Kindergarten Math Instructional Focus Units 2015/2016
Instructional Focus Units
Focus 1 Foundations of Counting
Estimated Time
9 Weeks
Focus 2 Foundations in Number Patterns
3 Weeks
Focus 3 Extending Counting Through Measurement and
Composing/Decomposing Numbers within 10
Focus 4 Classifying 2-Dimensional Shapes Composing and Decomposing
3-Dimensional Shapes: Extending Features of 2-D Shapes
Focus 5 Applying Number Concepts to Addition and Subtraction Within
10 and introduction to place value
Focus 6 Extending Addition and Subtraction Within 10
6 Weeks
Focus 7 Developing Foundations of Place Value
4 Weeks
Focus 8 Interpreting Numbers Through Data
3 Weeks
Focus 9 Extending Number System
2 Weeks
1
Standards in BOLD and UNDERLINED are found under major clusters.
3 Weeks
5 Weeks
2 Weeks
Kindergarten Math Instructional Focus Units 2015/2016
***Based on the standards, not all lessons within the resource may be needed to meet the
needs of your students.
2
Standards in BOLD and UNDERLINED are found under major clusters.
Kindergarten Math Instructional Focus Units 2015/2016
Focus 1: Foundations of Counting
At the beginning of the school year students practice the count sequence and start to develop
understanding of cardinality and one-to-one correspondence. Counting is started early and should be
continually practiced throughout the school year. Throughout this focus learners are connecting written
numeral to quantities which will further their understanding of 1:1 correspondence.
Standards
K.CC.A.1
K.CC.A.3
K.CC.B.4
K.CC.B.4
K.CC.B.5
K.CC.C.6
K.CC.C.7
K.G.A.1
K.G.A.2
K.MD.A.1
K.MD.B.3
Estimated
Time
9 weeks
Principal Resource
IDS Unit 1 & IDS Unit
2
Additional Resource
Developing Number Concepts, Book 1: Lesson
1.21, 1.23, 1.24, 1.25, 1.27, 1.32, 3.1, 3.4, 3.6,
3.11, 3.12, 3.21
Developing Number Concepts, Book 2:
Lesson 1.2, 1.3
Van de Walle, pg. 44, 116, 118,
Routines
-IDS Classroom Routines need to be focused on
throughout this focus.
-Quick Images (explanation in Teaching StudentCentered Mathematics K-3, p.44); Number Talks
by Sherry Parrish, pp.70-81
-Problem Solving (see below)
Notes
K.CC.C.6 Make sure to integrate the use of objects when working on comparing. Compare different amounts of
different objects. Example- 4 toothpicks and 6 cubes.
Quick Images Routine This is an ongoing routine that needs to be established early in the school year. Begin with a
small frame of 5 and eventually move up to the use of 10 frames. Use dot arrangements that will support children’s
development of number up to at least 10. Make sure to include 10 and some more later in the school year.
Dreambox has Teacher Tools that incorporate ten frames that can be used at this time.
Problem solving routines can be introduced during or outside of your regular math block. Write story problems (refer
to Common Core, Table 1) and share them under the document camera or Smartboard. Use visuals or objects to
assist with comprehension. Read the problem out loud to your students. Have the students read the problem as a
group. Before students begin to solve the problem ask questions such as, “What does the problem say?” “What
numbers do you see?” “Are we putting together or taking apart?” “Will we have more or less?” “What are you trying
to find out?” This should be completed as a whole group for most of the quarter. Model various problem solving
strategies. Talk aloud to solve the problem. Number equations do not need to be introduced at this time. Eventually
allow student to use math tools and white boards to solve the problems. This routine should grow to be daily and
continue the entire year. Number choices should focus on combinations/differences within 10. Informal
observations will help guide your number choices. Refer to Table 2 for problem types appropriate for kindergarten
students.
Working with data during the Investigations routines is a way to give meaning to number.
Fluency Standards By End Of Year
K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number by using
objects or drawings, and record the answer with a drawing, number or equation.
K.OA.A.5 Fluently add and subtract within 5.
3
Standards in BOLD and UNDERLINED are found under major clusters.
Kindergarten Math Instructional Focus Units 2015/2016
Focus 2: Foundations in Number Patterns
This focus develops ideas about patterns, sequences, and functions. These ideas are an important part of
noticing and describing regularities that occur in the relationships among mathematical objects-both
numbers and shape.
Additionally, counting should be continually practiced.
Standards
K.MD.A.1
K.MD.B.3
K.G.A.1
K.G.A.2
K.CC.A.1
K.CC.A.2
K.CC.B.4
K.CC.B.5
K.CC.C.6
Estimated Time
3 weeks
Principal Resource
IDS Unit 3 (exclude 2.7
and 2.8)
Additional Resource
Teaching Number, pg. 90, 5.2.6
Developing Number Concepts: Book 11-1, pp. 26-27, 1-2, p. 28, 1-3, p. 29, 14, pp. 30-32, 1-6, p. 34, 1-7, p. 34, 113, p. 42, 1-31, p. 62, 1-37, p. 65
Routines
-IDS Classroom Routines (substitute
routines especially when routine is
focused on patterning see notes
below)
-Quick Images : Mini-Lessons for Early Addition and Subtraction (Fosnot)
-Number Talks pp. 70-81
Notes
*Investigations Unit 3, Sessions 2.1-2.9 (excluding 2.7 and 2.8) focuses on repeating patterns. A repeating pattern
activity or a "what comes next activity" should have a purpose more than guessing the right answer. The student
needs to explain their thinking. These activities assist children as they learn to look for pattern and structure in the
number systems (such a counting by 10s to 100, counting objects in a rectangular array and decomposing number.
*Counting should be reinforced throughout the day, not in isolation (see explanations and examples)*Teaching
Number is a great resource to reach all students. This is a great resource for strategies for the emerging, perceptual,
and figurative student. These exercises can become part of your routines and a quick check in. They can also provide
support for those that need additional practice. * This standard will continue throughout the year. The expectation
at the end of the second quarter is that a typical kindergartener will master numbers 0 to 50 with counting.
Fluency Standards By End Of Year
K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number by using
objects or drawings, and record the answer with a drawing, number or equation.
K.OA.A.5 Fluently add and subtract within 5.
4
Standards in BOLD and UNDERLINED are found under major clusters.
Kindergarten Math Instructional Focus Units 2015/2016
Focus 3: Extending Counting Through Measurement and Composing/Decomposing Numbers within 10
Counting and quantity are extended with the application of measurement. Within this focus students will
use nonstandard units to measure length and find the total after a small amount is added to or taken away
from a set. Students will begin making sense of the operations of addition and subtract as they act out
stories and play games involving combining and separating small amounts.
Additionally, counting should be continually practiced.
Standards
K.CC.A.1
K.CC.A.3
K.CC.B.4
K.CC.B.5
K.CC.C.6
K.CC.C.7
K.MD.A.1
K.MD.A.2
K.MD.B.3
K.OA.A.1
K.OA.A.2
K.OA.A.3
Estimated
Time
6 weeks
Principal Resource
IDS Unit 4, Common
Core IDS book Unit 4
1.6A, 1.6B, and 1.6C
Additional Resource
Teaching Number: 5.3.1 81-82, 5.3.2, p. 82,
5.3.3., p. 82: 5.3.3, p. 83: 5.3.4, p 83: 5.3.5, p.
83, Lesson 5B, pp. 94-95: Dice Patterns, Lesson
5C, pp. 96-97
Teaching Student Centered Mathematics, Van
De Walle, p. 41 Counting On With Counters
(2.6), p. 43 Learning Patterns (2.8), p. 44, Dot
Plate Flash (2.9)
Developing Number Concepts, Book 1: 3-1, pp.
146-147, 3-2, pp. 147-148, 3-3, p. 149, 3-4, pp.
150-151, 3-7, p. 15, 3-10, p. 158, 3-11, pp. 159160, 3-12, p. 160, 3-18, pp. 168-169
Games for Early Number Sense (Fosnot)
Routines
-IDS Classroom Routines (substitute routines if
needed for your individual population especially
when routine is focused on patterning)
-Quick Images : Mini-Lessons for Early Addition
and Subtraction (Fosnot)
pp. 12-22 or possibly introduce Math Rack Quick
images pp. 23-43 depending on your population
-Number Talks pp. 70-81
-Problem Solving
Notes
Use routines as appropriate for your population. When problem solving, ensure you are thinking about number
choices.
Fluency Standards By End Of Year
K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number by using
objects or drawings, and record the answer with a drawing, number or equation.
K.OA.A.5 Fluently add and subtract within 5.
5
Standards in BOLD and UNDERLINED are found under major clusters.
Kindergarten Math Instructional Focus Units 2015/2016
Focus 4: Classifying 2-Dimensional Shapes Composing and Decomposing 3-Dimensional Shapes: Extending Features
of 2-D Shapes
A major focus of this unit is observing and describing 2 –dimensional and 3-dimensional shapes in order to build
understandings of shapes and their properties. Students will develop their academic vocabulary to describe the
features of 2-dimensional and 3-dimensional shapes using their own words. Students will analyze, compare and
compose 2-dimensional and 3-dimensional shapes. Students will also begin to make connections between the
geometric concepts of composition and how it is related to composition in our number system.
Additionally, counting should be continually practiced.
Standards
K.G.A.1
K.G.A.2
K.G.A.3
K.G.B.4
K.G.B.5
K.G.B.6
K.CC.A.1
K.CC.A.2
K.CC.B.4
K.CC.B.5
K.CC.C.6
K.MD.B.3
Estimated Time
3 weeks
Principal Resource
IDS Unit 5
Additional Resource
Teaching Student-Centered
Mathematics p. 174
Routines
-IDS Classroom Routines (substitute
routines if needed for your individual
population especially when routine is
focused on patterning)
-Quick Images : Mini-Lessons for Early
Addition and Subtraction (Fosnot)
pp. 12-22 and Math Rack Quick images
pp. 23-43
-Number Talks pp. 70-81
-Problem Solving
-Quick Images: Ten-Frames
Notes
2-dimensional shapes include the following: squares, circles, triangles, rectangles, hexagons.
3- dimensional shapes include: cubes, cones, cylinders and spheres
Fluency Standards By End Of Year
K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number by using
objects or drawings, and record the answer with a drawing, number or equation.
K.OA.A.5 Fluently add and subtract within 5.
6
Standards in BOLD and UNDERLINED are found under major clusters.
Kindergarten Math Instructional Focus Units 2015/2016
Focus 5: Applying Number Concepts to Addition and Subtraction Within 10 and introduction to place value
In this focus students apply counting strategies and their experience with addition to begin to develop understanding
of subtraction as they encounter problems involving taking apart and taking from situations.
Exposure to composing and decomposing teen numbers will begin at the end of this focus unit but mastery
of the standard is not expected.
Additionally, counting should be continually practiced.
Standards
K.CC.A.1
K.CC.A.2
K.CC.A.3
K.CC.B.4
K.CC.B.5
K.CC.C.6
K.CC.C.7
K.OA.A.1
K.OA.A.2
K.OA.A.3
K.OA.A.4
K.OA.A.5
K.NBT.1
Estimated Time
5 weeks
Principal Resource
Additional Resource
IDS Unit 6, Investigations
Teaching Student-Centered Mathematics
1, 2, 3, & 4; Common Core Activity 2.9: p. 44 Dot Plate Flash
IDS book Unit 6, 5A.1-5A.5
Developing Number Concepts, Book 2
Internalizing Number Combinations to 10
(pp.42-160). There are many learning
opportunities centered on OA standards in this
resource that can be utilized for small group
instruction as needed.
Games for Early Number Sense (Fosnot)
Routines
-IDS Classroom Routines (substitute routines if
needed for your individual population
especially when routine is focused on
patterning)
-Mini-Lessons for Early Addition and
Subtraction: Quick Images on the Arithmetic
Rack pp. 23-43,
-Quick Images: Ten-Frames
Notes
Teacher-developed problem solving should take place during this focus. Refer to the problem types table attached to
this document for suggestions.
The end of IDS unit 6 common core lessons 5A.3-5A.5 are intended to provide a brief exposure to place value to give
students an opportunity to start working with teen numbers. K.NBT.A.1 will be addressed in-depth during focus
unit 7.
Fluency Standards By End Of Year
K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number by using
objects or drawings, and record the answer with a drawing, number or equation.
K.OA.A.5 Fluently add and subtract within 5
7
Standards in BOLD and UNDERLINED are found under major clusters.
Kindergarten Math Instructional Focus Units 2015/2016
Focus 6: Extending Addition and Subtraction Within 10
In this focus, students use addition and subtraction equations, and student writing of equations in
kindergarten is encouraged. Students choose and apply effective strategies for joining and separating
numbers.
Additionally, counting should be continually practiced.
Standards
K.OA.A.1
K.OA.A.2
K.OA.A.3
K.OA.A.4
K.OA.A.5
K.CC.A.1
K.CC.A.2
K.CC.A.3
K.CC.B.4
K.CC.B.5
K.CC.C.6
Estimated Time
2 weeks
Principal Resource
Fosnot Bunk Beds and
Apple Boxes
Additional Resource
Developing Number Concepts Book 2:
(Internalizing Number Combinations to
10 pg. 42-160. There are many
learning opportunities centered on OA
standards in this resource that can be
utilized for small group instruction as
needed.)
Games for Early Number Sense
(Fosnot)
Routines
-Quick Images with Dreambox using
teacher tools
-Number Talks using math racks
-Problem solving routine
-Fosnot mini-lessons included in unit
Notes
Problem solving routines should be continued within the context of this year.
Fluency Standards By End Of Year
K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number by using
objects or drawings, and record the answer with a drawing, number or equation.
K.OA.A.5 Fluently add and subtract within 5.
8
Standards in BOLD and UNDERLINED are found under major clusters.
Kindergarten Math Instructional Focus Units 2015/2016
Focus 7: Developing Foundations of Place Value
In this focus, students are building a foundational understanding of the base-ten system by developing an
understanding of the teen numbers as being composed of ten ones and some more ones. The number range in this
standard emphasizes the understanding of ten ones rather than an understanding of the tens place. This work is an
opportunity for students to start counting on, which is a Level 2 strategy for addition that will be emphasized in Grade
1. Teachers are encouraged to use addition and subtraction equations to model the situations.
Additionally, counting should be continually practiced.
Standards
Estimated Time
Principal Resource
K.NBT.A.1
4 weeks
Replacement Unit (will
K.CC.A.1
be posted on
K.CC.A.2
SchoolWires)
K.CC.A.3
Common Core IDS book
K.CC.B.4
Unit 6, 5A.3-5A.5
K.OA.A.1
(review from IFU 5)
K.OA.A.2
K.OA.A.3
K.OA.A.4
Additional Resource
Games for Early Number Sense
(Fosnot)
Developing Number Concepts Book 2
p.157 (3-30) Focus on Addition: Ten
Plus a Number and Subtraction: Minus
Ten
Routines
-Minilessons for Early Addition and
Subtraction
-Number Talks
Notes
Within this focus students will compose and decompose numbers from 11 to 19 into ten ones and some further ones
using objects or drawings, and record each composition or decomposition by a drawing or equation (such as
18=10+8); understand that these numbers are composed of ten ones and one, two three, four, five six, seven, eight,
or nine ones.
The teachers role within this unit will be to provide opportunities for children to discuss the meaning of a composition
or decomposition problem (e.g., “What does 19=10+9 mean, one group of 10 and 9 ones, can you draw something to
represent this problem?” Application with problem solving will ensure students are moving toward understanding vs.
rote learning of this crucial mathematical idea.
Fluency Standards By End Of Year
K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number by using
objects or drawings, and record the answer with a drawing, number or equation.
K.OA.A.5 Fluently add and subtract within 5.
9
Standards in BOLD and UNDERLINED are found under major clusters.
Kindergarten Math Instructional Focus Units 2015/2016
Focus 8: Interpreting Numbers Through Data
In this focus, students will utilize their number foundations to collect, represent, and interpret information.
Students are using counting as a tool for describing their world and solving problems.
Additionally, counting should be continually practiced.
Standards
K.CC.A.1
K.CC.A.2
K.CC.B.4a
K.CC.B.4b
K.CC.B.4c
K.CC.B.5
K.CC.C.6
K.MD.B.3
Estimated Time
3 Weeks
Principal Resource
IDS Unit 7,
Investigations 1, 2 (2.6
only), 3
Common Core IDS book
Unit 7, 1.7A
Additional Resource
Teacher-created
Routines
-Quick Images with Dream box using
teacher tools
-Number Talks using math racks and
ten frames
-Problem solving routine
-Mini-lessons for Early Addition and
Subtraction
Notes
Working with data gives students the opportunity to apply addition and subtraction in a natural context. Problem
types of result unknown, total unknown and two addends unknown are the kindergarten problem sub-types (see
attached Table 2). The types of questioning used by the teacher to compare data can be used to extend children’s
problem solving experiences.
10
Standards in BOLD and UNDERLINED are found under major clusters.
Kindergarten Math Instructional Focus Units 2015/2016
Focus 9: Extending Number System
In this focus, students will explore doubles while strengthening their understanding of one-to-one
correspondence.
Additionally, counting should be continually practiced.
Standards
K.CC.A.1
K.CC.A.2
K.CC.A.3
K.CC.B.4
K.CC.B.4a
K.CC.B.4b
K.CC.B.4c
K.CC.B.5
K.OA.A.1
K.OA.A.2 (numbers
extend beyond 10)
K.OA.A.3
Estimated Time
2 weeks
Principal Resource
Fosnot Unit, Beads and
Shoes Making Twos
Additional Resource
Games for Early Number Sense
(Fosnot)
Routines
-Quick Images with Dreambox using
teacher tools
-Number Talks using math racks and
ten frames
-Problem solving routine
-Mini-lessons for Early Addition and
Subtraction
Notes
Fluency Standards By End Of Year
K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number by using
objects or drawings, and record the answer with a drawing, number or equation.
K.OA.A.5 Fluently add and subtract within 5.
11
Standards in BOLD and UNDERLINED are found under major clusters.
Kindergarten Math Instructional Focus Units 2015/2016
Table 1: Common addition and subtraction situations.6
Result Unknown
Two bunnies sat on the grass.
Three more bunnies hopped there.
How many bunnies are on the grass
now?
2+3=?
Add to
Difference Unknown
(“How many more?” version):
Lucy has two apples. Julie has five
apples. How many more apples
does Julie have than Lucy?
Bigger Unknown
(Version with “more”):
Julie has three more apples than
Lucy. Lucy has two apples. How
many apples does Julie have?
Some apples were on the table. I
ate two apples. Then there were
three apples. How many apples
were on the table before?
?–2=3
Both Addends Unknown1
Grandma has five flowers. How
many can she put in her red vase
and how many in her blue vase?
5 = 0 + 5, 5 = 5 + 0
5 = 1 + 4, 5 = 4 + 1
5 = 2 + 3, 5 = 3 + 2
Smaller Unknown
(Version with “more”):
Julie has three more apples than
Lucy. Julie has five apples. How
many apples does Lucy have?
(“How many fewer?” version):
Lucy has two apples. Julie has five
apples. How many fewer apples
does Lucy have than Julie?
2 + ? = 5, 5 – 2 = ?
(Version with “fewer”):
Lucy has 3 fewer apples than Julie.
Lucy has two apples. How many
apples does Julie have?
2 + 3 = ?, 3 + 2 = ?
(Version with “fewer”):
Lucy has 3 fewer apples than Julie.
Julie has five apples. How many
apples does Lucy have?
5 – 3 = ?, ? + 3 = 5
Five apples were on the table. I ate
two apples. How many apples are
on the table now?
5–2=?
Take from
Put Together /
Take Apart2
Compare3
Total Unknown
Three red apples and two green
apples are on the table. How many
apples are on the table?
3+2=?
Change Unknown
Two bunnies were sitting on the
grass. Some more bunnies hopped
there. Then there were five
bunnies. How
many bunnies hopped over to the
first two?
2+?=5
Five apples were on the table. I
ate some apples. Then there were
three apples. How many apples
did I eat?
5–?=3
Addend Unknown
Five apples are on the table. Three
are red and the rest are green.
How many apples are green?
3 + ? = 5, 5 – 3 = ?
Start Unknown
Some bunnies were sitting on the
grass. Three more bunnies hopped
there. Then there were five
bunnies. How many bunnies were
on the grass before?
?+3=5
6
Adapted from Box 2-4 of Mathematics Learning in Early Childhood, National Research Council (2009, pp. 32, 33).
1These
take apart situations can be used to show all the decompositions of a given number. The associated equations, which have the total on the
left of the equal sign, help children understand that the = sign does not always mean makes or results in but always does mean is the same number
as.
2Either
addend can be unknown, so there are three variations of these problem situations. Both Addends Unknown is a productive extension of this basic situation,
especially for small numbers less than or equal to 10.
3For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version using more for the bigger unknown and using less for
the smaller unknown). The other versions are more difficult.
12
Standards in BOLD and UNDERLINED are found under major clusters.