask them to
write a number on a sticky note that is either greater than, less than, or
equal to that given number.
Skill-Based Task: Students will explain how they know a number is more, less
or equal to another given numbers in all forms including pictures, numbers
and words.
Problem-Based Task: On their birthday, the twins, Meg and Troy broke their
piñata. Meg had 64 pieces of candy and Troy had 59. Who has less candy?
Explain how you know this.
1.NBT.4
Add within
100, including
Add 2-digit
and 1-digit
numbers, and
Students will use concrete materials, models, drawings and place value
strategies to add within 100. They will also practice with numbers as they use
the base-ten system to solve problems.
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson 6.1 (447452)
Lesson 6.2 (453-
Virtual
36
adding a twodigit and a
one-digit
number, and
adding a twodigit number
and a
multiple of
10, using
concrete
models, or
drawings and
strategies
based on
place value,
properties of
operations
and/or the
relationship
between
addition and
subtraction;
relate the
strategy to a
written
method and
explain the
reasoning
used.
Understand
that in adding
two-digit
numbers, one
adds tens and
tens, ones
and ones;
and
sometimes it
is necessary
to compose a
ten.
Prerequisite
add 2-digit
numbers and
a multiple of
10, using
concrete
models or
drawings,
including
decomposing
2-digit
numbers
and/or
composing
an additional
ten (within
50); e.g., 18
+ 20 equals
10 + 8 + 20
equals 30 +
8 equals 38;
and, 37 + 5
equals 30 +
7 + 5 equals
30 + 12
equals 30 +
10 + 2
equals 40 +
2 equals 42.
(3)
Example: 63 apples are in the basket. Mary put 20 more apples in the basket.
How many apples are in the basket?
63 + 10 = 73
73 + 10 = 83
458)
Lesson 6.3 (459464)
Lesson 6.4 (465470)
Lesson 6.5 (471476)
Manipulatives:
http://www.connec
tED.mcgrawhill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingreso
urces.com/1stgrade-numberactivities.html
www.illuminations.
nctm.org
www.quantiles.com
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare students
for the lessons.
Real-World Problem Solving Library:
Math and Science-Look Again
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Trenton BOE Approved August 26, 2013-revised June 2014
37
Skills:
K.NBT.1
Wrap It Up
My Homework SE
See unit
overview
above for full
description of
standard(s).
Examples: Students will pick two cards that each have a two digit number on
them. Provide numbers on the cards that don’t require regrouping. Students
will draw one card, represent it with base-10 blocks, draw a second card,
represent it and finally combine the base-10 blocks to identify the sum.
Students write a number between 1 and 9 and show it with base-10 blocks.
Each student rolls a number cube and adds that many tens to the original
number. Students then write the new number on their recording sheet and
roll again until they pass 100. Students then begin again with a new number.
Formative Assessments:
Response Cards: Students will write the sums for given problems.
Tell students an addition story. Have them use the guess, check, and revise
strategy to solve the problem.
Journal Writing: Invite students to construct a short written response
explaining what they learned about adding tens, including a diagram.
Invite students to construct a short written response that describes how to
use the guess, check, and revise strategy to solve math word problems.
Quick Draw: Invite students to draw a picture of tens rods and unit cubes to
show how to as 56 + 30 using manipulatives.
Line Up: Present quick problems that involve counting on by tens or ones.
Each group rolls a 0-5 number cube and add the number rolled to the
number on their card. As groups answer correctly, have them line up.
Interviews: Ask students to describe the steps they learned in how to add
tens and ones, while modeling with base-ten blocks.
Example/Non-Example: Invite students to model one example of a two-digit
plus a one-digit number that involves regrouping.
Skill-Based Task: Add these two-digit numbers.
36
+40
Trenton BOE Approved August 26, 2013-revised June 2014
38
Problem-Based Task:
In Joel’s seashell collection he counted twenty-two seashells. His father came
home from a vacation and gave him four seashells and a bag filled with
thirty. How can Joel figure out how many seashells are in his collection now?
1.NBT.5
Given a twodigit number,
mentally find
10 more or
10 less than
the number
without
having to
count;
explain the
reasoning
used.
Mentally find
ten more or
ten less than
a number
without
having to
count and
explain the
reasoning
used. (4)
Students mentally add ten more and ten less than any number less than 100.
Students should be given various experiences with ten frames and the
number line to practice problem solving strategies mentally.
Example: There are 74 birds in the park. 10 birds fly away. How many birds
are in the park now?
I thought about a number line. I started at 74. Then, because 10 birds flew
away, I took a leap of 10. I landed on 64. So, there are 64 birds left in the
park.
Prerequisite
Skills:
K.NBT.1
See unit
overview
above for full
description of
standard(s).
Lesson 5.8 (391396)
Virtual
Manipulatives:
http://www.connec
tED.mcgrawhill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingreso
urces.com/1stgrade-numberactivities.html
www.illuminations.
nctm.org
www.quantiles.com
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare students
for the lessons.
Real-World Problem Solving Library:
Math and Science-Look Again
Trenton BOE Approved August 26, 2013-revised June 2014
39
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Examples: Draw pictures to show 10 more/less.
Provide the students with clue cards for the game Who is/I am. The first
student reads the clue and the student who has the answer reads their clue
next.
Student 1: Who is 10 more than 40?
Student 2: Who is 10 less than 10?
Formative Assessment:
Hand Signals: Invite students to work in pairs. One student in each pair will
choose a number between 20 and 100. The students will ask his or her
partner to write the number that is ten more or ten less from that number
using hand signals.
(ten more=thumbs up
ten less=thumbs down)
Exit Slip: Write numbers on the board and ask the students to wrote the
numbers that are ten less and ten more.
Skill-Based Task: Write the number that it 10 more than 61.____
Write the number that is 10 less than 28. ____
Problem-Based Task:
Think of something you would like to buy. How many dollars would you
need? Record the price.
The cost of the item changes $10.
What is the new price?
Explain what happened to your price.
Trenton BOE Approved August 26, 2013-revised June 2014
40
1.NBT.6
Subtract
multiples of
10 in the
range 10 - 90
from
multiples of
10 in the
range 10 - 90
(positive or
zero
differences),
using
concrete
models or
drawings and
strategies
based on
place value,
properties of
operations,
and/or the
relationship
between
addition and
subtraction;
relate the
strategy to a
written
method and
explain the
reasoning
used.
Subtract
multiples of
ten from
multiples of
ten (numbers
less than
100) and
explain the
reasoning
used. (5)
Students will use concrete models, drawings and place value strategies to
subtract multiples of 10 from decade
numbers (e.g., 30, 40, 50).
Example: There are 60 students in the gym. 30 students leave. How many
students are still in the gym?
Lesson 6.6 (479484)
Lesson 6.7 (485490)
Lesson 6.8 (491496)
Virtual
Manipulatives:
http://www.connec
tED.mcgrawhill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingreso
urces.com/1stgrade-numberactivities.html
www.illuminations.
nctm.org
www.quantiles.com
My Math Words and
My Vocabulary Cards
Foldable: TE
Prerequisite
Skills:
K.NBT.1
Model the Math: using assorted manipulatives and materials TE
See unit
overview
above for full
Real-World Problem Solving Library:
Math and Science-Look Again
Literature Connection: Specified trade titles can be read to prepare students
for the lessons.
Trenton BOE Approved August 26, 2013-revised June 2014
41
description of
standard(s).
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Examples: Play race to 0 with a hundreds chart. Start at 100 and roll a
number cube. Take away that many tens. The student that lands exactly on 0
first wins the game.
Orally give the students subtraction problems. Students will write the
difference on dry erase boards.
Formative Assessments:
Think-Pair-Share: Students will work with a partner to think about 8-5 can
help them solve 80-50. Have students walk through their reasoning out loud
and then work to construct a written response on paper.
Word Sort: Have students model and sort examples using the number lines.
Exit Slip: Have students write the difference to a count back by tens problem.
Response Cards: Ask students to write the number sentences that are related
facts.
Line Up: As you call students from their seats to dismiss one at a time, give
them an addition or subtraction fact with tens. Ask them to give either a
related addition fact or a related subtraction fact.
Skill-Based Task: Solve the problem. 60 - ___ = 40
Problem-Based Task:
Jared’s class had 30 caterpillars.10 turned into butterflies. How many
butterflies are there? How many caterpillars are there? Explain your
reasoning for solving the problem. Write an equation to show how you solved
the problem.
Trenton BOE Approved August 26, 2013-revised June 2014
42
Stage 2 – Assessment Evidence
Other Evidence:
 Classwork
 Exit slips
 Homework
 Individual and group tests
 Open-ended questions
 Portfolio
 Quizzes
Suggested Performance Tasks:
 Exemplars
 Extended projects
 Math Webquests
 Writing in Math/Journal
Stage 3 – Learning Plan
Lesson Plan Template
Suggested Pacing for Required 80 Minute Math Block
Instructional Components
Lesson
Objective
Opening/Do Now
(10-15 minutes)
Homework
Review
(5-10 minutes)
Using 3-part
objective in
student-friendly
language
For example,
“I will solve 10
addition word
problems with
80% accuracy.”
Do Now may
include:
 spiral review of
prerequisite
skills for day’s
lesson
 pretest to
assess skills and
to see where
students are
regarding
today’s objective
 a writing in
math type of
prompt/question
for students to
explain/expand
upon their
thinking
May choose to
review a few
specific problems
from previous
nights’ homework
to assess for
understanding.
Students may
also self-assess
by identifying
specific problems
or areas that they
had difficulty with
and topics in
which they may
require additional
support.
Trenton BOE Approved August 26, 2013-revised June 2014
Mini Lesson
I DO/ WE DO
(15-20 minutes)
Whole group mini-lesson
with a built-in check for
understanding upon
completion. √
Independent/Partner/Group
Work
YOU DO
(20-30 minutes)
Lesson activity including at least
one check for understanding. √
Math centers should be
implemented during this time.
Suggestions:
 Technology
 Problem-based/Skillbased Task
 Vocabulary Work
 Writing in Math
 Art/Music Connections
Summary and
Exit Slip
(10 minutes)
As a class, teacher
should facilitate a
summary of the
day’s targeted
objective then
provide an exit
question (last check
for understanding)
that allows students
to individually prove
their understanding
of the objective. √
43
UNIT NAME: Measurement and Shapes
Grade level:
Unit 4:
1
District-Approved Text: My Math, McGraw-Hill
Stage 1 – Desired Results
Enduring Understandings/Goals:
 Measurement processes are used in everyday life to describe and quantify the world.
 Data displays describe and represent data in alternate ways.
 Time is measured in hours and minutes.
 Objects can be compared and described using their geometric attributes.
Essential Questions:
 How do I determine length and time?
 How can I recognize two-dimensional shapes and equal shares?
 How can I identify three-dimensional shapes?
 How do you add numbers?
 How do you subtract numbers?
 How do I use strategies to add numbers?
 What strategies can I use to subtract?
 How can I use place value?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Trenton BOE Approved August 26, 2013-revised June 2014
44
Standard:
1.MD.1
Order three
objects by
length;
compare the
lengths of
two objects
indirectly by
using a third
object.
Prerequisite
Skills:
K.MD.1
K.MD.2
See unit
overview
above for full
description of
standard(s).
Student
Learning
Objectives
Compare the
lengths of
two objects
by using a
third object
(e.g., if the
crayon is
shorter than
the marker
and the
marker is
shorter than
the pencil
then the
crayon is
shorter than
pencil). (1)
Assessment/ Evidence
Students continue to use direct comparison to compare lengths. ( Direct
comparison means that students compare the amount of an attribute in two
objects without measurement.)
Example: Who is taller?
Student: Let’s stand back to back and compare our heights. Look! I’m taller!
Example: Find at least 3 objects in the classroom that are the same length as,
longer than, and shorter than your
forearm.
Example: The snake handler is trying to put the snakes in order- from shortest
to longest. She knows that the red snake is longer than the green snake. She
also knows that the green snake is longer than the blue snake. What order
should she put the snakes in?
My Math
Resources
Lesson 8.1 (563568)
Lesson 8.2 (569574)
Other Resources
Virtual
Manipulatives:
http://www.connect
ED.mcgraw-hill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingresou
rces.com/1st-gradenumberactivities.html
www.illuminations.n
ctm.org
www.quantiles.com
My Math Words and My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare students for
the lessons.
Real-World Problem Solving Library:
Math and Science-A Wet Week
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
HomeworkJune
SE 2014
Trenton BOE Approved August 26, My
2013-revised
Formative Assessments: Response Cards: Have students model the situation and
write their answers out.
45
Line-Up: Have students work together in small groups to compare the lengths of
three classroom objects.
Skill-Based Task:
Students use a paper clip to measure how long two given objects of different
lengths are. Compare the lengths of the two objects and tell which length is
longer/shorter.
Problem-Based Task:
On Alicia’s street, the green house is 14 feet tall. The blue house is two feet
shorter than the green house. The yellow house is four feet taller than the blue
house. How many feet long is the blue house?
1.MD.2
Express the
length of an
object as a
whole
number of
length units;
by laying
multiple
copies of a
shorter object
end to end;
understand
that the
length
measurement
of an object
is the number
same-size
length units
that span it
with no gaps
Use an object
to measure
another
object’s
length by
laying
multiple
copies end to
end with no
overlaps
giving
measurement
s in whole
number
units. (2)
Students will use objects to measure items to focus on the attribute being
measured. They will utilize multiple copies of one object to measure the length
of the larger object.
Example: How long is the pencil, using paper clips to measure?
Student: I carefully placed paper clips end to end.
The pencil is 5 paper clips long. I thought it would take about 6 paperclips.
My Math Words and
My Vocabulary Cards
Lesson 8.3 (575580) Lesson 8.4
(581-586)
Virtual
Manipulatives:
http://www.connect
ED.mcgraw-hill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingresou
rces.com/1st-gradenumberactivities.html
Foldable: TE
www.illuminations.n
ctm.org
Model the Math: using assorted manipulatives and materials TE
www.quantiles.com
Literature Connection: Specified trade titles can be read to prepare students for
the lessons.
Trenton BOE Approved August 26, 2013-revised June 2014
46
or overlaps.
Limit to
contexts
where the
object being
measured is
spanned by a
whole
number of
length units
with no
overlaps.
Prerequisite
Skills:
K.MD.1
K.MD.2
See unit
overview
above for full
description of
standard(s).
Real-World Problem Solving Library:
Math and Science-A Wet Week
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Examples: Students use popsicle sticks to estimate and measure the length of
different objects around the room.
Students can also use paper clips to measure other classroom objects: crayons,
books, glue sticks, etc.
Formative Assessments:
Line Up: Invite the students in each group to find an object in the classroom
that matches the length of their given cube train.
Journal Writing: Ask students to construct a written response that answers,
“When choosing a unit to measure the length of an object, do you want a unit
that is shorter or longer than the object you are measuring? Why?”
Provide students with a problem and ask them to construct a short written
response on how they would use the Guess, Check, and Revise strategy to solve
it.
Response Cards: Holding up 3 classroom objects, ask students to choose an
object and write down a guess for how many cubes long the object is.
Skill-Based Task: About how long are these objects? (Use drawings of every day
objects on a worksheet.) Use connecting cubes to measure.
Problem-Based Task:
Each student is given 2 pieces of yarn of different lengths. (24 in. and 18 in.)
Have students decide what unit they should use in order to measure their
lengths and explain their choices. Students record the measurements on a
worksheet.
Trenton BOE Approved August 26, 2013-revised June 2014
47
1.MD.3
Tell and write
time in hours
and halfhours using
analog and
digital clocks.
Prerequisite
Skills:
None
Tell and write
time to the
half-hour
using
“o’clock” and
digital
notation. (3)
Students must understand the
differences between the two hands on the clock and the functions of these
hands. They will practice reading both analog (numbers and hands) and digital
clocks, orally tell the time, and write the time to the hour and half-hour.
*All of these clocks depict the hour of “two”, although they look slightly
different. This is an important idea for students as they learn to tell time.
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Lesson 8.5
(589-594)
Lesson 8.6
(595-600)
Lesson 8.7
(601-606)
Lesson 8.8
(607-612)
Lesson 8.9
(613-618)
Virtual
Manipulatives:
http://www.connect
ED.mcgraw-hill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingresou
rces.com/1st-gradenumberactivities.html
www.illuminations.n
ctm.org
www.quantiles.com
Literature Connection: Specified trade titles can be read to prepare students for
the lessons.
Real-World Problem Solving Library:
Math and Science-A Wet Week
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Examples: Show students a large clock that can be used to tell time to the hour.
Ask students to think of different ways to count numbers. Have students figure
out the best way to count the minutes on the clock. Show students how
counting by 5s can help you tell time. Students practice counting by 5s with
individual clocks.
Distribute individual clocks to each student. After discussing what times students
do certain activities, ask students to show what time they wake up? Eat
breakfast? Eat dinner? Go to bed? Etc.
Formative Assessments:
Trenton BOE Approved August 26, 2013-revised June 2014
48
Line Up: When students line up for recess, lunch, or dismissal, ask “Where are
the analog clocks in the room?”
Response Cards:
Ask students: “Where is the minute hand when it is two o’clock, nine o’clock, or
four o’clock?”
Exit Slip: Show six o’clock on a demonstration analong clock. Ask students to
write the same time as it would look on a digital clock.
Debriefing: Ask students to construct a short written response which describes
the similarities and differences in analog and digital clocks.
Think-Pair-Share: Show the minute hand pointing to the 6 and the hour hand
pointing directly to the 9. Ask students what is wrong with the clock. Have them
work with a partner to discuss this.
Skill-Based Task:
On a worksheet, provide pictures of a clocks showing various times in hours and
half-hours. Students write matching times beneath each clock using “o’clock”
and digital notations.
Problem-Based Task:
Aaliyah gets up at 7 o’clock in the morning to get ready for school. She arrives
to school at 8:30 am to eat breakfast. Draw the minute hands and the hour
hands on the clocks below to show what time Aaliyah gets up and eats
breakfast. Write the times in the digital clocks as well.
1.G.1
Distinguish
between
defining
attributes
(e.g.,
triangles are
closed and
three sided)
versus nondefining
Name the
attributes of
a given twodimensional
shape
(square,
triangle,
rectangle,
regular
hexagon)
distinguishing
Students will use their beginning knowledge of defining and non-defining
attributes of shapes to identify, name, build and draw shapes (including
triangles, squares, rectangles, and trapezoids).
Example:
All triangles must be closed figures and have 3 sides. These are defining
attributes. Triangles can be different colors, sizes and be turned in different
directions. These are non-defining attributes.
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson 9.1
(635-640)
Lesson 9.2
(641-646)
Lesson 9.3
(647-652)
Lesson 9.4
(653-658)
Lesson 10.1
(711-716)
Lesson 10.2
Virtual
Manipulatives:
http://www.connect
ED.mcgraw-hill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingresou
49
attributes
(e.g., color
orientation,
overall size);
build and
draw shapes
to possess
defining
attributes.
Prerequisite
Skills:
K.G.2
K.G.5
K.G.6
See unit
overview
above for full
description of
standard(s).
between
defining and
non-defining
attributes.
(4)
Draw and
build shapes
when given
defining
attributes
(e.g., 3 sides,
4 sides, 3
corners, 4
corners). (5)
(717-722)
Lesson 10.3
(725-730)
Student:
I know that this shape is a triangle because it has 3 sides.
It’s also closed, not open.
Student:
I used toothpicks to build a square. I know it’s a square because it has 4 sides.
And, all 4 sides are the same size.
rces.com/1st-gradenumberactivities.html
www.illuminations.n
ctm.org
www.quantiles.com
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare students for
the lessons.
Real-World Problem Solving Library:
Math and Science-Shapes in Nature
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Examples: Distribute a variety of pattern blocks to students working in pairs.
Ask students to find one way to sort the blocks. Have each group share how
they sorted the blocks. (Blocks can be sorted by color, shape, number of sides,
etc.) This is a good time to introduce vocabulary such as sides, corners,
vertices, etc.
Have one group of students make an organized list titled "Ways to Make a
Hexagon" and the other group make a list titled "Ways to Make a Trapezoid."
Trenton BOE Approved August 26, 2013-revised June 2014
50
Students should decide which pattern blocks can cover the shape, and then
record the answers in their lists.
ormative Assessments:
Quick Draw: Ask students to draw a line down the middle of their boards. On the
left side, ask students to draw a square. On the right side, have students draw a
rectangle. Have students use red to draw the sides and blue to draw the
vertices.
Exit Slip: Ask students to answer: “How is a square different from a rectangle?”
Line Up: Ask half of the class to identify a classroom object that is in the shape
of a triangle, and have them line up.
Self-Assessment: Ask students to rate their understanding on a scale of 0-3.
Word Sort: Have students place the appropriate shape under each description.
3-2-1 Strategy Form: Ask students to write three things that they have learned
about the list of shapes, two things they want to know more about, and one
question they might have.
Think-Pair-Share: Ask students to name two differences between a circle and a
triangle.
Skill-Based Task:
How many vertices are there on a triangle?
Problem-Based Task:
How many ways can you use the pattern blocks to make a trapezoid? Explain.
1.OA.1
Use addition
Use addition
and
and
subtraction
subtraction
within 20 to
within 20 to
solve word
solve word
problems
problems
involving
Trenton BOE Approved August
Explore numbers to 20 to solve various word problems. Amounts are compared
to find “How many more” or “How many less”.
Difference Unknown:
“How many more?”
Lucy has 7 apples. Julie as 9
apples. How many more apples
26, 2013-revised June 2014
Lesson 1.1 (1116)
Lesson 1.2
(17-22)
Lesson 1.3
(23-28)
Lesson 1.6
Virtual
Manipulatives:
http://www.connect
ED.mcgraw-hill.com
51
involving
situations of
adding to,
taking from,
putting
together,
taking apart,
and
comparing,
with
unknowns in
all positions,
e.g., by using
objects,
drawings,
and
equations
with a symbol
for the
unknown to
represent the
problem.
Prerequisite
Skills:
K.OA.1
K.OA.2
K.OA.5
See unit
overview
above for full
description of
standard(s).
situations of
adding to,
taking from,
putting
together,
taking apart,
and
comparing
with
unknowns in
all positions.
(6)
does Julie have than Lucy?
Bigger Unknown:
“More” (suggests operation)
Julie has 2 more apples than Lucy. Lucy has 7 apples. How many apples does
Julie have?
“How many fewer?”
Lucy as 7 apples. Julie has 9
apples. How many fewer apples does Lucy have than Julie?
=9
9–7=

Smaller Unknown:
“Fewer” (suggests operation)
(43-48)
Lesson 2.1
(109-114)
Lesson 2.2
(115-120)
Lesson 2.3
(121-126)
Lesson
2.6(141-146)
Lesson 2.7 (147152) Lesson
3.6 (243-248)
Lesson 3.8 (255260) Lesson 4.4
(299-304)
K-5 Math Teaching
Resources:
http://www.k5mathteachingresou
rces.com/1st-gradenumberactivities.html
www.illuminations.n
ctm.org
www.quantiles.com
Lucy has 2 fewer apples than Julie. Julie has 9 apples. How many apples does
Lucy have?
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare students for
the lessons.
Real-World Problem Solving Library:
Math and Science-Healthful Snacks
Math and Science-What Do They Eat?
Math and Science-Double the Number
Math and Science-Rock Collections
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Trenton BOE Approved August 26, 2013-revised June 2014
52
Example: Have students work in pairs to make three towers of ten. Student A
rolls one number cube and then connects that many number cubes using the
same color. Student B repeats the process using different colored cubes.
Repeat this pattern until they make a tower of ten. If there are cubes left over
then they use those cubes to begin a new tower. Repeat until there are three
towers of ten. Students come up with an equation for each tower of ten (3 red
+ 5 orange + 2 blue = 10 cubes.
Formative Assessments:
Exit Slip: Tell students an addition number story that relates to their daily
classroom experience.
Quick Draw: Have students draw pictures to represent and explain the meaning
of vocabulary words: add, parts, and whole.
Think-Pair-Share: Invite students to work in pairs to discuss an addition number
sentence.
Have students answer a question on their own, tell their answer to a partner,
and then share it with the entire class.
Have students use a work mat to show a partner how they would model a
problem.
Response Cards: Describe a take away situation in your classroom. Have
students record their answers.
Journal Writing: Have students write a journal response to explain how to write
a subtraction number sentence.
Skill -Based Task: Fill in the missing numbers to solve the addition problem.
19 =9
Problem-Based Task:
On Tuesday Tim read 7 pages in his new book. On Wednesday Tim read some
more pages and then he was up to page 10. How many pages did Tim read on
Wednesday?
Write a number sentence to solve the problem.
Trenton BOE Approved August 26, 2013-revised June 2014
53
1.OA.6
Add and
subtract
within 20,
demonstratin
g fluency for
addition and
subtraction
within 10.
Use
strategies
such as
counting on;
making 10
(e.g., 8 + 6 =
8+2+4=
10 + 14);
decomposing
a number
leading to a
ten (e.g. 134=13-31=10-1=9);
using the
relationship
between
addition and
subtraction
(e.g. knowing
that 8+4=12,
one knows
12-8=4); and
creating
equivalent
but easier
known sums
(e.g., adding
6+7 by
creating the
known
equivalent
6+6+1=12+1
Add or
subtract
whole
numbers
within 20
(various
strategies:
counting on,
composition,
etc.). (7)
Students learn about and use various strategies to solve addition and subtraction
problems.
Example: There were 14 birds in the tree. 6 flew away. How many birds are in
the tree now?
Back Down Through Ten
I know that 14 minus 4 is 10. So, I broke the 6 up into a 4 and a 2. 14 minus 4
is 10. Then I took away 2 more to get 8.
6=4+2
14 – 4 = 10
10 – 2 = 8
Relationship between Addition & Subtraction
I thought 6 and what makes 14? I know that 6 plus 6 is 12 and two more is 14.
That’s 8 in all. So, that means that 14 minus 6 is 8.
6 + 8 = 14
14 – 6 = 8
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare students for
the lessons.
Real-World Problem Solving Library:
Math and Science-Healthful Snacks
Math and Science-What Do They Eat?
Math and Science-Double the Number
Math and Science-Rock Collections
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Trenton BOE Approved August 26, 2013-revised June 2014
Formative
Assessments:
Exit Slip:
Students write
and solve a math
problem, both
horizontally and
vertically.
Have students
write two ways of
making a sum of
5.
Quick Draw:
Have students
draw pictures to
represent all of
the ways to make
6 on one side of
the paper. Then
have them draw
all of the ways to
make 7 on the
other side of the
paper.
Virtual
Manipulatives:
http://www.connect
ED.mcgraw-hill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingresou
rces.com/1st-gradenumberactivities.html
www.illuminations.n
ctm.org
www.quantiles.com
Response Cards:
Have students
write two number
sentences that
have a sum of 8.
Example/NonExample: Have
students write
one example of
an addition
number sentence
that equals 9 and
one nonexample.
54
=13).
Prerequisite
Skills:
K.OA.1
K.OA.2
K.OA.3
K.OA.4
K.OA.5
See unit
overview
above for full
description of
standard(s).
Examples:
Students can join 8 counters with the red side up and 7 counters with the yellow
side up. What addition fact tells what happened?
Write 8 + 7 =
Students can separate the groups into red and yellow. What subtraction fact
tells what happened? Write 15 – 8 =
Discuss related facts. Students should understand that every addition fact has at
least one related subtraction fact. Show that these facts use the same numbers.
Have each student build a train of 5 or 6 cubes in 2 or 3 different colors and
write an addition expression to match. The class examines the trains and
expressions to find equivalent equations.

My Math:
Lesson 1.5 (37-42)
Lesson 1.7 (49-54)
Lesson 1.8 (55-60)
Lesson 1.9 (61-66)
Lesson 1.10 (69-74)
Lesson 1.11 (75-80)
Lesson 2.5 (133-138) Lesson 2.8 (153-158) Lesson 2.9 (159-164) Lesson 2.10
(167-172) Lesson 2.11 (173-178)
Lesson 2.12 (179-184)
Lesson 2.13 (185-190) Lesson 3.4 (229-234) Lesson 3.5 (235-240) Lesson 3.7
(249-254) Lesson 4.3 (293-298) Lesson 4.5 (307-312) Lesson 4.7 (319-324)
Self-Assessment:
Have students
use a work mat
an counters to
show various
ways to make 10.
Skill -Based Task:
Show different
ways to make 17.
Problem-Based
Task:
Ian and John
went apple
picking. Ian
picked 6 apples.
John picked 9
apples. How
many fewer
apples did Ian
pick?
Write a
subtraction
sentence to
answer the
question.
____ - ____ =
_____
____ fewer
apples
Now, write the
fact families for
the apples.
Trenton BOE Approved August 26, 2013-revised June 2014
__+__=__
__=__
__-
__+__=__
__-
55
__=__
1.NBT.1
Count to 120,
starting at
any number
less than 120.
In this range,
read and
write
numerals and
represent a
number of
objects with a
written
numeral.
Prerequisite
Skills:
K.NBT.1
See unit
overview
above for full
description of
standard(s).
Read and
write
numerals to
120 starting
at any
number and
represent any
number of
objects with
a written
numeral. (8)
Students will count forward to 120 by counting on from any number less than
120.
They should continue to be given opportunities to build on the understanding of
how the numbers in the counting sequence are related—each number is one
more (or one less) than the number before (or after).
Students will continue to read and write numerals to represent a given amount.
My Math Words and
My Vocabulary Cards
Foldable: TE
Lesson 5.1 (347352)
Lesson 5.2
(353-358)
Lesson 5.4
(365-370)
Lesson 5.5
(371-376)
Lesson 5.6
(379-384)
Lesson 5.7 (385390
Virtual
Manipulatives:
http://www.connect
ED.mcgraw-hill.com
K-5 Math Teaching
Resources:
http://www.k5mathteachingresou
rces.com/1st-gradenumberactivities.html
Model the Math: using assorted manipulatives and materials TE
www.illuminations.n
ctm.org
Literature Connection: Specified trade titles can be read to prepare students for
the lessons.
www.quantiles.com
Real-World Problem Solving Library:
Math and Science-Look Again
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Example: Vertically list these numbers on a whiteboard: 17, 117, 217, 317, 417,
517, 617, 717, 817, 917. Ask, “What do you notice about these numbers? Which
digits remain the same each time? Which digits change? What is the place value
of the digit that changes?
Example: Read “If You Give a Mouse a Cookie” by Laura Joffe Numeroff. Have
students work in groups. Give each group 30 counters. Write "Number of Mice"
and "Number of Cookies" on the table. Fill in 1–5 in the top row. A child gives a
mouse 2 "cookies" (counters). Fill in 2 on the bottom row of the table. Continue
by giving 2 mice 4 cookies and so on.
Trenton BOE Approved August 26, 2013-revised June 2014
56
Formative Assessments:
Quick Draw: Students will be asked to draw the number 13 on a double ten
frame.
Exit Slip: Ask students to write how many when given a number and a certain
number more.
Example/Non-Example: Have students draw one example to match the given
description. They will write one non-example on the other side.
Have students work with connecting cubes and ask them to model one example
of 34 as tens and some more. Ask them to model one non-example.
Think-Pair-Share: Have students work in pairs and point to numbers on the
hundred chart. The other partner must tell how many tens and ones make up
that number.
Skill -Based Task: What number comes before 79? After 79?
Problem-Based Task:
There are 6 dogs.
Each dog chased 3 balls in the park. How many balls did they chase altogether?
Trenton BOE Approved August 26, 2013-revised June 2014
57
Stage 2 – Assessment Evidence
Other Evidence:
 Classwork
 Exit slips
 Homework
 Individual and group tests
 Open-ended questions
 Portfolio
 Quizzes
Suggested Performance Tasks:
 Exemplars
 Extended projects
 Math Webquests
 Writing in Math/Journal
Stage 3 – Learning Plan
Lesson Plan Template
Suggested Pacing for Required 80 Minute Math Block
Lesson
Objective
Using 3-part
objective in
student-friendly
language
For example,
“I will solve 10
addition word
problems with
80% accuracy.”
Opening/Do Now
Homework Review
(10-15 minutes)
(5-10 minutes)
Do Now may include:
 spiral review of
prerequisite skills
for day’s lesson
 pretest to assess
skills and to see
where students
are regarding
today’s objective
 a writing in math
type of prompt/
question for
students to
explain/expand
upon their
thinking.
May choose to review
a few specific
problems from
previous nights’
homework to assess
for understanding.
Students may also
self-assess by
identifying specific
problems or areas
that they had
difficulty with and
topics in which they
may require additional
support.
Trenton BOE Approved August 26, 2013-revised June 2014
Instructional Components
Mini Lesson
I DO/ WE DO
(15-20 minutes)
Whole group minilesson with a built-in
check for
understanding upon
completion. √
Independent/Partner/Group
Work
YOU DO
(20-30 minutes)
Lesson activity including at least
one check for understanding. √
Math centers should be
implemented during this time.
Suggestions:
 Technology
 Problem-based/Skillbased Task
 Vocabulary Work
 Writing in Math
 Art/Music Connections
Summary and
Exit Slip
(10 minutes)
As a class, teacher
should facilitate a
summary of the
day’s targeted
objective then
provide an exit
question (last check
for understanding)
that allows students
to individually prove
their understanding
of the objective. √
58
UNIT NAME: Reasons with Shapes and their Attributes
Grade level:
1
District-Approved Text: My Math, McGraw-Hill
Unit 5:
Stage 1 – Desired Results
Enduring Understandings/Goals:
 Objects can be described, compared, and classified by geometric attributes.
 Many geometric shapes can be divided into equal parts.
 Everyday objects have a variety of attributes that can be measured in many ways.
Essential Questions:
 How can I recognize two-dimensional shapes and equal shares?
 How can I identify three-dimensional shapes?
 How can I add and subtract two-digit numbers?
 How do you add numbers?
 How do you subtract numbers?
 How do I use strategies to add numbers?
 What strategies can I use to subtract?
 How do I make and read graphs?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Standard:
1.G.2
Compose twodimensional
shapes
(rectangles,
squares,
Student
Learning
Objectives
Compose twodimensional
shapes
(rectangles,
squares,
trapezoids,
Assessment/ Evidence
Have students create composite shapes, a figure made up of two or more
geometric shapes to begin to see how shapes fit together to create different
shapes.
They can identify shapes within an already existing shape, utilizing tools
such as pattern blocks, tangrams, attribute blocks, or virtual shapes to
Trenton BOE Approved August 26, 2013-revised June 2014
My Math
Resources
Other
Resources
Lesson 9.1 (661666)
Lesson 9.2 (667672)
Lesson
9.7 (673-678)
Lesson 10.4
Virtual
Manipulatives:
http://www.con
nectED.mcgrawhill.com
59
trapezoids,
triangles, halfcircles, and
quartercircles) or
threedimensional
shapes
(cubes, right
rectangular
prisms, right
circular cones,
and right
circular
cylinders) to
create a
composite
shape, and
compose new
shapes from
the composite
shape.
Prerequisite
Skills:
K.G.2
K.G.3
K.G.4
K.G.5
K.G.6
See unit
overview
above for full
description of
standard(s).
triangles, halfcircles and
quarter circles)
or threedimensional
shapes (cubes,
right
rectangular
prisms, right
circular cones,
and right
circular
cylinders) to
create a
composite
shape, and
compose new
shapes from
the composite
shape. (1)
compose different shapes.
Example:
What shapes can you create with triangles? Student A: I made a square. I
used 2 triangles.
My Math Words and My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
(731-736)
K-5 Math
Teaching
Resources:
http://www.k5mathteachingre
sources.com/1st
-grade-numberactivities.html
www.illuminatio
ns.nctm.org
www.quantiles.c
om
Literature Connection: Specified trade titles can be read to prepare students
for the lessons.
Real-World Problem Solving Library:
Math and Science-Shapes in Nature
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
 Make a number using pattern blocks. Draw a picture to show the
shapes you used to make the number. Explain what kind of pattern
blocks you used and how many.

Students use a set of shapes to create two different composite shapes,
then compare/contrast how the composite shapes are alike and
different.
Formative Assessments:
Quick Draw: Ask students to draw a line down the middle of their boards.
On the left side, ask students to draw a square.
Create a composite shape from 8 pattern blocks. Remove 2 or 3 shapes. Ask
students to draw the missing shapes on a piece of paper.
Trenton BOE Approved August 26, 2013-revised June 2014
60
Display a composite shape made by three geometric solids: cube,
rectangular prism, and cylinder. Place these shapes in a row next to the
composite shape: cylinder, cube, cone, and rectangular prism. Have
students draw on their boards the shape that was not used.
On the right side, have students draw a rectangle. Have students use red to
draw the sides and blue to draw the vertices. Tell students an addition
number story that relates to their daily classroom experience.
Exit Slip: How is a square different from a rectangle?
Line Up: Ask half of the class to identify a classroom object that is in the
shape of a triangle, and have them line up. Ask the other half to identify a
classroom object in the shape of a trapezoid, and have them line up.
Skill-Based Task:
Which two shapes could you use to create this composite shape?
1.
2.
3.
Problem-Based Task: Create and record a composite shape using two or
more shapes. Create and record a different composite shape using those
same shapes.
1.G.3
Partition
circles and
rectangles into
two and four
equal shares,
describe the
shares using
Partition circles
and rectangles
into two or four
equal shares,
describing the
shares using
halves, fourths,
and, quarters,
Students will partition regions into equal shares using a context (e.g.,
cookies, pies, pizza) and related vocabulary: halves, fourths, and quarters.
Example: Let’s take a look at this pizza. What do you notice about the slices
on the pizza?
Student: There are two slices on the pizza. Each slice is the same size.
Those are big slices!
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson 9.8 (681686)
Lesson 9.9 (687692)
Lesson 9.10
(693-698)
Virtual
Manipulatives:
http://www.con
nectED.mcgrawhill.com
K-5 Math
61
the words
halves,
fourths, and
quarters, and
use the
phrases half
of, fourth of,
and quarter of.
Describe the
whole as two
of, or four of
the shares.
Understand for
these
examples that
decomposing
into more
equal shares
creates smaller
shares.
Prerequisite
Skills:
K.G.2
K.G.3
K.G.4
K.G.5
K.G.6
See unit
overview
above for full
description of
standard(s).
and use the
phrases half of,
fourth of, and
quarter of. (2)
Describe the
whole circle (or
rectangle)
partitioned into
two or four
equal shares as
"two of", or
"four of" the
shares. (3)
If we cut the same pizza into four slices (fourths), do you think
the slices would be the same size, larger, or smaller as the slices on this
pizza?
Teaching
Resources:
http://www.k5mathteachingre
sources.com/1st
-grade-numberactivities.html
When you cut the pizza into fourths, the slices are smaller than the other
pizza. More slices mean that the slices get
smaller and smaller. I want a slice from that first pizza!
www.illuminatio
ns.nctm.org
Fold and cut your paper pizza into two equal slices (halves). Use pencils
or crayons to draw a different topping on each slice of your pizza. If you
cut the pizza into four equal slices (quarters) would the pieces be the
same size, smaller, or larger than the two slices? Explain your thinking.

www.quantiles.c
om
Use Geoboards to create rectangles and circles and divide them into
halves and fourths
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare students
for the lessons.
Real-World Problem Solving Library:
Math and Science-Shapes in Nature
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Formative Assessments:
Modeling: Ask students to use pattern blocks to model separating shapes
into equal parts.
Trenton BOE Approved August 26, 2013-revised June 2014
62
Line Up: Using two-dimensional shapes, have students identify which shapes
have equal parts.
Quick Draw: Have students draw three different shapes-circles, rectangles,
or squares. Ask students to shade in one half of each shape and write the
number of halves.
Skill -Based Task:
Divide the square into fourths.
Divide the circle in half.
Problem-Based Task:
Liza is having a party. Help her cut the cookie pizza into equal parts.
How much of the cookie pizza did each guest eat?
1.NBT.4
Add within
100, including
adding a twodigit and a
one-digit
number, and
adding a twodigit number
and a multiple
of 10; using
concrete
models, or
drawings and
Add within 100,
including
adding a twodigit and a onedigit number,
and adding a
two-digit
number and a
multiple of 10;
using concrete
models, or
drawings and
strategies
based on place
Students will use concrete materials, models, drawings and place value
strategies to add within 100, while utilizing the base-ten system to solve
problems.
Example: 24 red apples and 8 green apples are on the table. How many
apples are on the table?
Student A: I used ten frames. I put 24 chips on 3 ten frames. Then, I counted
out 8 more chips. 6 of them filled up the third ten frame.
That meant I had 2 left over. 3 tens and 2 left over. That’s 32. So, there are
32 apples on the table.
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson 6.1
(447-452)
Lesson 6.2
(453-458)
Lesson 6.3
(459-464)
Lesson 6.4
(465-470)
Lesson 6.5
(471-476)
Virtual
Manipulatives:
http://www.con
nectED.mcgrawhill.com
K-5 Math
Teaching
Resources:
http://www.k5mathteachingre
sources.com/1st
-grade-number-
63
strategies
based on place
value,
properties of
operations
and/or the
relationship
between
addition and
subtraction;
and relate the
strategy to a
written
method and
explain the
reasoning
used.
Understand
that in adding
two-digit
numbers, one
adds tens and
tens, ones and
ones; and
sometimes it is
necessary to
compose a
ten.
value,
properties of
operations
and/or the
relationship
between
addition and
subtraction;
and relate the
strategy to a
written method
and explain the
reasoning used.
Understand
that in adding
two-digit
numbers, one
adds tens and
tens, ones and
ones; and
sometimes it is
necessary to
compose a ten.
(4)
activities.html
www.illuminatio
ns.nctm.org
www.quantiles.c
om
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare students
for the lessons.
Real-World Problem Solving Library:
Math and Science-Shapes in Nature
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Prerequisite
Skills:
K.NBT.1
See unit
overview
above for full
description of
standard(s).
Wrap It Up
My Homework SE
Formative Assessments:
Response Cards: Students will write the sums for given problems.
Tell students an addition story. Have them use the guess, check, and revise
strategy to solve the problem.
Trenton BOE Approved August 26, 2013-revised June 2014
64
Journal Writing: Invite students to construct a short written response
explaining what they learned about adding tens, including a diagram.
Invite students to construct a short written response that describes how to
use the guess, check, and revise strategy to solve math word problems.
Quick Draw: Invite students to draw a picture of tens rods and unit cubes to
show how to as 56 + 30 using manipulatives.
Line Up: Present quick problems that involve counting on by tens or ones.
Each group rolls a 0-5 number cube and add the number rolled to the
number on their card. As groups answer correctly, have them line up.
Interviews: Ask students to describe the steps they learned in how to add
tens and ones, while modeling with base-ten blocks.
Example/Non-Example: Invite students to model one example of a two-digit
plus a one-digit number that involves regrouping.
Skill -Based Task:
Add these two-digit numbers.
62
+25
Problem-Based Task:
In Joel’s seashell collection, he counted twenty-two seashells. His father
came home from a vacation and gave him four seashells and a bag filled
with thirty. How can Joel figure out how many seashells are in his collection
now?
1.OA.1
Use addition
and
subtraction
within 20 to
solve word
problems
Use addition
and subtraction
within 20 to
solve word
problems
involving
situations of
My Math Words and
My Vocabulary Cards
Foldable: TE
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson
16)
Lesson
22)
Lesson
28)
Lesson
1.1 (111.2 (171.3 (23-
Virtual
Manipulatives:
http://www.con
nectED.mcgrawhill.com
1.6 (43-
65
involving
situations of
adding to,
taking from,
putting
together,
taking apart,
and
comparing,
with unknowns
in all positions,
e.g., by using
objects,
drawings, and
equations with
a symbol for
the unknown
number to
represent the
problem.
Prerequisite
Skills:
K.OA.1
K.OA.2
K.OA.5
See unit
overview
above for full
description of
standard(s).
adding to,
taking from,
putting
together,
taking apart,
and comparing,
with unknowns
in all positions,
e.g., by using
objects,
drawings, and
equations with
a symbol for
the unknown
number to
represent the
problem. (5)
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare students
for the lessons.
Real-World Problem Solving Library:
Math and Science-Shapes in Nature
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
48)
Lesson 2.1 (109114)
Lesson 2.2 (115120)
Lesson 2.3 (121126)
Lesson 2.6(141146)
Lesson
2.7 (147-152)
Lesson 3.6 (243248)
Lesson 4.4 (299304)
K-5 Math
Teaching
Resources:
http://www.k5mathteachingre
sources.com/1st
-grade-numberactivities.html
www.illuminatio
ns.nctm.org
www.quantiles.c
om
Formative Assessments:
Exit Slip: Tell students an addition number story that relates to their daily
classroom experience.
Response Cards: Tell the following addition story and ask students how they
solved the problem.
Have students draw a diagram and solve a problem.
Describe a take away situation in your classroom and ask-“How many xx
remain?”
Quick Draw: Have students draw pictures to represent and explain the
meaning of the vocabulary words, add, parts, and whole.
Modeling: Have students use a work mat to place counters and find the
whole.
Exit Slip: Have students write a number sentence to match/solve the
problem.
Response Cards: Tell an addition story and ask-“How will you solve this
problem?”
Think-Pair-Share:
Instruct students to show the following scenario to a classmate. Then have
students share with the entire class.
Trenton BOE Approved August 26, 2013-revised June 2014
66
Journal Writing: Have students write a journal response to explain how to
write a subtraction number sentence.
Self-Assessment: Ask students to reflect upon the steps they used to solve a
previous exercise.
1.OA.6
Add and
subtract within
20 (fluently
within 10).
Use strategies
such as:
counting on;
making ten
(e.g., 8 + 6 =
8+2+4=
10 + 4 = 14);
decomposing a
number
leading to a
ten (e.g., 13 4 = 13 - 3 - 1
= 10 - 1 = 9);
relationship
between
addition and
subtraction
(e.g., knowing
that 8 + 4 =
12, one knows
12 - 8 = 4);
and creating
equivalent
sums (e.g.,
adding 6 + 7
by creating the
known
equivalents 6
+ 6 + 1 = 12
Add and
subtract within
20 (fluently
within 10). Use
strategies such
as: counting
on; making ten
(e.g., 8 + 6 =
8 + 2 + 4 = 10
+ 4 = 14);
decomposing a
number leading
to a ten (e.g.,
13 - 4 = 13 - 3
- 1 = 10 - 1 =
9); relationship
between
addition and
subtraction
(e.g., knowing
that 8 + 4 =
12, one knows
12 - 8 = 4);
and creating
equivalent
sums (e.g.,
adding 6 + 7
by creating the
known
equivalents 6 +
6 + 1 = 12 + 1
= 13).
(6)
Students learn about and use various strategies to solve addition and
subtraction problems.
Example: Two frogs were sitting on a log. 6 more frogs hopped there. How
many frogs are sitting on the log now?
Counting‐ On…
I started with 6 frogs and then counted up, 6…,7, 8. So there are 8 frogs on
the log.
6+2=8
Internalized Fact…
There are 8 frogs on the log. I know this because 6 plus 2 equals 8. 6 + 2
=8
Example: Sam has 8 red marbles and 7 green marbles. How many marbles
does Sam have in all?
Making 10 and Decomposing a Number…
I know that 8 plus 2 is 10, so I broke up (decomposed) the 7 up into a 2 and
a 5. First, I
added 8 and 2 to get 10, and then added the 5 to get 15.
7=2+5
8 + 2 = 10
10 + 5 = 15
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare students
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson 1.5
(37-42)
Lesson 1.7
(49-54)
Lesson 1.8
(55-60)
Lesson 1.9
(61-66)
Lesson 1.10
(69-74)
Lesson 1.11
(75-80)
Lesson 2.5
(133-138)
Lesson 2.8
(153-158)
Lesson 2.9
(159-164)
Lesson 2.10
(167-172)
Lesson 2.11
(173-178)
Lesson 2.12
(179-184)
Lesson 2.13
(185-190)
Lesson 3.4
(229-234)
Lesson 3.5
(235-240)
Lesson 3.7
(249-254)
Lesson 4.3
(293-298)
Virtual
Manipulatives:
http://www.con
nectED.mcgrawhill.com
K-5 Math
Teaching
Resources:
http://www.k5mathteachingre
sources.com/1st
-grade-numberactivities.html
www.illuminatio
ns.nctm.org
www.quantiles.c
om
67
+ 1 = 13).
Prerequisite
Skills:
K.OA.1
K.OA.2
K.OA.3
K.OA.4
K.OA.5
for the lessons.
Real-World Problem Solving Library:
Math and Science-Shapes in Nature
Lesson 4.5
(307-312)
Lesson 4.7
(319-324)
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
See unit
overview
above for full
description of
standard(s).
Wrap It Up
My Homework SE
Formative Assessments:
Exit Slip: Have students write the vertical number sentence that they would
use to solve the problem.
Have students write two ways of making a sum of 5.
Have students write a vertical subtraction problem to represent the
situation.
Modeling: Ask students to model the addition number sentences using
counters and a work mat.
Response Cards: Have students write two number sentences that have a
sum of 8.
Example/Non-Example: Have students write one example of an addition
number sentence that equals 9 and one non-example.
Quick Draw: Assess students’ learning by giving them 3-5 minutes to draw
every instance of making 10 that they can.
Journal Writing: Have students write a short journal response to answer the
question: “How do you subtract from 4 and 5?”
1.MD.4
Organize,
represent and
interpret data
with up to
three
Organize,
represent, and
interpret, data
with up to
three
categories, and
Students will collect and use categorical data (e.g., eye color, shoe size,
age) to answer a question.
The data collected should be organized into a chart or table. Students will
interpret the data to determine the answer to the question(s) posed;
including the total number of answers, which category had the most/least
Trenton BOE Approved August 26, 2013-revised June 2014
Lesson 7.1 (509514)
Lesson 7.2 (515520)
Lesson 7.3 (521526)
Virtual
Manipulatives:
http://www.con
nectED.mcgrawhill.com
68
categories; ask
and answer
questions
about the total
number of
data points,
how many in
each category,
and how many
more or less
are in one
category than
in other.
Prerequisite
Skills:
none
compare the
number counts
of data points
among the
categories,
e.g., equal to,
more than, or
less than
another
category. (7)
responses, and interesting differences/similarities between the categories.
Numerous opportunities should be given to create questions, determine up
to 3 categories of possible responses, collect data, organize data, and
interpret the results.
My Math Words and
My Vocabulary Cards
Foldable: TE
Model the Math: using assorted manipulatives and materials TE
Literature Connection: Specified trade titles can be read to prepare students
for the lessons.
Lesson 7.4 (527532)
Lesson 7.5 (535540)
K-5 Math
Teaching
Resources:
http://www.k5mathteachingre
sources.com/1st
-grade-numberactivities.html
www.illuminatio
ns.nctm.org
www.quantiles.c
om
Real-World Problem Solving Library:
Math and Science-Shapes in Nature
Differentiated Instruction:
Hands-On Activities
Lesson Animation (Reteach and Enrich)
Wrap It Up
My Homework SE
Examples:
 Create a pictograph of the weather each day. Ask questions about the
data.

Using a daily question (like how did you come to school), have students
respond on a graph
then discuss: “How many are the same? How many are different? How
do you know? How many more __ than __?” etc.
Formative Assessments:
Journal Writing: Invite students to construct a short written explanation that
describes the purpose of the tally charts.
Interviews: As students work in pairs, assign one to be the interviewer and
the other to ask the questions about the make-a-table strategy.
Have the interviewer ask the following questions: “What is a picture graph?”
Trenton BOE Approved August 26, 2013-revised June 2014
69
and “How do you make a picture graph?” Have the students switch roles
and repeat.
Modeling: Provide students with a picture which represents various
quantities of objects that could be organized into a table.
3-2-1 Strategy: Ask students to consider what they have learned about
picture graphs.
Example/Non-Example: Invite students to work in pairs to draw an example
of a picture graph and a non-example of a picture graph
Response Cards: Ask students to answer questions about a graph and
record their responses on an index card.
Line-Up: Have students line up by the season of their birthday month.
Quick Draw: Provide each student with connecting cubes of various colors
and ask them to make a bar graph showing how many there are of each
color.
Skill -Based Task:
Mrs. Brown’s class took a survey of their favorite pets.
Our Favorite Pet
dog
cat
fish
Problem-Based Task:
A first grade class was asked what their favorite ice cream was.
Organize the data below to answer the questions.
Trenton BOE Approved August 26, 2013-revised June 2014
70
http://images.search.yahoo.com/images/view;_ylt=A0PDoX56AdBP5
UgA4WuJzbkF;_ylu=X3oDMTBlMTQ4cGxyBHNlYwNzcgRzbGsDaW1n?
back=http%3A%2F%2Fimages.search.yahoo.com%2Fsearch%2Fima
ges%3Fp%3Dfree%2Bchocolate%2Bice%2Bcream%2Bcone%2Bclipa
rt%2Bimages%26phrase%3D1%26imgc%3Dcolor%26ei%3Dutf8%26y%3DSearch%26fr%3Dushdir%26tab%3Dorganic%26ri%3D164&w=300&h=300&imgurl=www.
polyvore.com%2Fcgi%2Fimgthing%3F.out%3Djpg%26amp%3Bsize%3Dl%26amp%3Btid%3D213
8918&rurl=http%3A%2F%2Fchocolate-chipscookies.blogspot.com%2F2009%2F10%2Fcho
How many flavors are in each category? How many more students like
chocolate than vanilla? How many fewer students like strawberry than
chocolate?
Trenton BOE Approved August 26, 2013-revised June 2014
71
Stage 2 – Assessment Evidence
Other Evidence:
 Classwork
 Exit slips
 Homework
 Individual and group tests
 Open-ended questions
 Portfolio
 Quizzes
Suggested Performance Tasks:
 Exemplars
 Extended projects
 Math Webquests
 Writing in Math/Journal
Stage 3 – Learning Plan
Lesson Plan Template
Suggested Pacing for Required 80 Minute Math Block
Lesson
Objective
Opening/Do Now
(10-15 minutes)
Using 3-part
objective in
student-friendly
language
For example,
“I will solve 10
addition word
problems with
80% accuracy.”
Do Now may include:
 spiral review of
prerequisite skills
for day’s lesson
 pretest to assess
skills and to see
where students are
regarding today’s
objective
 a writing in math
type of
prompt/question
for students to
explain/expand
upon their thinking
Homework
Review
(5-10 minutes)
May choose to
review a few
specific problems
from previous
nights’ homework
to assess for
understanding.
Students may also
self-assess by
identifying specific
problems or areas
that they had
difficulty with and
topics in which they
may require
additional support.
Trenton BOE Approved August 26, 2013-revised June 2014
Instructional Components
Mini Lesson
I DO/ WE DO
(15-20 minutes)
Whole group mini-lesson
with a built-in check for
understanding upon
completion. √
Independent/Partner/Group
Work
YOU DO
(20-30 minutes)
Lesson activity including at least
one check for understanding. √
Math centers should be
implemented during this time.
Suggestions:
 Technology
 Problem-based/Skillbased Task
 Vocabulary Work
 Writing in Math
 Art/Music Connections
Summary and
Exit Slip
(10 minutes)
As a class, teacher
should facilitate a
summary of the
day’s targeted
objective then
provide an exit
question (last check
for understanding)
that allows students
to individually prove
their understanding
of the objective. √
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