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

RIT scores between 161 and 170

• Solve simple addition word problems

New Vocabulary in this Range: how many, not, in all, altogether

New Signs and Symbols: none

RIT scores between 171 and 180

• 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

RIT scores between 181 and 190

• 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
• 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
• 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, ¢

RIT scores between 191 and 200

• 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
• Determine what operation is needed to solve a word problem (all four operations)
• 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

RIT scores between 201 and 210

• Estimate the answers to word problems
• Solve written word problems involving the addition or subtraction of monetary amounts
• List the prime and composite numbers less than 50 in a word problem
• Order integers on a number line
• Interpret data given in percent form on a circle graph and broken line graph
• Solve word problems involving customary and metric measurement
• Solve word problems involving distance, rate and time
• Use logic to solve problems
• Solve word problems using proportional reasoning
• Solve geometry problems by making a drawing or diagram
• 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

RIT scores between 211 and 220

• Compute word problems with time and calendars
• Investigate experimental probability of an event using a coin or spinner
• Solve practical word problems involving perimeter and area of a square, rectangle or triangle
• Understand and identify the place value and value of each digit in numerals through the billions
• 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
• Understand the properties of integers: commutative, associative, identity, zero property of multiplication, distributive property of multiplication over addition, and inverse property of addition
• Calculate the square of any number less than 100
• 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: %

RIT scores between 221 and 230

• 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
• Write and solve an equation using ratios, given a word problem
• Write and solve an equation for a word problem
• Analyze circles: center, chord, diameter, radius, arc, semicircle, and circumference
• Solve simple interest problems (amount x rate x time)
• Use estimation to determine if solutions to word problems are reasonable
• 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

RIT scores between 231 and 240

• Use logic to predict outcomes
• Work backwards to solve problems
• Solve multi-step problems involving computation
• Find correct mathematical expressions to represent word problems
• Find simple interest earned
• Find missing numbers in a diagram by using patterns
• Use map scales to solve problems
• Solve if-then logic problems
• Solve complex word problems involving ratio, percent, discount, sale price, rounding and estimation, averaging, length, volume, rate, calendars, probability, money, and time
• Given the answer to a problem, determine the question
• Formulate expressions and equations to model problem solving situation

New Vocabulary in this Range: regression equation

New Signs and Symbols: none

RIT scores between 241 and 250

• Solve complex word problems involving rate, ratio, percent, averages, and sale price
• Solve problems involving regression equations
• Manipulate problems with time and a half and overtime wages
• Actual versus precise measurements
• Use of symmetry to determine grouping properties
• Compare volume of different dimensional containers
• Use a matrix to identify given figure on a graph
• Write the converse of a geometric statement
• Select appropriate unit of measure

New Vocabulary in this Range: matrix

New Signs and Symbols: none

RIT scores between 251 and 260

• Solve problems involving ratio of a side of a figure to its area, perimeter, or volume
• Determine proportional parts of a number
• Use proportional relationships to determine lengths of sides of a figure that are represented by algebraic relationships
• Solve complex word problems with surface area, area, circumscribed figures, Pythagorean Theorem, consecutive integers
• Use clues given in word problems to decode correct answer
• Determine correct formula needed to solve problem
• Multiplication of matrices

New Vocabulary in this Range: none

New Signs and Symbols: none

RIT scores between 261 and 270

• Solve complex geometry, algebra, and probability problems

New Vocabulary in this Range: none

New Signs and Symbols: none

RIT scores between 271 and 280

• Solve problems involving successive discounts and rate of interest

New Vocabulary in this Range: none

New Signs and Symbols: none