Download Curriculum - Lansing-Math

Draft 3/21/06
Lansing School District Curriculum
7th Grade: The main areas of emphasis for seventh grade are:
(6th grade honors curriculum)
Communication
 Discuss, write, or
draw to show
depth of
mathematical
ideas and
relationships


Develop math
vocabulary and
symbols



Reflect on or
clarify thinking
about
mathematical
ideas and
situations


Restate math
concepts


Explain and
justify answers
 Develop rules and
procedures

Explain methods
of solving a
problem
Describe what extra
information is needed to
solve a problem
1

Year long instructional strategies, processes, skill development, or content expectations
Reasoning
Connections
Problem Solving
Verify and justify
 Recognize mathematical connections that  Use students prior
answers
occur in everyday experience
knowledge of
mathematical content and
process
Use logical spatial and
 Recognize relationships using number lines,
proportional
calendars, graphing, and money
reasoning
 Solve a simpler problem
to suggest a solution for a
 Recognize mathematical relationships that
more complex problem
Generalize from a set
occur between various mathematical topics
of observations
 Identify mathematical concepts that occur in  Solve multi-step
problems
Evaluate accuracy of a
other disciplines
solution to a
problem
 Recognize the need for math in order to  Formulate problems for
real world situations
pursue various careers
Solve a variety of
non-routine, real Use mathematics to describe the physical  Use manipulative
world problems
world
 Draw a figure
Make and test
 Use technology to enhance mathematical
conjectures
understanding
 Guess and check

Look for a pattern

Retell a story problem

Explain a problem
solution

Make a list

Simplify

Draw a diagram or table

Work backwards

Data Analysis
Collect,
organize,
interpret and
describe data
from tables

Analyze data

Analyze patterns

Formulate and
solve problems
using given data

Construct and
interpret graphs

Create a variety
of graphic
displays using
appropriate
scales with given
sets of numerical
data
Draft 3/21/06
Integration
Teacher
Notes
Curriculum
What do we want students to learn?
Instructional Strategies
How will we deliver the curriculum?
Resources
What materials/resources will
we need to ensure mastery.
Assessment
How will we know if
students learn?
1st Quarterly focused instructional strategies, processes, skill development, or content expectations
Unit:
Math Toolbox 1 for Seventh
Seventh Grade Level Content Problem-solving skills
Grade (St. Clair County)
Expectations
Students will use one or more of
Use resources to assess, re-teach
the following problem solving
concepts
Pilot Items
N.FL.07.07
strategies to demonstrate
Create a Human Number Line to
Solve problems involving
mastery in tested content areas:
explore integers
MEAP released items
operations with integers.
 Draw a Diagram
N.FL.07.09
 Make a Model
Develop and analyze algorithms Coach
Estimate results of
 Guess and Test
for computing with integers and
computations with rational
 Work Backward
develop fluency in their use
numbers.
 Find a Pattern
(assess student thinking for
N.FL.07.08
 Make a Table
alternative algorithms)
Holt Middle School Math
Add, subtract, multiply and
 Solve a Simpler
Course 3 Ch
divide negative rational
Problem
Use concrete objects and
numbers.

Use Logical Reasoning
pictures to develop and analyze
A.FO.07.12
1.1 – 1.6, 2.1 – 2.5, 3.1 –

Use a Venn Diagram
algorithms for computing with
Add, subtract, and multiply
3.5, 8.1, Lab 8A, 8.5, 8.6
 Make an Organized
fractions, decimals and integers
simple algebraic expressions
List
of the first degree, e.g., (92x
www.nctm.org
Explore and discuss the
+ 8y) – 5x + y, or – 2x (5x –
Effective Questioning (see
ILLUMINATIONS
relationship between fractions,
4), and justify using
appendix)
Figure This
decimals and percents
properties of real numbers.
www.lessonplanspage.com
www.mathgoodies.com
www.math.com
coolmath4kids.com
mathforum.org/dr.math
edhelper.com
thatquiz.com
Classroom observation and
discussion
Student Reasoning and
Justification
Student Math Journals
(Writing & Reflection)
Holt Middle School Math
Course 3:
 Chapter tests
 End-of-chapter review
pages
 Cumulative assessment
2
Draft 3/21/06
Connected Mathematics Project
Units:
 Check-up
 Quiz
 Unit Test
 Unit Project
Give students grades in fraction
form for them to compute
(ongoing)
Peer grading
Integration
Teacher
Notes
Curriculum
What do we want students to learn?
Instructional Strategies
How will we deliver the curriculum?
Assessment
How will we know if students
learn?
2nd Quarterly focused instructional strategies, processes, skill development, or content expectations
Unit:
Explore and discuss different uses of
Holt Middle School
N.ME.07.01
variables
Understand derived quantities
such as density, velocity, and
Math Course 3
Use symbolic algebra to represent
weighted averages
situations
A.FO.07.13
Ch 3.6, 3.7, 10.1- 10.5
From applied situations, generate
Explore and discuss the use of inverse
and solve linear equations of the
Math Toolbox 1 for Seventh
relationships to solve problems
form ax + b = c and ax + b = cx +
Grade
d, and interpret solutions.
Explore and discuss alternative ways to
A.FO.07.08
www.nctm.org
Know that the solution to a linear think about solving problems (undo, cover
ILLUMINATIONS
equation corresponds to the point at up method, hands on equations)
Figure This
which its graph crosses the x-axis.
(Redefining the zero for the equation Explore and discuss equivalent forms for
www.lessonplanspage.com
where y = 0).
simple algebraic expressions
www.mathgoodies.com
www.math.com
coolmath4kids.com
mathforum.org/dr.math
Explore and discuss using the inverse
3
Resources
What materials/resources
will we need to ensure
mastery.
Students will use one or
more of the following
problem solving strategies to
demonstrate mastery in
tested content areas:
 Draw a Diagram
 Make a Model
 Guess and Test
 Work Backward
 Find a Pattern
 Make a Table
 Solve a Simpler
Problem
 Use Logical
Reasoning
 Use a Venn
Diagram
Draft 3/21/06
relationship of squaring and finding square
roots
edhelper.com
thatquiz.com

Make an Organized
List
Effective Questioning (see
appendix)
Classroom observation and
discussion
Student Reasoning and
Justification
Student Math Journals
(Writing & Reflection)
Holt Middle School Math
Course 3:
 Chapter tests
 End-of-chapter
review pages
 Cumulative
assessment
Connected Mathematics
Project Units:
 Check-up
 Quiz
 Unit Test
 Unit Project
Give students grades in
fraction form for them to
compute (ongoing)
Peer grading
4
Draft 3/21/06
Integration
Teacher
Notes
5
Curriculum
What do we want students to learn?
Instructional Strategies
How will we deliver the curriculum?
Resources
Assessment
What materials/resources
How will we know if
will we need to ensure
students learn?
mastery.
3rd Quarterly focused instructional strategies, processes, skill development, or content expectations
Unit:
Explore and discuss linear and
A.PA.07.11
Holt Middle School Math Course 3
Students will use one or more of the
Understand and use basic nonlinear functions
following problem solving strategies
properties of real numbers:
additive
and
multiplicative Use concrete objects and real-life
Ch 5.5, Lab 5A, 11.1 -11.3, Lab 5B to demonstrate mastery in tested
content areas:
identities,
additive
and situations to explore and discuss
multiplicative
inverses, slope concepts
 Draw a Diagram
www.nctm.org
commutative, associative, and
 Make a Model
the distributive property of Explore and discuss calculating the
 Guess and Test
slope using rise/run, y=mx + b, (y2 – ILLUMINATIONS
multiplication over addition.
 Work Backward
Figure This
y1)/(x2 – x1)
G.SR.07.01
 Find a Pattern
Use a ruler and other tools to
 Make a Table
www.lessonplanspage.com
Explore relationships between
draw squares, rectangles,
 Solve a Simpler Problem
www.mathgoodies.com
triangles and parallelograms with symbolic expressions and graphs of
 Use Logical Reasoning
www.math.com
lines, paying particular attention to
specified dimensions.
 Use a Venn Diagram
coolmath4kids.com
the meaning of slope and intercept
G.SR.07.02
 Make an Organized List
mathforum.org/dr.math
Use compass and straightedge
edhelper.com
Explore and discuss multiple ways
to perform basic geometric
Effective Questioning (see appendix)
thatquiz.com
of solving equations (inverse
constructions: the perpendicular
bisector of a segment, an
equilateral triangle, and the
bisector of an angle; understand
informal justifications.
A.RP.07.02
Represent directly proportional
and linear relationships using
verbal descriptions, tables,
graphs, and formulas, and
translate among these
representations.
A.PA.07.03
Given a directly proportional or
linear situation, graph and
interpret the slope and
intercept(s) in terms of the
original situation; evaluate y = kx
operations, isolating the variable,
undo, cover up method)
Explore and discuss variety form of
linear equations and their
graphs(slope-intercept form, point
slope form,)
Represent, analyze, and generalize
patterns with tables, graphs, words,
and symbolic rules
(direct variation, line of best fit,
functions, inverse variation)
Classroom observation and
discussion
Student Reasoning and Justification
Student Math Journals
(Writing & Reflection)
Holt Middle School Math
Course 3:
 Chapter tests
 End-of-chapter review
pages
 Cumulative assessment
Connected Mathematics Project
Units:
Draft 3/21/06
for specific x values, given k,
e.g., weight vs. volume of water,
base cost plus cost per unit.
A.PA.07.04
For directly proportional or linear
situations, solve applied
problems using graphs and
equations, e.g., the heights and
volume of a container with
uniform cross-section, height of
water in a tank being filled at a
constant rate, degrees Celsius
and degrees Fahrenheit,
distance and time under constant
speed.
A.PA.07.09
Recognize inversely proportional
relationships in contextual
situations; know that quantities
are inversely proportional if their
product is constant, e.g., the
length and width of a rectangle
with fixed area and that an
inversely proportional
relationship is of the form y = k/x
where k is some non-zero
number.
A.RP.07.10
Know that the graph of y = k/x is
not a line; know its shape; and
know that it crosses neither the x
nor the y-axis.
A.PA.07.06
Calculate the slope from the
graph of a linear function as the
ratio of “rise/run” for a pair of
points on the graph, and express
the answer as a fraction and a
decimal; understand that linear
functions have slope that is a
constant rate of change.
A.PA.07.05
Understand and use directly
proportional relationships of the
6




Check-up
Quiz
Unit Test
Unit Project
Give students grades in fraction form
for them to compute (ongoing)
Peer grading
Draft 3/21/06
form y = mx, and distinguish from
linear relationships of the form y
= mx + b, b non-zero; understand
that in a directly proportional
relationship between two
quantities one quantity is a
constant multiple of the other
quantity.
A.PA.07.07
Represent linear functions in the
form y = x + b, y = mx, and y =
mx + b, and graph, interpreting
slope and y-intercept.
Integration
Teacher
Notes
7
Resources
What materials/resources will we
need to ensure mastery.
4th Quarterly focused instructional strategies, processes, skill development, or content expectations
Unit:
Use concrete objects to explore and
Holt Middle School Math Course 3
D.AN.07.03
discuss geometric figures
Calculate and interpret relative
frequencies and cumulative
Ch 3.8, 3.9, Lab 3B, 4.1-4.5, 4.7,
Describe, classify, and understand
frequencies for given data sets.
5.3, 5.6, 7.1-7.4, 7.6, 7.7, 9.1, 9.2,
relationships among types of twoD.AN.07.04
9.4, 9.7, 11.7
and three-dimensional objects
Find and interpret the median,
quartiles, and inter-quartile range
The Math Form-Ask Dr. Math
Use coordinate geometry to
of a given set of data.
Archives: Triangle Congruence.
represent and examine the properties
D.RE.07.01
http://mathforum.org/library/drmath/
of geometric shapes
Represent and interpret data
sets/select/dm_tri_congruence.html
using circle graphs, stem and
Describe sizes, positions, and
leaf plots, histograms, and boxwww.nctm.org
orientations of shapes under
and-whisker plots and select
ILLUMINATIONS
transformations such as scaling
appropriate representation to
Figure This
address specific questions.
Explore and discuss solving
D.AN.07.02
Create and interpret scatter plots problems involving scale factors,
www.lessonplanspage.com
and use an estimated line of best using ratio and proportion
www.mathgoodies.com
fit to answer questions about the
www.math.com
Curriculum
What do we want students to learn?
Instructional Strategies
How will we deliver the curriculum?
Assessment
How will we know if students learn?
Students will use one or more of the
following problem solving strategies
to demonstrate mastery in tested
content areas:
 Draw a Diagram
 Make a Model
 Guess and Test
 Work Backward
 Find a Pattern
 Make a Table
 Solve a Simpler Problem
 Use Logical Reasoning
 Use a Venn Diagram
 Make an Organized List
Effective Questioning (see
appendix)
Draft 3/21/06
data.
G.TR.07.03
Understand that in similar
polygons, corresponding angles
are congruent and the ratios of
corresponding sides are equal;
understand the concepts of
similar figures and scale factor.
G.TR.07.05
Show that two triangles are
similar using the criteria:
corresponding angles are
congruent (AAA similarity); the
ratios of two pairs of
corresponding sides are equal
and the included angles are
congruent (SAS similarity); ratios
of all pairs of corresponding
sides are equal (SSS similarity);
use these criteria to solve
problems and to justify
arguments.
G.TR.07.04
Solve problems about similar
figures and scale drawings.
G.TR.07.06
Understand and use the fact that
when two triangles are similar
with scale factor of r, their areas
are related by a factor of r2.
N.MR.07.04
Convert ratio quantities between
different systems of units such as
feet per second to miles per hour.
N.FL.07.03
Calculate rates of change
including speed.
N.FL.07.02
Solve problems involving derived
quantities.
N.FL.07.05
Solve simple proportion problems
using such methods as unit rate,
scaling, finding equivalent
8
Use concrete data and real-life
situations to design studies, collect
data, display data and interpret data
Model discuss organizing data,
measures of central tendency, and
variability
Explore and discuss the
correspondence between data sets
and their graphical representations
Explore and discuss using the
inverse relationship of squaring and
finding square roots
coolmath4kids.com
mathforum.org/dr.math
edhelper.com
thatquiz.com
Classroom observation and
discussion
Student Reasoning and Justification
Student Math Journals
(Writing & Reflection)
Holt Middle School Math
Course 3:
 Chapter tests
 End-of-chapter review
pages
 Cumulative assessment
Connected Mathematics Project
Units:
 Check-up
 Quiz
 Unit Test
 Unit Project
Give students grades in fraction
form for them to compute (ongoing)
Peer grading
Draft 3/21/06
fractions, and solving the
proportion equation a/b = c/d;
know how to see patterns about
proportional situations in tables.
A.PA.07.01
Recognize when information
given in a table, graph, or
formula suggests a proportional
or linear relationship.
N.MR.07.06
Understand the concept of square
root and cube root, and estimate
using calculators
9