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