Differentiating Instruction in Mathematics

Differentiating Math
Heather Hardin
Arkansas Department of Education
Professional Development
Anthony Owen
Arkansas Department of Education
Curriculum & Instruction
Key Shifts in Mathematics
 Focus - the major focus in each grade allows
the emphasis on the concept to deepen
 Coherence - there are coherent progressions
from grade to grade
 Rigor - with equal concentration, the three
aspects of rigor must be practiced:
1. Conceptual Understanding
2. Procedural Skills and Fluency
3. Application
 Greater focus on fewer topics:
 Grades K–2: Concepts, skills, and problem solving related to
addition and subtraction
 Grades 3–5: Concepts, skills, and problem solving related to
multiplication and division of whole numbers and fractions
 Grade 6: Ratios and proportional relationships, and early
algebraic expressions and equations
 Grade 7: Ratios and proportional relationships, and arithmetic
of rational numbers
 Grade 8: Linear algebra and linear functions
 Progression charts show coherence across
 Where to find them:
 Members on the working team:
Richard Askey (reviewer), Sybilla Beckmann (writer),
Douglas Clements (writer), Phil Daro (co-chair), Skip
Fennell (reviewer), Brad Findell (writer), Karen Fuson
(writer), Roger Howe (writer), Cathy Kessel (editor),
William McCallum (chair), Bernie Madison (writer), Dick
Scheaffer (writer), Denise Spangler (reviewer), Hung-Hsi
Wu (writer), Jason Zimba (co-chair)
More progression examples…
 Rigor is achieving at high levels, not making
things harder
 3 aspects of rigor:
1. Conceptual Understanding- comprehension of
mathematical understandings that use prior
knowledge and new learnings
2. Procedural Skills and Fluency – skillfully and
efficiently performing accurate procedures
3. Application- applying and modeling skills and
concepts to unfamiliar circumstances
How can you differentiate math
instruction across grades and
and RIGOR?
The answer…
Let’s try one…
ACT 1:
How big is the killer’s
shoe size?
What do you notice?
What questions do you have?
What does a wrong answer look like?
What’s your guess?
What is an answer that would be way too high?
Too low?
ACT 2:
What more information do you need to answer our
How would you get it?
Let’s compare the
original guesses…
Largest 1st guess:_____
Smallest 1st guess:_____
Largest answer:_____
Smallest answer:_____
ACT 3:
Why was your answer close but not exact?
What did your model/ work not include that it
should have?
What did your model work include that it
should not have?
If we were going to title the lesson
for today, what would a good title
Consider these things:
What math did we use?
What math did we use that we already knew?
What new math did we use?
SEQUEL (optional)
How big would Bigfoot’s foot look next to the dollar bill?
How big would Mini me’s foot look next to the dollar bill?
(Mini me from Austin Powers)
Bone Collector
Three-Act Task
Standards addressed:
Use ratio and rate reasoning to solve real-world
and mathematical problems, e.g., by reasoning
about tables of equivalent ratios, tape diagrams,
double number line diagrams, or equations.
Ratio and Proportions
across grades:
6th grade:
Understand ratio concepts and use ratio
reasoning to solve problems.
7th grade:
Analyze proportional relationships and use them
solve real-world and mathematical problems.
8th grade:
Understand the relationships between
proportional relationships, lines, and linear
Three Act Task
 Act 1:
 Show students a video or picture that will “hook”
 Pose the question for the lesson. Avoid using
content “language” or vocabulary
 Possible questions to get students thinking:
 What do you notice in the video/ photograph?
 What’s your guess?
 What is a guess that is way to high? Too low?
 What questions do you have?
Three-Act Task cont’d
 Act 2:
 Ask: What information do you need to answer the
 Students begin gathering information and/ or tools to
answer the question
 Remember: Do not give students information,
resources, or tools until they realize they need it and
ask for it
 The teacher serves as a resources and supports the
students thinking as they work
Three-Act Task cont’d
 Act 3:
 Students are provided the answer
 Discuss answers that were too high/ too low
 Ask students what information they needed but did not
have and what information they had but did not need
 Have students create a title for the lesson that relates
to the math used
 Make sure the students know what was intended to be
Three-Act Task cont’d
 Sequel:
 Pose a question for the students that extends
the learning
Other Three Act Tasks
 threeacts.mrmeyer.com
 robertkaplinsky.com/lessons/
 http://mr-stadel.blogspot.com/p/3-actcatalog_17.html
 http://wyrmath.wordpress.com (Would
you Rather?)
Arkansas Department
of Education
Heather Hardin
Office of Professional Development
Director: Kevin Beaumont
Anthony Owen
Office of Curriculum & Instruction
Director: Stacy Smith
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