MATHRACKS:
TOOLS FOR BUILDING
FLUENCY
IN THE UNITED STATES, THE
MANIPULATIVES MOST COMMONLY USED
WITH YOUNG CHILDREN ARE SINGLE
OBJECTS THAT CAN BE COUNTED…
Catherine Fosnot
“MATHRACKS SUPPORT
CHILDREN TO MOVE AWAY FROM
COUNTING BY ONES, TOWARDS
THE USE OF STRATEGIES LIKE
DOUBLES, ADDITION,
SUBTRACTION AND MAKING
TENS - A GREAT WAY TO HELP
AUTOMATIZE THE BASIC FACTS.”
Catherine Fosnot
WHAT IS FLUENCY?
▸ Fluency has three components.
▸ 1. Accuracy
▸ 2. Efficiency
▸ 3. Flexibility
RUSSELL, 2000
Borrowed with permission from Christina Tondevold, “Fluency Through Flexibility” March 2015
TYPICALLY DEVELOP FROM EXPERIENCES BY 4 1/2 YEARS OLD
4 ASPECTS OF EARLY NUMERACY
▸ Counting
▸ Enumerating
▸ Cardinality
▸ Subitizing
Clements and Sarama, 2004
4 NUMBER SENSE RELATIONSHIPS
▸ Spatial Relationships
▸ One & Two More, One & Two Less
▸ Benchmarks of 5 & 10
▸ Part-Part-Whole
Van De Walle, 2014
Contexts
for Using
Mathracks
From Mastering the MathRack by Christina Tondevold 2011
SHOW ME
▸ Students will model problems using the mathrack
▸ Give students a context and a number
▸ Students build it (concrete), draw it or show it on a number
path (representational), and write equation (abstract)
▸ Continue with other numbers
▸ Challenge students to find other/all ways to represent
number
From Mastering the MathRack by Christina Tondevold 2011
I WISH I HAD
▸ Show 10 or less on a MathRack
▸ Children respond with how many more to make 10
▸ Can use their MathRacks to double check their response
▸ Can also show problem on a number path
▸ Can extend with larger numbers to 20 or with subtraction
From Mastering the MathRack by Christina Tondevold, 2011
HIDDEN NUMBERS
▸ Have the children build 13 on the MathRack and write that
number down.
▸ Then, show number with Place Value Cards. Partner up so
one child can flip cards over to see MathRack
representation.
▸ Talk about the hidden number and write the equation 13 =
10 + 3
▸ Can reverse it by showing on Place Value Cards first
From Mastering the MathRack by Christina Tondevold 2011
ADDING IT UP
▸ Tell a story, using a context, for the students to solve using
their MathRack.
▸ Have them show how they solved it on their Number Path.
▸ Have them write the equation for how they solved it, too.
▸ Look for different ways students solve it.
▸ Continue with other stories.
From Mastering the MathRack by Christina Tondevold 2011
FILL IT UP
▸ Tell a story, in context, that forces children to fill a row in
the MathRack before they add beads to another row.
▸ Write down the number sentences that show how the
MathRack was filled (for example: 8 + 7 becomes 8 + 2 + 5
From Teaching Channel video
GUESS MY WAY
▸ Build a number on your demonstration MathRack and hide
it.
▸ Tell the students the number and ask them to guess your
way.
▸ Students build the number on the MathRacks seeing
different ways to build the same number.
TEXT
RESOURCES
▸ Mastering the MathRack by Christina Tondevold
▸ Fluency Through Flexibility by Christina Tondevold
▸ Contexts for Learning Mathematics by Catherine Fosnot
▸ Young Mathematicians at Work by Catherine Fosnot
▸ Teaching Student-Centered Mathematics by John Van de
Walle
TEXT
CONTACT ME
▸ Join the “Teaching and Understanding Mathematics”
group in Microsoft SharePoint
▸ email ken_hall@ycjusd.us
▸ Twitter @kennygarten