Download Problem Solving Tasks Open Middle (1)

Open Middle
Middle School Alignment
Problem
Operations with Rational
Numbers
Fraction Division
Dividing Mixed Numbers
Dividing Fractions
Equivalent Ratios
Finding Equivalent Ratios
Adding Decimals to Make
Them As Close To One As
Possible
Order of Operations 1
Order of Operations 2
Order of Operations 3
Product of Distributive
Property
Inequality with Infinitely
Many Solutions
6th Grade Intro
AKS
8.NS.1 interpret and compute quotients of fractions, and
solve word problems involving division of fractions by
fractions, including reasoning strategies such as visual
fraction models and equations to represent the
problem.
8.NS.1 interpret and compute quotients of fractions, and
solve word problems involving division of fractions by
fractions, including reasoning strategies such as visual
fraction models and equations to represent the
problem.
8.NS.1 interpret and compute quotients of fractions, and
solve word problems involving division of fractions by
fractions, including reasoning strategies such as visual
fraction models and equations to represent the
problem.
8.NS.1 interpret and compute quotients of fractions, and
solve word problems involving division of fractions by
fractions, including reasoning strategies such as visual
fraction models and equations to represent the
problem.
4.RP.3a make tables of equivalent ratios relating
quantities with whole-number measurements, find
missing values in the tables, and plot the pairs of values
on the coordinate plane (e.g., use tables to compare
ratios)
4.RP.3a make tables of equivalent ratios relating
quantities with whole-number measurements, find
missing values in the tables, and plot the pairs of values
on the coordinate plane (e.g., use tables to compare
ratios)
22.NS.3 fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each
operation
23.EE.1 write and evaluate numerical expressions
involving whole-number exponents by applying order of
operations.
23.EE.1 write and evaluate numerical expressions
involving whole-number exponents by applying order of
operations.
23.EE.1 write and evaluate numerical expressions
involving whole-number exponents by applying order of
operations.
28.EE.3 apply the properties of operations to generate
equivalent expressions (e.g., apply the distributive
property to the expression 3(2 + x) to produce the
equivalent expression 6 + 3x; apply the distributive
property to the expression 24x + 18y to produce the
equivalent expression 6(4x + 3y); apply properties of
operations to y + y + y to produce the equivalent
expression 3y)
30.EE.5 understand solving an equation or inequality as
a process of answering a question (e.g., which values
from a specified set, if any, make the equation or
inequality true?); use substitution to determine whether
a given number in a specified set makes an equation or
inequality true
Quarter
1
1
1
1
1
1
1
2
2
2
2
2
Equations
Rectangular Prism Surface
Area Versus Volume
Reduce Volume, Keep
Surface Area Constant
Maximizing Rectangular
Prism Surface Area
Rectangular Prism Surface
Area
Lower and Upper Quartiles
With Constraints
Median with Constraints
Mean, Median, and Range
30.EE.5 understand solving an equation or inequality as
a process of answering a question (e.g., which values
from a specified set, if any, make the equation or
inequality true?); use substitution to determine whether
a given number in a specified set makes an equation or
inequality true
36.G.2 find the volume of a right rectangular prism with
fractional edge lengths by packing it with unit cubes of
the appropriate unit fraction edge lengths ( ½ u ) and
show that the volume is the same as would be found by
multiplying the edge lengths of the prism; apply the
formulas V = (length) x (width) x (height) and V = (area
of base) x (height) to find volumes of right rectangular
prisms with fractional edge lengths in the context of
solving real world and mathematical problems
38.G.4 represent three-dimensional figures using nets
made up of rectangles and triangles, and use the nets
to find the surface area of these figures; apply these
techniques in the context of solving real-world and
mathematical problems
38.G.4 represent three-dimensional figures using nets
made up of rectangles and triangles, and use the nets
to find the surface area of these figures; apply these
techniques in the context of solving real-world and
mathematical problems
38.G.4 represent three-dimensional figures using nets
made up of rectangles and triangles, and use the nets
to find the surface area of these figures; apply these
techniques in the context of solving real-world and
mathematical problems
38.G.4 represent three-dimensional figures using nets
made up of rectangles and triangles, and use the nets
to find the surface area of these figures; apply these
techniques in the context of solving real-world and
mathematical problems
43.SP.5 summarize numerical data sets in relation to their
context, such as by reporting the number of
observations; describing the nature of the attribute
under investigation, including how it was measured and
its units of measurement; giving quantitative measures
of center (median and/or mean) and variability
(interquartile range) as well as describing any overall
pattern and any striking deviations from the overall
pattern with reference to the context in which the data
was gathered; relating the choice of measures of
center and variability to the shape of the data
distribution and the context in which the data were
gathered
43.SP.5 summarize numerical data sets in relation to their
context, such as by reporting the number of
observations; describing the nature of the attribute
under investigation, including how it was measured and
its units of measurement; giving quantitative measures
of center (median and/or mean) and variability
(interquartile range) as well as describing any overall
pattern and any striking deviations from the overall
pattern with reference to the context in which the data
was gathered; relating the choice of measures of
center and variability to the shape of the data
distribution and the context in which the data were
gathered
43.SP.5 summarize numerical data sets in relation to their
context, such as by reporting the number of
observations; describing the nature of the attribute
2
3
3
3
3
3
3
3
Area of a Quadrilateral on
a Coordinate Plane
Problem
under investigation, including how it was measured and
its units of measurement; giving quantitative measures
of center (median and/or mean) and variability
(interquartile range) as well as describing any overall
pattern and any striking deviations from the overall
pattern with reference to the context in which the data
was gathered; relating the choice of measures of
center and variability to the shape of the data
distribution and the context in which the data were
gathered
37.G.3 draw polygons in the coordinate plane given
coordinates for the vertices; use coordinates to find the
length of a side joining points with the same first
coordinate or the same second coordinate; apply
these techniques in the context of solving real-world
and mathematical problems
7th Grade Intro
AKS
4
Quarter
Adding Two-Digit Numbers
9.NS.1a show that a number and its opposite have a
sum of 0 (are additive inverses). Describe situations in
which opposite quantities combine to make 0. For
example, your bank account balance is -$25.00. Your
deposit $25.00 into your account. The net balance is
$0.00.
10.NS.1b identify p + q as the number located a
distance (|q|) from p, in the positive or negative
direction depending on whether q is positive or
negative; interpret sums of rational numbers by
describing real-world contexts
10.NS.1b identify p + q as the number located a
distance (|q|) from p, in the positive or negative
direction depending on whether q is positive or
negative; interpret sums of rational numbers by
describing real-world contexts
12.NS.1d apply properties of operations as strategies to
add and subtract rational numbers
Subtracting Two-Digit
Numbers
12.NS.1d apply properties of operations as strategies to
add and subtract rational numbers
1
Adding Decimal Integers
12.NS.1d apply properties of operations as strategies to
add and subtract rational numbers
1
Subtracting Decimal
Integers
12.NS.1d apply properties of operations as strategies to
add and subtract rational numbers
1
Creating Zero
Absolute Value
Absolute Value 2
Multiply to Make -64
Undefined Quotient with
Fraction Division
14.NS.2a recognize that multiplication is extended from
fractions to rational numbers by requiring that
operations continue to satisfy the properties of
operations, particularly the distributive property, leading
to products such as (-1)(-1) = 1 and the rules for
multiplying signed numbers; interpret products of
rational numbers by describing real-world contexts
15.NS.2b recognize that integers can be divided,
provided that the divisor is not zero and every quotient
of integers (with a non-zero divisor) is a rational number
(if p and q are integers, then -(p/q) = (-p)/q = p/(-q));
interpret quotients of rational numbers by describing
real world contexts
1
1
1
1
1
1
Multiplying Two-Digit
Numbers
16.NS.2c apply properties of operations as strategies to
multiply and divide rational numbers
1
Dividing Two-Digit Numbers
16.NS.2c apply properties of operations as strategies to
multiply and divide rational numbers
16.NS.2c apply properties of operations as strategies to
1
Multiplying Decimal
1
Integers
Dividing Decimal Integers
Equivalent Equations
Converting Between
Fractions and Decimals
Equal Tips
Two-Step Equations
Unit Fraction Proportion
Which Rectangle Is More
Like a Square
Square and Circle Area
What Measurements Make
a Circle?
Reduce Volume, Keep
Surface Area Constant
Maximizing Rectangular
Prism Volume
Maximizing Rectangular
Prism Surface Area
Rectangular Prism Surface
Area Versus Volume
multiply and divide rational numbers
16.NS.2c apply properties of operations as strategies to
multiply and divide rational numbers
16.NS.2c apply properties of operations as strategies to
multiply and divide rational numbers
17.NS.2d convert a rational number to a decimal using
long division; know that the decimal form of a rational
number terminates in 0s or eventually repeats
21.EE.3 solve multi-step real-life and mathematical
problems posed with positive and negative rational
numbers in any form (whole numbers, fractions, and
decimals) by applying properties of operations as
strategies to calculate with numbers, converting
between forms as appropriate and assessing the
reasonableness of answers using mental computation
and estimation strategies (e.g., If a woman making $25
an hour gets a 10% raise, she will make an additional
1/10 of her salary an hour, or $2.50, for a new salary of
$27.50. If you want to place a towel bar 9 3/4 inches
long in the center of a door that is 27 1/2 inches wide,
you will need to place the bar about 9 inches from
each edge; this estimate can be used as a check on
the exact computation)
23.EE.4a solve word problems leading to equations of
the form px + q = r and p(x+q) = r, where p, q, and r are
specific rational numbers and solve equations of these
forms fluently. Compare an algebraic solution to an
arithmetic solution identifying the sequence of the
operations used in each approach (e.g., the perimeter
of a rectangle is 54 cm. Its length is 6 cm. What is its
width?)
1.RP.1 compute unit rates associated with ratios of
fractions, including ratios of lengths, areas and other
quantities measured in like or different units (e.g., if a
person walks 1/2 mile in each 1/4 hour, compute the
unit rate as the complex fraction (1/2)/(1/4) miles per
hour, equivalently 2 miles per hour)
26.G.1 solve problems involving scale drawings of
geometric figure, including computing actual lengths
and areas from scale drawing and reproducing a scale
drawing at a different scale
29.G.4 given the formulas for the area and
circumference of a circle, use them to solve problems;
give an informal derivation of the relationship between
the circumference and area of a circle
29.G.4 given the formulas for the area and
circumference of a circle, use them to solve problems;
give an informal derivation of the relationship between
the circumference and area of a circle
31.G.6 solve real-world and mathematical problems
involving area, volume and surface area of two- and
three-dimensional objects composed of triangles,
quadrilaterals, polygons, cubes and right prisms
31.G.6 solve real-world and mathematical problems
involving area, volume and surface area of two- and
three-dimensional objects composed of triangles,
quadrilaterals, polygons, cubes and right prisms
31.G.6 solve real-world and mathematical problems
involving area, volume and surface area of two- and
three-dimensional objects composed of triangles,
quadrilaterals, polygons, cubes and right prisms
31.G.6 solve real-world and mathematical problems
involving area, volume and surface area of two- and
three-dimensional objects composed of triangles,
1
1
1
1
1
2
2
3
3
3
3
3
3
Rectangular Prism Surface
Area
Probability of Rolling Two Six
Sided Dice
Rolling With the Same
Probability
Problem
One Solution, No Solutions,
Infinite Solutions
Create an Equation with a
Given Solution
Solve Linear Equations with
Special Cases
Transformations – Three
Sequences
Simplifying Exponential
Expressions
Exponents and Order of
Operations
Exponents
Exponents: Power of a
Power Rule
Scientific Notation
Rational and Irrational
Numbers
quadrilaterals, polygons, cubes and right prisms
31.G.6 solve real-world and mathematical problems
involving area, volume and surface area of two- and
three-dimensional objects composed of triangles,
quadrilaterals, polygons, cubes and right prisms
38.SP.7 develop a probability model and use it to find
probabilities of events. Compare experimental and
theoretical probabilities of events. If the probabilities
are not close, explain possible sources of the
discrepancy.
41.SP.8 determine the probability of compound simple
events using organized lists, tables, tree diagrams, and
simulation
8th Grade Intro
AKS
9.EE.7/7_a solve linear equations both algebraically
and graphically, including examples of linear equations
in one variable with one solution, infinitely many
solutions, or no solutions (e.g. equivalent equations of
the form x = a, a = a, or a = b results (where a and b are
different numbers))
9.EE.7/7_a solve linear equations both algebraically
and graphically, including examples of linear equations
in one variable with one solution, infinitely many
solutions, or no solutions (e.g. equivalent equations of
the form x = a, a = a, or a = b results (where a and b are
different numbers))
9.EE.7/7_a solve linear equations both algebraically
and graphically, including examples of linear equations
in one variable with one solution, infinitely many
solutions, or no solutions (e.g. equivalent equations of
the form x = a, a = a, or a = b results (where a and b are
different numbers))
22.G.2 understand that a two-dimensional figure is
congruent to another if the second can be obtained
from the first by a sequence of rotations, reflections, and
translations; given two congruent figures, describe a
sequence that exhibits the congruence between them
3.EE.1 apply and know the properties of integer
exponents to generate equivalent numerical
expressions
3.EE.1 apply and know the properties of integer
exponents to generate equivalent numerical
expressions
3.EE.1 apply and know the properties of integer
exponents to generate equivalent numerical
expressions
3.EE.1 apply and know the properties of integer
exponents to generate equivalent numerical
expressions
6.EE.4 add, subtract, multiply, and divide numbers
expressed in scientific notation, including problems
where both decimal and scientific notation are used;
interpret and use scientific notation and choose units of
appropriate size for measurements of very large or very
small quantities (e.g. use millimeters per year for seafloor
spreading); interpret scientific notation that has been
generated by technology (e.g. calculators)
1.NS.1 know that numbers that are not rational are
called irrational; understand informally that every
number has a decimal expansion; for rational numbers
3
4
4
Quarter
1
1
1
1
1
1
1
1
2
2
Pythagorean Shell *
extension
show that the decimal expansion repeats eventually,
and convert a decimal expansion which repeats
eventually into a rational number
2.NS.2 use rational approximations of irrational numbers
to compare the size of irrational numbers, locate them
approximately on a number line and estimate the value
of expressions
27.G.7 apply the Pythagorean Theorem to determine
unknown side lengths in right triangles in real-world and
mathematical problems in two and three dimensions
27.G.7 apply the Pythagorean Theorem to determine
unknown side lengths in right triangles in real-world and
mathematical problems in two and three dimensions
27.G.7 apply the Pythagorean Theorem to determine
unknown side lengths in right triangles in real-world and
mathematical problems in two and three dimensions
Cone and Cylinder
Volumes Ratio
29.G.9 solve real world and mathematical problems
involving the volume of cylinders, cones, and spheres
Decimal Approximations of
Roots
Pythagorean Theorem
Equilateral Triangle Side
Length
Linear Function from Table
of Values
Slope from Two Points
Write a Linear Function
X-Intercept
Functions
Comparing Functions
Positive Correlation
Create a System of
Equations, Given 1
18.F.4 construct a function to model a linear relationship
between two quantities. Determine the rate of change
and initial value of the function from a description of a
relationship or from two (x, y) values, including reading
these from a table or from a graph. Interpret the rate of
change and initial value of a linear function in terms of
the situation it models, and in terms of its graph or a
table of values.
8.EE.6 determine the meaning of slope by using similar
right triangles to explain why the slope m is the same
between any two distinct points on a non-vertical line in
the coordinate plane; derive and graph linear
equations in slope intercept form y = mx + b
7.EE.5 graph proportional relationships, interpreting the
unit rate as the slope of the graph. Compare two
different proportional relationships represented in
different ways (e.g. compare a distance-time graph to
a distance-time equation to determine which of the two
moving objects has greater speed).
7.EE.5 graph proportional relationships, interpreting the
unit rate as the slope of the graph. Compare two
different proportional relationships represented in
different ways (e.g. compare a distance-time graph to
a distance-time equation to determine which of the two
moving objects has greater speed).
7.EE.5 graph proportional relationships, interpreting the
unit rate as the slope of the graph. Compare two
different proportional relationships represented in
different ways (e.g. compare a distance-time graph to
a distance-time equation to determine which of the two
moving objects has greater speed).
16.F.2 compare properties of two functions each
represented among verbal, tabular, graphic and
algebraic representations of functions (e.g. given a
linear function represented by a table of values and a
linear functions represented by an algebraic equation,
determine which function has a greater rate of change)
30.SP.1 construct and interpret scatter plots for bivariate
measurement data to investigate patterns of
association between two quantities. Describe patterns
such as clustering, outliers, positive or negative
association, linear association, and nonlinear
association.
11.EE.8 solve systems of equations algebraically and
estimate solutions by graphing the equations
2
2
2
2
2
3
3
3
3
3
3
3
4
Equation and the Solution
System of Equations – Table
of Value and SlopeIntercept Form
Solution of Two Linear
Equations
System of Equations,
Special Case Infinitely
Many Solutions
Systems of Equations,
Special Case No Solution
11.EE.8 solve systems of equations algebraically and
estimate solutions by graphing the equations
12.EE.8_a correspond points of intersection of graphs to
solutions to a system of two linear equations in two
variables because points of intersection satisfy both
equations simultaneously
12.EE.8_a correspond points of intersection of graphs to
solutions to a system of two linear equations in two
variables because points of intersection satisfy both
equations simultaneously
13.EE.8_b solve systems of two linear equations in two
variables algebraically, and estimate solutions by
graphing the equations; solve simple cases by
inspection (e.g. 3x + 2y = 5 and 3x + 2y = 6 have no
solution because 3x + 2y cannot simultaneously be 5
and 6)
13.EE.8_b solve systems of two linear equations in two
variables algebraically, and estimate solutions by
graphing the equations; solve simple cases by
inspection (e.g. 3x + 2y = 5 and 3x + 2y = 6 have no
solution because 3x + 2y cannot simultaneously be 5
and 6)
4
4
4
4