Unit 2: Decomposing Unit Outline – Kindergarten
Unit Goal - Students are able to recognize that numbers can be decomposed in more than one way.
Unit Topic and Length
This unit focuses on initial addition concepts with objects,
drawings (mathematical diagrams), dramatization, verbal
explanations or expressions and equations. Students at the
standard will work on decomposing numbers up to 10 (up to
20 for extension), using and recording their work with
objects, drawings and or equations.
During the unit students will be given opportunities to
manipulate and group physical objects and drawings to
develop basic understanding of the concepts of number. They
group objects into sets (collections) and form simple
correspondences (relations) between two sets; for example,
in sharing pencils among students.
For developmental reasons this unit should happen in the
second half of the year and can last several weeks. (In
Kindergarten, routines and games that support the
mathematics in this unit should be happening all year
and are not limited to one unit.)
Common Core Learning Standards
K.OA.1 Represent addition and subtraction with objects,
fingers, mental images, drawings, sounds (e.g., claps), acting
out situations, verbal explanations, expressions, or equations.
K.OA.3 Decompose numbers less than or equal to 10 into
pairs in more than one way, e.g., by using objects or drawings,
and record each decomposition by a drawing or equation
(e.g., 5 = 2 + 3 and 5 = 4 + 1).
K.CC.4 Understand the relationship between numbers and
quantities; connect counting to cardinality.
Standards of Mathematical Practice
MP. 1 Make sense of problems and persevere in solving them.
MP. 3 Construct viable arguments and critique the reasoning
of others.
MP. 4 Model with mathematics
MP. 6 Attend to precision
Big Ideas/Enduring Understandings
Essential Questions
- Mathematicians can organize, represent, and compare the
same number using different groupings (numbers or objects).
- Mathematicians can explain how numbers are organized,
represented, and compared.
- How do we show that numbers work together?
- How can we show and explain our thinking?
- Have we found all the possibilities? How do we know?
- Can you see a pattern? Can you order your solutions? What
you notice when you order them?
- What made you decide to do it that way?
Content
Skills
Numbers and quantities up to 10
- Order of numbers
- One to one correspondence
- Count
- Written numbers up to 10
- Quantities up to 10
_________________________________________________________
Addition and subtraction (this mentioned in the Instructional
Bundle but not covered in the unit) up to 10 with objects
_________________________________________________________
Number composition and decomposition
- Put together/take apart number strategies.
Numbers less than and up to 10, not including zero, can be
composed and put back together in more than one way.
- Recognize and name numbers up to 10
Development Stages to Consider
1) Students recognize that 4 + 6 has the same answer as 6 + 4.
If they know the answer to one, then they know the answer to
the other.
- Count up to 10 orally
- Match a written number to objects
- Sequence numbers 1-up to 10
- Write numbers 1 – up to 10
- Count a number of objects
- Demonstrate that numbers have a quantity using objects
_________________________________________________________
- Add objects to a set to show a number
- Take away objects in a set to show a number
- Manipulate objects to show a number sentence
- Demonstrate at least 2 different combinations of objects for
one number
- Explain how to add or subtract objects to show a different
number
2) Students can use the known fact to solve missing numbers
tasks. For example, if they know 6 + 4 = 10, they can use this
fact to solve tasks like 6 + ? = 10 or ? + 6 = 10.
3) Students recognize the relationship between addition and
subtraction, and that if they know 6 + 4 = 10, then they know
that 10 − 6 = 4 and 10 − 4 = 6.
Key Terms/Vocabulary
Add, Subtract, Explain, Equals, The Same As, Put Together,
More Than, Less Than, Plus, Altogether, Addition, Biggest,
Number Line, Count On, Count All
Differentiation Strategies/Grouping
Decisions
Tiered assignments - Tiered assignments are
designed to instruct students on essential skills that
are provided at different levels of complexity,
abstractness, and open-endedness. The curricular
content and objective(s) are the same, but the
process and/or product are varied according to the
student’s level of readiness.
Compacting - Compacting is the process of adjusting
instruction to account for prior student mastery of
learning objectives. Compacting involves a threestep process: (1) assess the student to determine
his/her level of knowledge on the material to be
studied and determine what he/she still needs to
master; (2) create plans for what the student needs
to know, and excuse the student from studying what
he/she already knows; and (3) create plans for
freed-up time to be spent in enriched or accelerated
study.
Interest Centers or Interest Groups - Interest
centers (usually used with younger students) and
interest groups (usually used with older students)
are set up so that learning experiences are directed
toward a specific learner interest. Allowing students
to choose a topic can be motivating to them.
Flexible Grouping1∗ - Students work as part of
many different groups depending on the task and/or
content. Sometimes students are placed in groups
based on readiness, other times they are placed
based on interest and/or learning profile. Groups
can either be assigned by the teacher or chosen by
the students. Students can be assigned purposefully
to a group or assigned randomly. This strategy
allows students to work with a wide variety of peers
and keeps them from being labeled as advanced or
struggling.
Learning Contracts - Learning contracts begin with
an agreement between the teacher and the student.
The teacher specifies the necessary skills expected
to be learned by the student and the required
components of the assignment, while the student
identifies methods for completing the tasks. This
strategy (1) allows students to work at an
appropriate pace; (2) can target learning styles; and
(3) helps students work independently, learn
planning skills, and eliminate unnecessary skill
practice.
Choice Boards - Choice boards are organizers that
contain a variety of activities. Students can choose
1
one or several activities to complete as they learn a
skill or develop a product. Choice boards can be
organized so that students are required to choose
options that focus on several different skills.
Initial (pre) Assessment – Goldfish (from
Common Core Instructional Bundle)
Formative Assessment – Total of Six, Seven
Butterflies in the Net, Counters in a Cup
Summative Assessment (Final
Performance Task) Making Apple Eight
Packs
Learning Intention
- Exploring combinations of 5
and begin to realize that some
problems have more than one
answer.
- Use numbers, pictures
and/or words to represent a
solution to a problem.
- Exploring combinations of 5
and begin to realize that some
problems have more than one
answer.
- Decomposing numbers in
different ways.
- Using numbers to record
Differentiation
Strategy
Main Activity
Pre-Assessment - Goldfish
Goldfish (from Common Core Instructional Bundle)
Investigations Unit 6, Session 4.1, page 138 – Five Crayons in All.
Flexible Grouping
Extension – Try to find all possible solutions. How do you know you
have found them all?
Flexible Grouping
Sums of Five game – From Common Core Instructional Bundle
Investigations Unit 6, Session 4.2, page 143 – Combinations of Six.
Center Projects
Center One – Toss the Chips
how many.
Center Two – Racing Bears
Extension – Challenge students to collect as many counters as they can
on each turn. Students will need to consider splitting a roll among bears
on different tracks.
- Finding combinations of Six
- Combining two single-digit
Center Projects
numbers with totals of six
- To use numbers and addition
notation when recording
- Finding combinations of Six
- Make a T Table to represent
their thinking
Investigations Unit 6, Session 4.3, page 143 – Total of Six.
Center One – Total of Six (formative assessment)
Center Two – Toss the Chips
Center Three – Racing Bears
Extension – Try to find all possible solutions. Can you see a pattern? Can
you order your solutions?
Investigations Unit 6, Session 4.3, page 143 – Total of Six .
Center Projects
- Finding Combinations of Five
and Eight
- Explore problem solving
Tiered
strategies to support their
Investigation
thinking
Center One – Total of Six (formative assessment)
Center Two – Toss the Chips
Center Three – Racing Bears
Center Four – Six Crayons in All
Five Fingers
One hand behind back, three, two, one countdown. Pairs put fingers up
to make the number five together. Did it make five? Too many, too less?
Try again. How many different ways have you made 5?
Seven Butterflies in the Bug Catcher (formative assessment).
There are seven butterflies in the butterfly net. They are blue and pink.
How many are blue? How many are pink? What are some other ways?
Possible Problem Solving Strategies:
Draw a Diagram - . : etc
Make a Model – use unifix cubes
Make a Table –
Write a Number Sentence
Look for a Pattern
Solve a Simpler Related Problem
- Finding a combination of 10
- Students to think of a story
that represent their TenFrame
- Finding different
combinations that make 10
- Explore problem solving
strategies to support their
thinking
Problem Based
Inquiry
Tiered Activity
Extension: Add a third colour, change the number from 10 to 12
Counters in a Cup – From Common core Instructional Bundle (formative
assessment)
Warm Up
Ten children stand up. How can we divide this group of children into
two groups? Range of responses, eg. Boys/girls, blond hair/not blond
hair, sneakers/school shoes. What can you tell me about numbers in
each group? Model responses
Main Activity
Tell Me the Story of Ten – Give blank 10s frames and twenty colored
counters. I want you to make ten on the ten-frame then tell me about it.
Record stories on whiteboard. Ten can be made in many different ways.
10 is 5 and 5. 10 is 4 and 6…etc. Children to complete their own tens
frames and record findings.
Ms Castronovo received a phone call saying there are 10 new students
coming into our classroom. What are the possible combinations of boys
and girls?
Draw a diagram showing boys and girls. Write a number sentence (5
boys + ? girls) = 10.
Possible Problem Solving Strategies:
Draw a Diagram - . : etc
Make a Model – use unifix cubes
Make a Table –
Write a Number Sentence
Look for a Pattern
Solve a Simpler Related Problem
- To consider different
combinations of a given
number
Ability Group
Number line and the Frog
With number line on the floor and frog on zero, while I wasn’t looking it
jumped. When I turned around it was on number ?? (Give students a
different number based on their ability - up to 20). I know I heard it land
at least once. What length of jumps would the frog have jumped to get
there? Alternatives: Number line to ten, one long jump and one short
jump, two jumps, three or more jumps.
Individual Group
Work
Performance Task - Making Apple Eight Packs
Worksheet attached to the wiki.
Learning Plan and Activities
Some Extra Examples of Rich Tasks we could use:
1. Make 10 on the Ten Frame, Bunk Bed Problem, Counters in a Cup
2. Math Continuum Support Ideas:
http://www.education.vic.gov.au/studentlearning/teachingresources/maths/common/11subitisingtool.htm
http://www.education.vic.gov.au/studentlearning/teachingresources/maths/common/12mentalobjecttool.htm