Teaching Math
in an
8th Grade Science
Classroom
Cheryl Allison and Lisa Ellermann
What does Science look like
in the Math classroom?
Science based questions for Math (under the new Math TEKS) from TEA’s Released
Questions
Surprised? Concerned? Or was it what you expected?
Similarities with Science Test? Differences from Science Test?
Do you use the same vocabulary, symbolism and representations as used in these questions?
Where Do the Math and Science Align?
Or Do They?
Calculation Concept Math
Intro
E/I Science Intro E/I Math
Vocab/Formula
Science
Vocab/Formula
Speed, distance and
time
Density, mass and
volume
Net force, mass and
acceleration
Work, force and
distance
Where Do the Math and Science Align?
Or Do They?
Calculation Concept Math
Intro
E/I Science Intro E/I Math
Vocab/Formula
Science
Vocab/Formula
Speed, distance and
time
7th
Grade
E 6th Grade E Distance
d=rt
Average Speed
s=𝑑
𝑡
Density, mass and
volume
Net force, mass and
acceleration
Work, force and
distance
Where Do the Math and Science Align?
Or Do They?
Calculation Concept Math
Intro
E/I Science Intro E/I Math
Vocab/Formula
Science
Vocab/Formula
Speed, distance and
time
7th
Grade
E 6th Grade E Distance
d=rt
Average Speed
s=𝑑
𝑡
Density, mass and
volume
7th
Grade
I 6th Grade E Constant of
Proportionality
𝑘 =𝑦
𝑥
𝐷 =𝑚
𝑣
Net force, mass and
acceleration
Work, force and
distance
Where Do the Math and Science Align?
Or Do They?
Calculation Concept Math
Intro
E/I Science Intro E/I Math
Vocab/Formula
Science
Vocab/Formula
Speed, distance and
time
7th
Grade
E 6th Grade E Distance
d=rt
Average Speed
s=𝑑
𝑡
Density, mass and
volume
7th
Grade
I 6th Grade E Constant of
Proportionality
𝑘 =𝑦
𝑥
𝐷 =𝑚
𝑣
Net force, mass and
acceleration
8th
Grade
I 8th Grade E Direct Variation
y=kx
F=ma
Work, force and
distance
Where Do the Math and Science Align?
Or Do They?
Calculation Concept Math
Intro
E/I Science Intro E/I Math
Vocab/Formula
Science
Vocab/Formula
Speed, distance and
time
5th
Grade
7th
Grade
I
E
6th Grade E y=ax
Distance
d=rt
Average Speed
s=𝑑
𝑡
Density, mass and
volume
7th
Grade
I 6th Grade E Constant of
Proportionality
𝑘 =𝑦
𝑥
𝐷 =𝑚
𝑣
Net force, mass and
acceleration
8th
Grade
I 8th Grade E Direct Variation
y=kx
F=ma
Work, force and
distance
8th
Grade
I 7th Grade E Direct Variation
y=kx
W=Fd
So … What do you think about the alignment?
Turn to your elbow partner and discuss the following:
Concerning the Math/Science vertical/horizontal alignment, I feel like ...
The fact that many of the Math concepts are introduced first in Science
…
The difference in vocabulary and formula presentation …
As a first step to bridging this gap between Math and Science, I believe
we should …
Distance, speed/rate and time
Taught implicitly in Math in 5th grade, explicitly in Math in 7th grade , but is taught in Science in 6th grade
Vocabulary – Same, Same, but Different
speed vs velocity
speed vs rate
Formula Presentation
Multiplication vs Division: they should get that, right?
Algebraically, they see Multiplication and Division as inverse operations with variables for the first time in 6th
Grade Math
Form is different, letters are different
Triangle model?
Understanding the mathematics of the model
Advantages
Disadvantages
Since you are all Science teachers, you
obviously understand this:
So if the is 12 and the
is 30, find the
მ ს
მმოცულობამასობრივი სიმჭიდროვე.
Density, Mass and Volume
Taught Implicitly in Math (constant of proportionality)
What effect does that have in Science?
Vocabulary
Density – Only a Science Term
Constant of Proportionality – Only a Math term
How do we join the terms?
Volume is used in both subjects
Formula Presentation
Form is the same, letters are different
Net Force, mass and acceleration
Work, Force and distance
Taught implicitly in Math (direct variation)
Balanced and Unbalanced Forces
Aligns in Math with 6.7(C) determine if two expressions are equivalent using
concrete models, pictorial models, and algebraic representations; and Supporting
Standard
Vocabulary
Formula Presentation
Work, Force and distance is a conceptual understanding only, TEKS does not
specify calculation. The formula is only offered as a reference for understanding.
Now that we have the technical stuff out
of the way, how do we do the math?
Good News! –
Number Sets
8th grade math includes All Rational Numbers (positive, negative, fractions, decimals, etc.) and a limited set of Irrational Numbers (π, square roots of numbers less than 225)
8th grade science includes Positive whole and decimal values (with rounding considerations for significant figures)
Units of Measurement
8th grade math includes both standard and metric measurement and conversion between the two measurement sets
8th grade science includes only metric measurements
Bad News! - Calculators vs. No Calculators
8th Grade Math must provide a calculator for assessment according to Former TEA Commissioner Williams
8th Grade Science may not provide a calculator for assessment except as an accommodation for a student with an IEP.
Real News! – Models for Addition, Subtraction, Multiplication and Division
Decompose! Decompose! Decompose!
Rewrite as an inverse operation
Ratio Tables for multiplication and division
Area models for multiplication
Let’s do some examples
Decompose! Decompose! Decompose!
Most errors in operations on whole numbers and decimals occur
because of incorrect place value understanding
Expanded Form vs. Expanded Notation (presented in Math, 1st – 5th grades)
Science Benefits?
Math Benefits?
Addition and Subtraction
Multiplication and Division
Rewrite as an Inverse Operation
Vocabulary: Please don’t say “opposite operation”. Opposite refers to the relationship of positive and
negative numbers (in Math).
If the operation is subtraction, have the student think of it as a missing additive piece (math terminology:
part-part-whole)
Bar model – helps students to visualize the math that needs to occur
Number line model – familiar tool, can be used in conjunction with other strategies
Decomposition – take it apart into pieces that are easier to manipulate: expanded form or expanded notation
Numeracy Strategies (Building Powerful Numeracy by Pamela Weber Harris)
Give and Take/Partitioning
Over and Under
If the operation is division, have the student think of it as a missing multiplicative piece (8x9=72, 8 groups
of 9 result in 72 items; if I begin with 72 items, how many groups of 9 do I need?).
Ratio tables
Area models
Ratio Tables for Multiplication and Division
Based on the math concepts of Partial products
and the Distributive property
Start by applying the multiplication that is easy for
me, then build up or down to achieve the number
I want
Area Models
Combines decomposition of a number into
expanded form and couples it with a geometric
organizer
Works well for both multiplication and division
Can be expanded for larger numbers and can
include variables
Let’s Do some Science and
Practice some Math
Apply these strategies for
Released Test Items