Laura Kunz
CCLM^2 Project
Summer 2012
DRAFT DOCUMENT. This material was developed as part of the
Leadership for the Common Core in Mathematics (CCLM^2) project at the University of Wisconsin-Milwaukee.
Part 1: Standard
Grade: Kindergarten
Domain: Operations and Algebraic Thinking
Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart
and taking from.
Standard: For any number from 1 to 9, find the number that makes 10 when added to the given number,
e.g., by using objects or drawing, and record the answer with a drawing or equation.
Part 2: Explanation and Examples of the Standard
a) Explanation: Use resources to help you interpret concepts, key terms or phrases within the standard.
Write an explanation of the standard in a teacher-friendly language, pulling it apart as needed for analysis.
Teacher Friendly Language of K.OA.4à Students should be proficient at finding addition combinations with
sums to 10 using numbers 1-9. Students should be able to communicate their thinking through the use of
objects, drawings and or written equations.
b) Examples: Provide examples of what these mathematical ideas may look like in classroom practice (what
students are expected to do), and how teachers and students should be talking about these mathematical
ideas.
Students need to be fluent in these mathematical problems with sums to 10:
1+9=10
2+8=10
3+7=10
4+6=10
5+5=10
9+1=10
8+2=10
7+3=10
6+4=10
In order for students to enhance their mathematical understanding… Their sense of how numbers relate to
one another needs to improve. Students will be able to extend their thinking when they are demonstrating
proficiency in K.OA. 5 (Fluently add and subtract within 5) to support and progress to achieving K.OA.4.
Examples that support K.OA.4 for teachers to utilize within their classroom are as follows:
Tens Frame
A ten-frame is a 5x2 array used to support the development of this important landmark numbers five and
ten (Conklin, 2010, p. XV). A ten-frame operates horizontally and left to right. The ten-frame allows
students to visualize numbers based on K.OA.3 and building upon their understanding to reach proficiency in
understanding sums to 10. Ten-frames are a model to help students efficiently gain and develop
understanding of addition and subtraction (as cited in Culkin, 2010, p. xvii). In relation to the Common Core
Kindergarten K.OA.4 standard, the ten-frame is a useful tool for students to apply in relation to sums to 10.
The tens frame can be manipulated in many ways to enforce sums to 10. Here’s a list of games that
stemmed from It Makes Sense! Using Ten-Frames to Build Number Sense. Written by Melissa Conklin,
2010.
Game/Lesson
Look, Quick!
Conklin, 2010, p.4
Dot Card Memory
Conklin, 2010, p.70
More or Less- Recording
Combinations of 10
Conklin, 2010, p.86
Make 5
Conklin, 2010, p.92
Collect Ten
Conklin, 2010, p.100
How to play…
Using the tens frame, place
counters on the board and ask
students to analyze what they
saw.
Student subitize the dots on the
card in relation to the tens frame.
This encourages students to figure
out how many dots are on the
card in relation to grouping.
Students play in pairs where they
roll die to place X amount of
counters on the tens frame.
Conclude that squares with
counters + empty squares=10
Utilizing the top portion of a tenframe, students will explore with
the various combinations in
making sums to 5. Discovering
sums to 5 builds upon Level 1
counting on strategy when
working with sums to 10.
Students use numbered cards 1-9
where students are dealt 5 cards
and they determine the
pairs/sums to 5 are. Rules then
proceed to mimic “Go Fish” where
you ask player 2 for the partner
card.
Relation to K.OA.4
Reinforcing base 10; if there are
X counters on the board, how
many blank squares are there= 10
If there are 9 dots on the ten
frame- students can rationalize
that by saying 10 total squares
and one was empty, therefor
9+1=10
Making sums of 10 while
recording the combinations.
Five is an important milestone for
students to manipulate and
discover within addition and
subtraction (K.OA.3) Therefore
knowing 5+5= 10 as a doubles
problem will aide in students’
fluency to knowing sums to 10.
Showing sums of ten in a
numerical representation. While
allowing students to use the tens
frame prior to asking their
partner the card they are looking
for.
Within the Mequon- Thiensville School District, we currently teach mathematics utilizing the
Everyday Mathematic Curriculum. Relating the Common Core Standard (K.0A.4) in particular to the
Everyday Math Curriculum, here are examples in which reinforce the K.0A.4 standardàFor any number
from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or
drawing, and record the answer with a drawing or equation.
Game/Lesson
Lesson 1.14 Finger Count Fun
Details
Utilizing their fingers they are
presented with a number and
need to count on until they reach
10.
Lesson 2.9 Number Board
Presenting the students with a
visualization of the meaning of
numbers.
Relation to K.OA.4
Reinforces counting and building upon
their understanding numbers 0-10
1
2
3
4
5
6
7
8
9
10
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Allowing students to see the
relationship similar to a tens-frame
where 1+9=10 etc…
Lesson 2.14 Number Stories:
Stage 1
Lesson 4.14 Number Stories:
Stage 2
This is the beginning stages of
acquainting students with story
problems through the use of
addition.
Asking students to represent their
thinking using objects or drawings.
Project 2 p. 124 Mathematic
and Our Bodies
Encouraging students to use their Providing students with various
bodies as an opportunity to help strategies/outlets in obtaining sums
them solve mathematical
to 10.
equations. Specifically, using
fingers as a way to show sums
to 10.
Lesson 3.13 Train Games
Tweaking this lesson to have
student make cube trains to
sums of 10. Find the missing
number.
Maintain one to one correspondence
with counting while familiarizing
students with addition and
subtraction within 0-10.
Lesson 4.4 The Addition Symbol
(_)
Introduce students with
terminology and symbols in
relation to number stories.
Expanding upon the idea of students
reaching sum of 10 through a visual
representation.
Lesson 7.2 Class Number Story
Book
Heighten students understand of
story problems.
Students will created story problems,
base 10, through drawings while
communicating their work with their
classmates to justify their reasoning.
Lesson 8.13 Missing Number
Problems
Students are presented with
concrete addition equations
where one addend is missing
revolving around sums to 10.
Focusing on the Communitive
Property
If 4+6=10 then 6+4=10
Part 3. School Mathematics Textbook Program
a) Textbook Development: Within the Kindergarten Everyday Mathematics curriculum, the Common Core
Standard K.0A.4 is intertwined throughout the text.
After previewing the 1st grade curriculum within Everyday Math, I have noted several observations:
-Within 1st grade, a large amount of time is allocated to games with emphasis on addition and subtraction to
10. The games are a stepping-stone from games learned in Kindergarten (ex: Top It)
-There is minimal exposure of sums to 20.
-The games played in 1st grade don’t promote discussions for students to develop that deeper level of
understanding.
- The first grade material still remains stagnant in level 1 counting and little emphasis on progression into
level 2 and 3counting strategies.
-As referenced in the Kindergarten curriculum, the 1st grade materials seem to operate in a similar “milewide, inch deep” mentality.
-The 1st grade curriculum continues to operate in the upward spiral notion.
b) Conclusions and Suggestions: I have been teaching within the Everyday Math Program for four years. I
have found the program to operate in an “upward spiral” notion. The content that is covered within the
Kindergarten curriculum is age appropriate yet doesn’t do an adequate job in “digging deeper” into various
concepts. The Everyday Math curriculum may have a teacher teaching about patterns on Monday and
measurement on Tuesday… The idea is that students are exposed to a concept and will continue to build on
their foundation when the concept is revisited again (roughly two weeks later).
In my opinion, I appreciate the fact that the Kindergarten curriculum allows for flexibility and
supplementation. As I continuously evaluate and assess my students on a daily basis, I may pause from the
curriculum to take extra time to reinforce particular concepts, which are critical to grasp before moving on. I
believe the curriculum could be revamped by spending more time on the introductory portion of
concepts/skills to develop students into thinking with a deeper understanding. Concepts are introduced too
quickly with a lack in supplementation at an independent level for the students to practice with.
I would like to see the Everyday Math curriculum put more emphasis on number writing, number
drawing and working with manipulatives. I have appendage this notion through the use of journaling to
encourage student thinking through pictures and visualizing. I am able to elaborate this concept through
small group instruction, which is not addressed throughout the material.