Research-based Math Intervention for Grades 3 –8 “Math ElevationsTM
How It Works: Math Elevations is a comprehensive math intervention program for Grades 3–8/ Levels C–H, designed to help all students reach their grade-level expectations in mathematics.
learning on a different level.” — From a 7th grade math teacher at a charter school in Washington D.C.
Name: 28 + 54 = ?
I can also use paper and pencil to find the total.
+
T O 1
2 8 5 4 2
a
67 + 25 T
works for educators
who understand that not every student learns the same way. For those students who become anxious at the sight of a chalkboard and a textbook, Math Elevations engages them in
3 ABSTRACT
4 a
+ 2 REPRESENTATIONAL a 3
+ 4 7
20 +
6 2 9
1 Add:
48 + 13 1
4 8 1 3 6 1
b 42 + 25 c 36 + 9 d 14 + 39 b 15 + 18
Date:
Now add the tens: 1 + 2 + 5 = 8
Write one in the tens column. 1
Regroup: is ten and ones.
First add the ones: 8 + 4 = 2
11 2
2 8
3 Write the addition expression in the chart, placing each digit in its proper column. c
19 + 32
3 Easy Steps with the CRA: Concrete, Representational, and Abstract method
in part b? 1 CONCRETE
O 7
5 2
+ T O + T O + d 57 + 8 T O +
T 1
2 5
O 8
4 2
Challenge! Fill in numbers so that the sums are correct. b
3
+ 4 8
How did you find your answer in part a?
How We Know It Works: Research Foundation
The CRA approach is a three-step method that begins by using three-dimensional (concrete) materials to illustrate math concepts. Then, students transform the activity into the semi-concrete or representational models (drawing pictures, circles, dots), which bridge the conceptual understanding to the abstract (or symbolic) form of mathematics. The CRA approach is grounded in the work of Jerome Bruner*, Lev Vygotsky**, and Jean Piaget*** on children’s learning of mathematical ideas.
* Bruner, J. (1960). The Process of Education. Cambridge, MA. Harvard University Press. ** Vygotsky, L.S. (1962). Thought and Language. E. Hanfmann & G. Vakar, Trans.. Cambridge, MA: MIT Press. (Original work published 1934.)
*** Piaget, J. (1957). Construction of Reality in the Child. London: Routledge & Kegan Paul. 16
CHOKING HAZARD (1) Not for under 3 yrs.
The representational step is the bridge between the “concrete” and the “abstract.”
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Six Levels Math Elevations reaches struggling students with proven hands-on instruction that covers skills for grades 3 –8. This program is also appropriate for high school early intervention classes.
The Scope and Sequence, correlations to various states and the Common Core Standards for each level as well as complete lesson samplers are available online.
Perfect for RtI, ELL, Special Education and General Math Education
3
TIER 2
TIER 1
TIER
“Touch the math”: Work through problems using a hands-on approach with manipulatives.
“Draw the math”: Translate 3-dimensional to 2-dimensional with paper and pencil. Representational
Concrete Abstract
“Think the math”: Understand the math in symbolic form.
Individualized practice, remediation and enrichment through engaging software activities.
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Step
Step
c Northpoint Horizons
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