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Problem
Solving – includes a variety of strategies such as guess and check, logical
reasoning, and working backwards to solve simple and multi-step problems in all
mathematical areas.
Important Note:
Many test versions do not have problem solving broken out as a separate goal,
but have it embedded it into the other goal areas as an integrated piece.
Skills and
Concepts
 |
Solve simple addition word
problems |
New Vocabulary
in this Range: how many, not, in all, altogether
New Signs and
Symbols: none
|
Solve simple subtraction word
problems |
|
Use a problem solving process (as
defined by text) |
|
Recognize and extend a pattern:
shape, color and size |
·
Identify position concepts: over, under, inside, outside, in
front, behind, top, middle, bottom
·
Combine and identify the value of a collection of coins and bills
up to and including $1.00
|
Compare objects by shape, size,
height, or length (larger, smaller, taller, shorter, longer) |
|
Complete and interpret simple
picture graphs, bar graphs or tables |
New Vocabulary
in this Range: product, number sentence, problem, how many more, multiples,
greater than, left, how much, money, answer, about, outside, inside, shape,
calendar, picture
New Signs and
Symbols: none
|
Find and extend patterns, both
increasing and decreasing |
|
Make predictions for events (likely
or unlikely) |
|
Determine what operation is needed
to solve a word problem (addition and subtraction) |
|
Solve simple word problems using
addition and subtraction |
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Solve simple word problems based on
data from picture and bar graphs |
|
Solve for missing addends in an
addition and subtraction number sentence |
|
Solve one-step word problems
involving addition or subtraction of four or fewer digits |
|
Solve one-step word problems
involving division |
|
Identify extra information or
missing information that is necessary to solve word problems |
|
Choose and apply an appropriate
problem solving strategy: Draw a picture, Make a model, Guess and test, Make a
list, Make a table, or Find a pattern |
|
Solve problems using information
from a bar graph |
|
Compute and count change up to and
including $5.00, addition and subtraction only |
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Construct and interpret line graphs
involving problem solving |
New Vocabulary
in this Range: add, subtract, multiply, divide, rate, kilometers, hours,
between, equals, cost, time, less than, closest to, equation, weigh, minutes,
pieces, dozen, cups, inches, pounds, miles, sum, dime, nickel, pennies, quarter
New Signs and
Symbols: +, $, decimal point for cents, ¢
|
Identify the correct information to
solve addition and subtraction word problems |
|
Solve one-step word problems
involving multiplication and division, including money |
|
Estimate the answers to word
problems |
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Determine what operation is needed
to solve a word problem (all four operations) |
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Choose and apply an appropriate
problem solving strategy: Draw a picture, Make a model, Guess and test, Make a
list, Make a table, Find a pattern, Work backwards, Solve a simpler problem,
or Draw a diagram |
|
Solve word problems involving any
combination of basic operations on whole numbers (one-step problems) |
|
Write a number sentence to solve
one-step word problems involving the operations of addition, subtraction, and
multiplication of fractions and decimals |
|
Solve multi-step word problems
involving any combination of basic operations |
|
Construct and solve word problems
involving information from a table |
|
Understand the concept of ratio
using concrete and pictorial models |
|
Solve one- and two-step word
problems involving any combination of basic operations on whole numbers,
decimals, and fractions |
New Vocabulary
in this Range: terms, meter, millimeters, kilogram, feet, yards, unit of
measurement, height, thousands, hundreds, tens, table, graph, length, width,
rectangular, area, square inches, exactly, coins, numeral, even, change,
average, opposite, percent, subtrahend, addend, formula, circle, diameter,
operation, total, fact, fraction, surfaces, cube, temperature, first – fifth
(ordinal names), difference, equivalent
New Signs and
Symbols: tally marks, =, - as an integer sign, %,
°C,
? for answer
|
Estimate the answers to word
problems |
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Solve written word problems
involving the addition or subtraction of monetary amounts |
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List the prime and composite
numbers less than 50 in a word problem |
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Order integers on a number line |
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Interpret data given in percent
form on a circle graph and broken line graph |
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Solve word problems involving
customary and metric measurement |
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Solve word problems involving
distance, rate and time |
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Use logic to solve problems |
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Solve word problems using
proportional reasoning |
|
Solve geometry problems by making a
drawing or diagram |
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Choose and use an appropriate
problem solving strategy: Draw a picture, Make a model, Guess and test, Make a
list, Make a table, Find a pattern, Work backwards, Solve a simpler problem,
Draw a diagram, Write an equation, or Logical Deduction |
New Vocabulary
in this Range: equation, product, increased, number line, information not
needed, division, estimate, odd, prime, cube, pattern, geometric patterns, extra
information
New Signs and
Symbols: r x t = d
|
Compute word problems with time and
calendars |
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Investigate experimental
probability of an event using a coin or spinner |
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Solve practical word problems
involving perimeter and area of a square, rectangle or triangle |
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Understand and identify the place
value and value of each digit in numerals through the billions |
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Solve practical problems involving
the mean (average) of a set of numbers |
|
Solve one- and two-step word
problems involving any combination of basic operations on whole numbers,
decimals, and fractions |
|
Determine the discount price and
sale price |
|
Choose and use an appropriate
problem solving strategy: Draw a picture, Make a model, Guess and test, Make a
list, Make a table, Find a pattern, Work backwards, Solve a simpler problem,
Draw a diagram, or Write an equation |
|
Solve problems involving
arrangements |
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Understand the properties of
integers: commutative, associative, identity, zero property of multiplication,
distributive property of multiplication over addition, and inverse property of
addition |
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Calculate the square of any number
less than 100 |
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Calculate the cost of one item or
the unit cost using a proportion |
New Vocabulary
in this Range: decimals, fractions, what shape, hour, minutes, gallons,
average, probability, graph, squares
New Signs and
Symbols: %
|
Choose and use an appropriate
problem solving strategy: Draw a picture, Make a model, Guess and test, Make a
list, Make a table, Find a pattern, Work backwards, Solve a simpler problem,
Draw a diagram, or Write an equation |
|
Select the appropriate unit of
measure for length and area |
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Write and solve an equation using
ratios, given a word problem |
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Write and solve an equation for a
word problem |
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Analyze circles: center, chord,
diameter, radius, arc, semicircle, and circumference |
|
Solve simple interest problems
(amount x rate x time) |
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Use estimation to determine if
solutions to word problems are reasonable |
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Predict outcomes using probability |
New Vocabulary
in this Range: mortality, odometer, magic square, deducted, less than twice,
addends, less than sum, rectangle, diameter, radius, label (units), area,
perimeter
New Signs and
Symbols: I = prt
|
Use logic to predict outcomes |
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Work backwards to solve problems |
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Solve multi-step problems involving
computation |
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Find correct mathematical
expressions to represent word problems |
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Find simple interest earned |
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Find missing numbers in a diagram
by using patterns |
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Use map scales to solve problems |
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Solve if-then logic problems |
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Solve complex word problems
involving ratio, percent, discount, sale price, rounding and estimation,
averaging, length, volume, rate, calendars, probability, money, and time |
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Given the answer to a problem,
determine the question |
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Formulate expressions and equations
to model problem solving situation |
New Vocabulary
in this Range: regression equation
New Signs and
Symbols: none
|
Solve complex word problems
involving rate, ratio, percent, averages, and sale price |
|
Solve problems involving regression
equations |
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Manipulate problems with time and a
half and overtime wages |
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Actual versus precise measurements |
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Use of symmetry to determine
grouping properties |
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Compare volume of different
dimensional containers |
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Use a matrix to identify given
figure on a graph |
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Write the converse of a geometric
statement |
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Select appropriate unit of measure |
New Vocabulary
in this Range: matrix
New Signs and
Symbols: none
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Solve problems involving ratio of a
side of a figure to its area, perimeter, or volume |
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Determine proportional parts of a
number |
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Use proportional relationships to
determine lengths of sides of a figure that are represented by algebraic
relationships |
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Solve complex word problems with
surface area, area, circumscribed figures, Pythagorean Theorem, consecutive
integers |
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Use clues given in word problems to
decode correct answer |
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Determine correct formula needed to
solve problem |
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Multiplication of matrices |
New Vocabulary
in this Range: none
New Signs and
Symbols: none
|
Solve complex geometry, algebra,
and probability problems |
New Vocabulary
in this Range: none
New Signs and
Symbols: none
|
Solve problems involving successive
discounts and rate of interest |
New Vocabulary
in this Range: none
New Signs and
Symbols: none
|
