Using Ten Frames to Teach
Number Sense with Students with
Significant Disabilities
Ann Jacobson, MEd, MRT
[email protected]
Nichole Kertis, LOT
[email protected]
Available electronically at
http://www.livebinders.com/edit?id=282660
or
http://tinyurl.com/883ndq3
or
INTRODUCTION
Concrete-Representational-Abstract (CRA) Sequence
The CRA sequence enables students to understand the concepts prior to
memorizing facts, algorithms, and operations. The CRA sequence helps
students with learning difficulties by showing the students meaningful
connections, teaching conceptual understanding, providing a graduated
framework for learning, and blending conceptual and procedural
learning.
Concrete
 Three-dimensional objects (i.e., manipulatives)
Representational
 Two-dimensional drawings
Abstract
 No objects or drawings
For students with learning difficulties the CRA sequence:

Shows students meaningful connections

Teaches conceptual understanding

Provides a graduated framework for learning

Blends conceptual and procedural learning
Concrete

Concept/skill modeled with concrete materials (i.e., manipulatives)

Manipulatives are objects that can be used to help students
understand mathematics

National Council of Teachers of Mathematics (NCTM) suggests
manipulatives should be used as part of the process of teaching
math

Manipulatives can be purchased or created
o Household (i.e., pennies, spoons) and classroom (i.e., paper
clip, construction paper) objects can be used
•
Manipulative examples:
o Bears, bugs, dinosaurs
o Colored chips
o Unifix cubes
o Golf tees
o Candy
o Bean bags
o Popsicle sticks
o Base-10 blocks
o Beans and bean sticks
o Dominoes
o Buttons
o Counters
o Fraction bars
o Pizza slices
o Tangrams
o Pentominoes
o Geoboards
o Algeblocks
Tips for using manipulatives:
o Don’t call manipulatives “toys”
o Allow students free play time (15-20 min) to explore and experiment
o Free play time reduces the likelihood that students will not
pay attention during lesson
o Establish rules and consequences
o Do not touch unless teacher directs
o Establish a routine for distributing and collecting
o Don’t ask student to memorize manipulative procedures
o Manipulatives are a tool, but not the focus of instruction
o Students don’t learn math simply because they use manipulatives
o Discussion, interaction
o Not all students benefit from using manipulatives
o Assist with the transition from manipulatives (concrete) to nonmanipulatives (representational)
o Work with other teachers to develop a manipulative library
NUMBER SENSE
Number sense is the ability to know what numbers mean. Some important
number sense activities include the following:
Counting
 One-to-one correspondence
 Counting forward
 Counting backward
 Counting on
 Skip counting – 2s, 5s, 10s
Comparing numbers
 Before and after
 More and less
BASIC FACTS
There are 390 “basic facts” for addition, subtraction, multiplication, and
division. Instruction should focus on the following:
Conceptual understanding
 What the operation means
Procedural development
 Step-by-stop procedures for advanced problems
 Strategies for answering non-memorized facts
Declarative knowledge
 Factual memory of facts
Problem-solving ability
 Transfer of previous learning to new situations
Addition and Subtraction Basic Facts
100 addition basic facts: Combinations of single-digit addends that result
in a single- or double-digit sum
100 subtraction basic facts: Combinations in which the subtrahend and
difference are single-digit numbers and the minuend is either a single- or
double-digit number
Addition and Subtraction Basic Facts

Suggested order of introduction
o Doubles (3 + 3, 14 – 7)
o Facts that involve one (3 + 1, 8 – 1)
o Facts that involve zero (4 + 0, 9 – 0)
o Facts that involve one more than doubles (5 + 6)
o Reciprocals (5 + 4 and 4 + 5)

Suggestions for instruction
o Introduce 3 or 4 facts at a time, beginning with the easiest
(+1, +2, doubles)
o Keep related facts together (2 + 1, 3 + 1, 4 + 1)
o Introduce reverse of facts soon after first fact is presented (3 +
2 and 2 + 3)
o Teach facts 0-9 and then 10-18

Whole-number properties of addition
o Commutative property (4 + 3 = 3 + 4)
o Associative property [ (5 + 1) + 2 = 5 + (1 + 2) ]

Strategies for addition and subtraction
o Number-after rule or one rule
o Zero rule
o One more strategy
o Counting-on strategy
o Doubles +1 strategy
o Related facts strategy
o Counting-up strategy
Ten Frame Activities
How Many?
-
Counters placed in a consistent order
-
Goal is to achieve automaticity – to recognize the amount
without counting
Build the Number
-
Student is able to place the correct number of counters on the
10 frame, in the appropriate places, when told a number
More or Less?
-
Student is able to compare two 10 frames or a 10 frame and a
number and determine which is more and which is less
Ten Frame Activities
How Many More to 10?
-
Student is able to determine how many empty spaces in a 10
frame
Addition Facts
-
Student is able to use counters to solve simple addition problems.
(Consider using a different color counter for each addend.)
The Double Ten Frame
-
May be used for above activities with larger numbers. (Look for
student readiness to move to a 100s chart.)
Skip Counting
-
Limited use for recognizing skip counting patterns – probably
time to move to the 100s chart!
Resources
Ten Frame Ideas
http://illuminations.nctm.org/ActivityDetail.aspx?ID=75
Complements to Ten
http://www.education.vic.gov.au/studentlearning/teachingresources/ma
ths/mathscontinuum/number/N15compten2.htm#1
Using Excel as a Graphic Organizer: Making a Ten Frame (to use on a
Smart Board)
http://www.internet4classrooms.com/excel_ten_frame.htm
Smartboard Ten Frame
http://www.youtube.com/watch?v=aQ0cpiD_dO4&feature=related
Dot Frames Lesson 1
http://www.youtube.com/watch?v=OBSO3PvC67c&NR=1
10 Facts with a 10 Frame
http://www.youtube.com/watch?v=h_xFBoSEyj8&feature=channel
Ten Frame
http://www.youtube.com/watch?v=vlrDL1qUdlA&feature=related
Games for developing a visual sense of number to 10
http://mindfull.files.wordpress.com/2007/10/games-we-played-today.pdf
Tens Frame and Place Value Games
http://nrich.maths.org/2479
Use Tens Frames to Teach Guided Math Lessons
http://guidedmath.wordpress.com/2010/03/31/use-ten-frames-to-teachguided-math-lessons/
Building Numbers Up to Ten
http://illuminations.nctm.org/LessonDetail.aspx?ID=L547
Must Have: Free Ten Frame Flashcards!
http://www.montgomeryschoolsmd.org/schools/oaklandes/mathstudent
workpages/gr1un2page6.html
Free Customizable Tens Frames Graphic Organizer
http://www.teachervision.fen.com/addition/graphicorganizers/44567.html
Five and Ten Frame Resources
http://www2.carrollk12.org/instruction/elemcurric/math/tframes.HTM
It’s a Fact!
http://www.uen.org/Lessonplan/preview.cgi?LPid=10985
Effective Uses for Ten Frames
http://lrt.ednet.ns.ca/PD/BLM/table_of_contents.htm
Mathematics Blackline Masters Grades P to 9
http://lrt.ednet.ns.ca/PD/BLM/table_of_contents.htm
Ten Frames War Game
http://elemed.ucps.k12.nc.us/parent_resources/PA%202_1_1%20Tens%20
Game.pdf