Northwest Evaluation Association

Introduction to the Learning Continuum

Purpose of the Learning Continuum

The Learning Continuum began as a cooperative partnership with one of NWEA’s member districts, Allentown, Pennsylvania. Its development is an example of how a spark of an idea can become a tool that benefits teachers across the country.

For years, teachers using NWEA’s Achievement Level Tests or Measures of Academic Progress have been getting valid and useful data on their students. But, they have also continually asked us the same question, “How do I actually put this information to use in my classroom?” In response to this need, and driven by our commitment to improve the learning experience for all children, we developed the NWEA Learning Continuum, which is but one answer to this question.

The purpose of this document is to help guide instruction based on reports from an Achievement Level Test or computerized Measure of Academic Progress. The Learning Continuum enhances a teacher’s ability to provide targeted instruction for individual students or groups of students. It is not intended to be a replacement for district curriculum or standards that are already in place.

Development and Organization of the Learning Continuum

We developed the continuum by looking at curriculum from an analytical point of view. NWEA researched each and every test item in our item banks (over 15,000 items) in mathematics, reading, and language usage. We used only the items that had successfully passed field testing and were available for use on tests. As we reviewed each item, we looked at the difficulty of the items, the skills and concepts being assessed, and any new vocabulary or symbols that were introduced. By doing this, a learning continuum of these skills and concepts began to unfold. Thus, this document was born.

The Learning Continuum contains separate sections for each subject (mathematics, reading, and language usage). Within each subject are the main goal strands commonly found in standards and curriculum documents. The goal strands are then broken down into ten-point RIT bands. Within each band, sub-categories, which further divide the content within the goal area, break down the skills and concepts found in the NWEA item banks. Skills that cross several RIT bands appear at the earliest RIT band where they are prominently seen, and these skills are not repeated in the following RIT bands. Therefore, it is important to not only focus on the RIT band where the student is functioning, but to watch for any holes that may have appeared earlier in the continuum.

Only skills and concepts showing up in the NWEA item banks are listed in this document. We realize that many districts have additional topic areas that will not show up here. We encourage them to use the Learning Continuum as a tool to supplement the documents already in use by a district.

Primary Use of the Learning Continuum

Given a student’s (RIT) achievement score (e.g. a mathematics RIT score of 187), teachers identify the portion of the Learning Continuum (e.g. mathematics RIT scores between 181-190) that represents the child’s instructional level. The skills and concepts listed at RIT ranges below that should be ones the student knows and has mastered.

A teacher uses the student’s overall RIT score as the starting place, then finds the appropriate RIT band within each goal area. As the teacher works on specific goals, he/she can use the Learning Continuum as a guide to watch for differences in students’ achievement levels.

These RIT bands can be helpful in preparing for flexible small group instruction within a classroom. By putting students together who have similar instructional needs, a teacher can better meet the needs of all students. Our goal is to create maximum growth for all students, whether they are in the lowest quartile or the highest quartile. As students master the skills and concepts within a RIT band, they can be shifted to another flexible group.

Educators should be aware of the achievement differences of students. For too long, school districts have used a student’s age (grade level) as the primary criterion for selecting instructional materials and lessons. We believe that a student’s current achievement level should be the dominant consideration when grouping for instruction, selecting materials, and providing instruction. The Learning Continuum will help teachers know when it is time to move a student, or students, beyond the conventional curriculum at a particular grade level and when it is time to develop skills that may have been presented in earlier grades.

In creating the Learning Continuum, we have attempted to create one continuous document representing skills and concepts as they progress in difficulty. Their order is not based on any one district’s “curriculum.” One important note about the mathematics portion of the Learning Continuum is that all skills and concepts are listed together in one document, regardless of the “typical” grade level we see them introduced. Therefore, elementary, middle school, and upper courses such as algebra and geometry content are included together. There is a natural progression that can be followed from one RIT band to the next. We challenge you to “think outside the box” in using this document.

If a student’s RIT score is borderline between two RIT bands, use the lower one first. Based on a student’s performance, teachers can do further assessments to determine where the student is and should be.

Other Uses of the Learning Continuum

The Learning Continuum will have many uses, and we urge districts in the NWEA community to explore these uses and report back to us on their experiences. Some possible uses of the continuum are:

• Materials Selection – As teachers begin to explore the diversity of students’ performance levels within a class, it will become necessary to get better at sharing materials. The Learning Continuum can guide teachers in finding more appropriate materials for students at the extreme ends of the spectrum.
• Sharing Resources – Following on the heels of materials selection is the ability to know who to go to for getting appropriate materials for students. We encourage districts to develop better ways to share resources, not only within a building but also across buildings.
• Gifted and Talented, Title I, and ESL Programs – We hope the Learning Continuum will serve as a guide to constantly “push the envelope” with all students in order to help them grow as much as possible.
• Curriculum Planning – The continuum may become an invaluable resource during curriculum development or program revision.
• School Improvement Planning – Knowledge of student achievement relative to the Learning Continuum will likely raise questions about how we group for instruction, how we use instructional time, how we structure our schools, how we organize our staff, and how we design our facilities.
• Monitoring Student Progress – The Learning Continuum can be used as a guide to keep track of where students are on the continuum. Checklists can be made from the document to assist with this tracking.
• Individual Education Plans – We should always focus on the targeted growth we, as educators, want a student to make. The Learning Continuum can help us identify specific skills that will ensure students’ growth.
• Parent Conferencing – The continuum may help parents think of activities that will engage their child in additional learning. It may also help parents better understand their child’s academic status and progress.

Future of the Learning Continuum

The Learning Continuum began as a collaborative effort among NWEA members and will now evolve as a result of the efforts and contributions of all who use it. This first edition is only the beginning of what promises to be a substantial contribution to the future of education. As always, NWEA client members will be called upon to share their ideas, insights, and the products of their work so that all NWEA members can benefit from an improved product and expanded services related to the Learning Continuum.

We have enclosed a fax-back form to gather your initial reactions to the Learning Continuum. We are eager to hear from you and urge you to share with us so that all educational agencies within the NWEA community, and the children they serve, may benefit from your experiences.

Goal Score Translation Charts

This chart is useful in translating the Hi, Av, and Lo goal scores from the NWEA class report. It is built from the 2002 Achievement Level Test norms with the traditional breakdown of Lo equal to percentile scores < 33, the Hi equal to percentile scores > 66, and Av equal to percentile scores between 33 and 66.

To use, find the student’s grade on the chart below and then find the descriptor for the goal that you are referencing. Use the student’s overall RIT score as another guide. Refer to the Learning Continuum for detailed skills and concepts that should be further assessed and instructed. There is a chart for each subject. Seasons are broken down within the charts.

Mathematics

	Fall			Winter			Spring
Grade Level	Lo	Av	Hi	Lo	Av	Hi	Lo	Av	Hi
2	< 173	173 – 182	> 182	< 178	178 – 188	> 188	< 183	183 – 193	> 193
3	< 185	185 – 196	> 196	< 190	190 – 200	> 200	< 195	195 – 205	> 205
4	< 196	196 – 206	> 206	< 200	200 – 210	> 210	< 203	203 – 214	> 214
5	< 204	204 – 215	> 215	< 207	207 – 219	> 219	< 210	210 – 223	> 223
6	< 209	209 – 222	> 222	< 212	212 – 225	> 225	< 215	215 – 229	> 229
7	< 214	214 – 228	> 228	< 217	217 – 232	> 232	< 220	220 – 236	> 236
8	< 220	220 – 235	> 235	< 223	223 – 239	> 239	< 226	226 – 243	> 243
9	< 223	223 – 238	> 238	< 230	230 – 244	> 244	< 236	236 – 250	> 250
10	< 226	226 – 241	> 241	< 236	236 – 248	> 248	< 245	245 – 255	> 255

Reading

	Fall			Winter			Spring
Grade Level	Lo	Av	Hi	Lo	Av	Hi	Lo	Av	Hi
2	< 170	170 – 186	> 186	< 176	176 – 191	> 191	< 181	181 – 195	> 195
3	< 183	183 – 197	> 197	< 188	188 – 201	> 201	< 192	192 – 205	> 205
4	< 194	194 – 206	> 206	< 197	197 – 209	> 209	< 200	200 – 212	> 212
5	< 201	201 – 213	> 213	< 203	203 – 215	> 215	< 206	206 – 218	> 218
6	< 206	206 – 218	> 218	< 208	208 – 220	> 220	< 211	211 – 222	> 222
7	< 210	210 – 222	> 222	< 212	212 – 224	> 224	< 214	214 – 226	> 226
8	< 214	214 – 226	> 226	< 216	216 – 228	> 228	< 219	219 – 230	> 230
9	< 217	217 – 228	> 228	< 218	218 – 230	> 230	< 220	220 – 231	> 231
10	< 219	219 – 231	> 231	< 220	220 – 231	> 231	< 220	220 – 232	> 232

Math Goal 1: Computation

– includes addition, subtraction, multiplication, division, and rounding of whole numbers, fractions, decimals, percents, and positive and negative numbers.

RIT scores lower than 150

Whole Numbers

• Identify fact families with sums 0-18 in horizontal format

· Understand the concept of subtraction using symbols; subtract two numbers in vertical format

New Vocabulary in this range: and

New Signs and Symbols: +, =, -

RIT scores between 151 and 160

Whole Numbers

• Combine sets through manipulative and pictorial addition problems
• Add three 1-digit numbers
• Add 2-and 3-digit numbers with no regrouping
• Subtract a 1-digit number from a 2-digit number with regrouping

· Understand the concept of multiplication using symbols; recall multiplication facts with one factor as 1,2,3,4,5 and other factor 0-9

New Vocabulary in this range: equals, facts

New Signs and Symbols: x (multiplication symbol)

RIT scores between 161 and 170

Whole Numbers

• Separate sets through manipulative and pictorial subtraction problems
• Add a 2-digit number and a 2-digit number with no regrouping
• Subtract a 1-digit number from a 2-digit number with no regrouping
• Subtract a 2-digit number from a 2-digit number with no regrouping
• Solve simple addition word problems
• Subtract 2-and 3-digit numbers with no regrouping

Decimals

• Subtract whole numbers and decimals to the hundredths place (same number of digits)

New Vocabulary in this range: none

New Signs and Symbols: $, decimal point

RIT scores between 171 and 180

Whole Numbers

• Solve simple subtraction word problems
• Add 1- and 2-digit numbers with regrouping
• Add two 2-digit and 3-digit numbers with regrouping
• Subtract two 2-digit numbers with regrouping
• Understand the concept of multiplication using concrete objects
• Add 2-, 3- and 4-digit numbers with regrouping
• Multiply a 2- or 3-digit number by a 1-digit number with no regrouping
• Multiply a 2-digit number by a 1-digit number with regrouping
• Identify the associative, commutative, identity and zero property of multiplication
• Divide a 2-digit number or a 3-digit number by a 1-digit number with remainder
• Round 2- and 3-digit numbers to the nearest hundred and tens
• Multiply a 3-digit number by a 2-digit number

Fractions

• Add fractions with like denominators

Decimals

• Add whole numbers and decimals to the hundredths place (same number of digits)

New Vocabulary in this range: closest, how many

New Signs and Symbols: division symbol (both forms)

RIT scores between 181 and 190

Whole Numbers

• Subtract a 2-digit number from a 3-digit number with a single regrouping

· Identify the division facts related to a multiplication fact with one factor as 1,2,3,4,5 and the other factor 0-9

• Understand the concept of division using concrete objects
• Subtract a 3- or 4-digit number from a 4-digit number with regrouping

· Use strategies to develop computational fluency with multiplication: “zero property,” “property of one,” “arrays,” doubles,” “nine patterns”

• Multiply a 3-digit by a 1-digit number with regrouping (including zero)
• Multiply three 1-digit numbers or 2-digit numbers
• Identify the division facts related to a multiplication fact
• Divide a 2-digit number by a 1-digit number with no remainder
• Solve one-step word problems involving division
• Add 2 or several multi-digit numbers with regrouping
• Subtract multi-digit numbers with regrouping
• Divide a 3-digit or 4-digit number by a 1-digit number
• Divide a 2-digit number by a 2-digit number with no remainder
• Add multi-digit numbers without using a calculator
• Multiply multi-digit numbers

Fractions

• Read, shade, and write fractional parts of a group
• Subtract mixed numbers with like denominators with regrouping

Decimals

• Subtract whole numbers and decimals to the hundredths place (same number of digits)

· Add decimals to hundredths place using both horizontal and vertical format (not the same number of digits)

• Subtract decimals to hundredths place (not the same number of digits)
• Multiply a decimal by a whole number
• Divide a decimal by a whole number and vice versa

New Vocabulary in this range: none

New Signs and Symbols: none

RIT scores between 191 and 200

Whole Numbers

• Solve simple addition word problems
• Find and extend patterns
• Demonstrate the associative, commutative, and zero property of addition
• Identify the associative, commutative, identity and zero property of multiplication
• Solve one-step word problems involving multiplication
• Subtract multi-digit numbers with regrouping
• Round 4- and 5-digit numbers to the nearest hundred thousand, thousand, hundred or ten
• Multiply a 2-digit number by a 2-digit number with no regrouping
• Multiply a 2-digit number by a 2-digit number with regrouping
• Subtract multi-digit numbers without using a calculator
• Multiply a 3-digit number by a 2-digit number with regrouping
• Multiply a 3-digit number or 4-digit number by a 2-digit number or 3-digit number with zeros

Fractions

• Express 1 in many different ways (1/1, 2/2, 4/4)
• Write improper fractions from picture presentations
• Subtract fractions with like denominators
• Add fractions having unlike denominators, answer in lowest terms

Decimals

• Add whole numbers and decimals to the hundredths place (not the same number of digits)
• Subtract whole numbers and decimals to the hundredths place (not the same number of digits)

· Compute basic operations with monetary amounts up to and including $20.00

· Round decimals to the nearest whole number

· Add decimals to thousandths, vertically and horizontally, with and without regrouping

• Subtract decimals to thousandths, vertically and horizontally, with and without regrouping
• Multiply a decimal by a decimal, vertical form (tenths or hundredths)

Percents

• Find a percent of a number (6% of 30)

New Vocabulary in this range: difference, not true, power of 10, rounded, thousands

New Signs and Symbols: ¢, %

RIT scores between 201 and 210

Whole Numbers

• Understand the concept of division using pictorial representation
• Use front-end estimation strategy for multiplication and division

· Divide a 2-digit number by a 2-digit number with a remainder

• Subtract multi-digit numbers without using a calculator
• Multiply by multiples of 10 and 100 with an emphasis on mental math
• Divide a 3-digit number by a multiple of 10
• Divide a 3-digit number by a 2-digit number (no zeros)

Fractions

• Add mixed numbers with like denominators with regrouping
• Subtract mixed numbers with like denominators with regrouping
• Subtract mixed numbers with unlike denominators with regrouping
• Multiply a fraction by a fraction; answer in lowest terms
• Multiply mixed numbers

Decimals

• Add decimals to hundredths place using both horizontal and vertical format
• Subtract decimals to hundredths place
• Compute and count change greater than $20.00
• Subtract decimals through hundred-thousandths with a calculator

Percents

• Write a decimal or fraction as a percent; write a percent as a decimal or fraction

New Vocabulary in this range: estimate, round, closest to, sum, of (used as in “½ of 36”)

New Signs and Symbols: square root symbol

RIT scores between 211 and 220

Whole Numbers

• Divide a 3-digit or 4-digit number by a 1-digit number
• Use multiplication as a check for division
• Multiply by multiples of 10 and 100 with an emphasis on mental math
• Divide a 4-digit number by a 2-digit number

Fractions

• Change a fractional numeral to its simplest form (lowest terms)
• Add fractions with like denominators, answer in lowest terms
• Add mixed numbers with unlike denominators with regrouping
• Multiply a whole number by a fraction
• Divide a fraction by a fraction
• Divide a mixed number by a whole number or a fraction
• Compare and order fractions and mixed numbers

Decimals

· Round decimals to nearest whole number, tenth, or hundredth

· Write a terminating decimal as a fraction or mixed number

• Round decimals to nearest whole number, tenth, hundredth, or thousandth
• Add decimals through hundred-thousandths with a calculator
• Multiply a decimal by a decimal, factors to thousandths
• Divide a decimal by a whole number and vice versa

Integers

· Identify the greater or lesser of 2 integers

• Add integers with like signs
• Add integers with unlike signs
• Add several integers

· Multiply integers with unlike signs

• Divide integers with unlike signs

New Vocabulary in this range: smallest, tenth

New Signs and Symbols: - as a negative, + as a positive

RIT scores between 221 and 230

Whole Numbers

• Solve for missing addends in an addition or subtraction sentence
• Develop computational fluency with division facts
• Divide multi-digit numbers using a calculator
• Introduce the math strategy of compatible numbers in estimating for all four operations

Fractions

· Add and subtract fractions with like denominators; change improper fractions to mixed numbers

• Change a fractional numeral to its simplest form (lowest terms)
• Subtract fractions having unlike denominators, answer in lowest terms
• Add and subtract whole numbers, fractions and mixed numbers
• Use estimation to solve problems involving mixed numbers
• Divide a whole number, fraction or mixed number by a mixed number

Decimals

· Relate fractions to decimals

• Subtract whole numbers and decimals to the hundredths place (same number of digits)

· Write a number sentence to solve one-step word problems involving the operations of addition, subtraction, and multiplication of fractions and decimals

• Write a decimal or mixed decimal for a fraction (2/3=0.66)
• Subtract decimals through hundred-thousandths with a calculator
• Multiply a decimal by multiples of 10, 100, or 1000
• Divide a whole number (or decimal) by a decimal to thousandths

Integers

• Divide integers, like signs

Percent

· Write a ratio (fraction) as a percent and percent as a ratio (fraction: denominators are factors of 100)

• Find the percent one number is of another (20 is what % of 90)
• Find a number from a percent (4 is 9% of what number)

New Vocabulary in this range: product, divide, most, if – then, compute, lowest terms

New Signs and Symbols: none

RIT scores between 231 and 240

Whole Numbers

• Divide a 2-digit number or a 3-digit number by a 1-digit number with remainder
• Divide multi-digit numbers using a calculator

Fractions

• Add fractions having unlike denominators with answer reduced to lowest terms
• Subtract fractions having unlike denominators with answer reduced to lowest terms
• Add and subtract mixed numbers with like denominators with regrouping
• Add and subtract mixed numbers with unlike denominators with regrouping
• Add and subtract whole numbers, fractions, and mixed numbers
• Multiply a fraction by a fraction; answer in lowest terms
• Multiply mixed numbers
• Divide a fraction by a fraction
• Divide a mixed number by a whole number or a fraction
• Multiply three factors using fractions, mixed numbers, and whole numbers in any combination, answer in lowest terms
• Divide a whole number, fraction, or mixed number by a mixed number

Decimals

• Add whole numbers and decimals to the hundredths place (same number of digits)
• Subtract decimals to the hundredths place (not the same number of digits)
• Subtract decimals to thousandths, vertically and horizontally, with and without regrouping
• Subtract a decimal from a whole number
• Multiply a decimal by a decimal, factors to thousandths place
• Divide a decimal by a whole number and vice versa
• Divide a whole number (or decimal) by a decimal to thousandths place

Integers

· Add integers with unlike signs

• Add several integers
• Multiply integers with like signs
• Divide integers with like signs

Percents

· Find the percent one number is of another (8 is what % of 20?)

• Find a number from a percent (20 is 45% of what number?)

New Vocabulary in this range: ‘Solve for n”

New Signs and Symbols: none

RIT scores between 241 and 250

Fractions

• Multiply a whole number by a fraction

Integers

• Understand the meaning of integers
• Subtract integers, subtracting a negative

New Vocabulary in this range: decimal fractions, opposite

New Signs and Symbols: none

RIT scores between 251 and 260

Integers

• Use the additive inverse property to solve problems
• Use order of operations rules

New Vocabulary in this range: sum of opposites

New Signs and Symbols: none

RIT scores between 261 and 270

Fractions

• Add and subtract rational numbers with unlike denominators (may involve integers)

Percents

• Solve problems with successive discounts and rate of interest

New Vocabulary in this range: none

New Signs and Symbols: none

RIT scores above 270

Fractions

• Multiply a mixed number by a whole number, fraction, or mixed number

New Vocabulary in this range: none

New Signs and Symbols: none

Math Goal 2: Number Sense and Numeration

– includes solving problems with ratios, proportions, fraction-decimal relationships, exponents, number theory, place value, and the relationship between numbers.

RIT scores between 151 and 160

Whole Numbers

• Match sets of objects to numerals 0-40 to demonstrate an understanding of one-to-one correspondence
• Identify and count numbers 0-20
• Identify and order ordinal numbers (first to tenth)

Fractions

• Identify equal parts of a region (halves, thirds, fourths)
• Represent fractions by using models and drawings

Ordering, Equalities and Inequalities

• Compare and order numbers and sets of objects 0-10

New Vocabulary in this Range: how many

New Signs and Symbols: — for answer

RIT scores between 161 and 170

Whole Numbers

· Identify missing numbers in a series through 100

• Identify the number that is “one more than”, “one less than”, “10 more than”, and “10 less than” a given number
• Count objects that are grouped into tens and ones

Fractions

• Identify one-half of an object from a picture

Place Value

• Identify and understand the place value and value of each digit in numbers through the hundreds

Ordering, Equalities and Inequalities

• Order numbers 0-100

New Vocabulary in this Range: ones, tens, hundreds, thousands, numeral, ordinal numbers through eleventh, counting

New Signs and Symbols: none

RIT scores between 171 and 180

Whole Numbers

• Compare two or more sets of objects (up to ten objects in each group) and identify which set is equal to, more than, or less than the other
• Count and write by 10’s to 100
• Compare, group, and order whole numbers to 100 by using the symbols for “less than”, equal to”, and “greater than” (<, =, >)
• Distinguish between odd and even numbers
• Count by 2’s to 20

Fractions

· Identify one-half of an object or set

• Identify fractional parts of a region or group

Place Value, Expanded and Standard Notation

• Write numerals in expanded form through the thousands place

Ordering, Equalities and Inequalities

• Use > or < symbols to compare two numbers

New Vocabulary in this Range: even numbers, same as, fewest

New Signs and Symbols: < and > signs, = sign

RIT Scores between 181 and 190

Whole Numbers

• Identify one more and one fewer
• Count and write by 2’s and 3’s
• Complete a number pattern
• Round 2- and 3-digit numbers to the nearest hundred and tens
• Identify the value of Roman Numerals using I, V, and X
• Apply rules of divisibility by 5
• Identify the greatest common factor of two whole numbers each of which is less than 100
• List some common multiples of two whole numbers

Fractions

• Separate regions into sub regions that are equivalent (halves, thirds, fourths)
• Change a fractional numeral to its simplest form (lowest terms)

Decimals

· Identify the greater or lesser of two decimals

· Place Value, Expanded and Standard Notation

• Match number words to numerals to the ten thousands place

· Identify and understand the place value and value of each digit in numbers through the hundred thousands

• Add whole numbers using place value
• Identify and understand place value for decimals (tenths, hundredths, and thousandths)

Ordering, Equalities and Inequalities

• Order sets of objects 0-20
• Identify the greater or lesser of two numerals
• Order numerals through 999
• Identify the numeral that comes before, between, or after any given numeral through 999

• Compare and order fractions

• Compare and order decimals to the hundredths place

New Vocabulary in this Range: first, second, third, etc., odd, one-fourth, one-half, reduce, fractions, order, divisible, round, smallest, largest, lowest terms, greatest common factor, least common multiple, closest, units, set, digit, greater than, greatest

New Signs and Symbols: none

RIT Scores between 191 and 200

Whole Numbers

• Order numerals through 9999
• Count and convert to dozens
• Round 4- and 5-digit numbers to the nearest hundred thousand, thousand, hundred or ten
• Identify numbers as prime or composite
• Apply rules of divisibility by 2’s
• Complete a factor tree for a number (prime factorization)
• Understand and demonstrate that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3)
• Identify the least common multiple of two whole numbers

Fractions, Ratio and Proportion

• Write equivalent fractions using pictorial representation
• Find equivalent fractions using multiples and factors
• Write mixed numbers as improper fractions and improper fractions as mixed numbers
• Identify the least (lowest) common denominator of two fractions
• Express a fraction as a decimal and vice versa

· Solve proportions using the cross product method

Decimals

• Write a decimal for a shaded region (to tenths place)
• Identify and understand place value for decimals (tenths, hundredths, and thousandths)

Percents

• Model percents using a 10 x 10 grid
• Write a decimal or fraction as a percent and vice versa

Place Value, Expanded and Standard Notation

• Identify the number and written word for ordinal numbers

• Write numerals in expanded form through the hundred thousands

• Match word names to numerals through billions

• Identify place value using model to count

· Add whole numbers using place value

Ordering, Equalities and Inequalities

· Identify and understand the greater or lesser of two numerals (use the symbols < and > through 999,999)

• Compare and order fractions and mixed numbers

Exponents

• Exponential representation of 3 multiplied numbers (2x2x2)

New Vocabulary in this Range: thirds, fourths, rounded, thousands, exponential form, mixed number, improper fraction, lowest common denominator, percent, expanded form, prime, factor, proportion

New Signs and Symbols: use of dot as a multiplication symbol

RIT scores between 201 and 210

Whole Numbers

• Round to the nearest millions and billions
• Apply rules of divisibility
• Identify the greatest common factor of two whole numbers each of which is less than 100
• Write the Roman numeral equivalent of Arabic numbers 1-2000 and vice versa

Fractions, Ratio and Proportion

• Change a fractional numeral to its simplest form (lowest terms)
• Write the missing number in two equivalent ratios
• Use a number line to identify a fractional point

Decimals

• Write a decimal for a shaded region (hundredths)
• Write a terminating decimal as a fraction or mixed number
• Round decimals to nearest whole number, tenth, hundredth, or thousandth
• Multiply a decimal by multiples of 10, 100, or 1000

Percents

• Find a percent of a number
• Write a decimal or fraction as a percent or vice versa

Place Value, Expanded and Standard Notation

• Understand and identify the place value and value of each digit in numerals through the billions

· Write the word name for a decimal and vice versa

• Write numerals in expanded form through the hundred billions

Ordering, Equalities and Inequalities

· Order numbers from least to greatest and greatest to least

• Compare and order numbers through the billions

· Order decimals and fractions to the hundred thousandths

• Identify the greater or lesser of 2 integers
• Ordering integers that include fractions and wholes
• Translate verbal statements into equations (all four operations; several operations)
• Ordering exponential values

Exponents and Scientific Notation

• Write whole number in exponential form and compute the power of a number

New Vocabulary in this Range: missing number, pentagon, simplest fraction, biggest, hundredths, one less, decimal numeral, squared, divisible, inequality, expanded numeral, equivalent, point, standard numeral, sequence

New Signs and Symbols: + used as positive symbol, - used as negative symbol

RIT scores between 211 and 220

Whole Numbers

• Understand and use rules of divisibility
• Identify the greatest common factor of two whole numbers: list the factors or prime factorization
• Identify the greatest common factor and least common multiple of two whole numbers

Fractions, Ratio and Proportion

• Write improper fractions from picture presentations
• Change a fractional numeral to its simplest form (lowest terms)

Decimals

· Round monetary amounts to the nearest single coin or bill which could be used to pay for a purchase up to and including $20.00

• Write the decimal equivalent of a fraction and label as repeating or terminating

Percents

• Express a fraction as a decimal and as a percent

Ordering, Equalities and Inequalities

• Compare and order fractions with the same denominator and with different denominators
• Order decimals to thousandths; identify the greater or lesser of two decimals to thousandths

Exponents and Scientific Notation

• Order of “powers”
• Write a whole number or a decimal in scientific notation
• Write a number expressed in scientific notation in standard form

New Vocabulary in this Range: counting number, portion, fractional part, lowest terms, reciprocal, order, scientific notation, prime factorization, not prime, factor tree, common multiples, greatest common denominator, equivalent, nearest dollar

New Signs and Symbols: square root symbol

RIT scores between 221 and 230

Fractions, Ratio and Proportion

• Model and write numerical fractions
• Understand the concept of ratio using concrete and pictorial models

· Identify the least common denominator for 3 or more fractions: list the multiples or prime factorization

• Determine if a pair of ratios is equal or not equal using the equivalent fractions method
• Write the missing number in 2 equivalent ratios
• Solve proportions using the cross product method

Decimals

• Identify and order decimal and fractional coordinates on a number line

Percents

• Write a ratio (fraction) as a percent and a percent as a ratio (fraction): denominators of 100

Integers

• Understand the meaning of integers

Place Value, Expanded and Standard Notation

• Match word names to numerals to the hundred thousands in decimals

Ordering, Equalities and Inequalities

• Order a set of integers from least to greatest

Exponents and Scientific Notation

• Identify and use powers of 10

Square Roots

• Evaluate expressions using square roots

New Vocabulary in this Range: always true, proportion, multiply, between, tens digit, standard numeral, ratio

New Signs and Symbols: none

RIT scores between 231 and 240

Fractions, Ratio and Proportion

• Define ratio
• Write ratios in a variety of ways

Decimals

• Write a decimal or mixed decimal for a fraction
• Write a whole number or a decimal in scientific notation (negative exponents)

Place Value, Expanded and Standard Notation

• Write numerals in expanded form through the billions
• Understand and identify place value and value of each digit in numerals through the hundred billions

Exponents and Scientific Notation

· Evaluate expressions using the order of operations that include exponents

· Find products by applying rules for exponents

Square Roots

• Identify perfect squares in a list of numbers and calculate the positive square root of a perfect square

New Vocabulary in this Range: none

New Signs and Symbols: none

RIT scores between 241 and 250

Square Roots

• Evaluate expressions using square roots

New Vocabulary in this Range: Base ten, prime factors

New Signs and Symbols: none

RIT scores between 251 and 260

Exponents and Scientific Notation

• Evaluate powers with a negative exponent

New Vocabulary in this Range: none

New Signs and Symbols: none

RIT scores between 261 and 270

Percents

• Change a percent to a fraction (including mixed numbers)

Square Roots

• Understand properties of square roots

Irrational Numbers

• Define irrational numbers

New Vocabulary in this Range: infinite non-repeating decimal

New Signs and Symbols: none

RIT scores between 271 and 280

Exponents and Scientific Notation

• Evaluate power of zero
• Identify the lowest common multiple of numbers in their prime factored state

Set Notation

• Use inequalities to represent set notation

New Vocabulary in this Range: none

New Signs and Symbols: none

Math Goal 3: Geometry

– includes properties of two- and three-dimensional objects, points, rays, lines, and angles including congruency, similarities, and transformations

RIT scores between 151 and 160

Shapes and Figures, 2- and 3-dimensional

• Identify and name the plane figures: circle, triangle, and square

Congruency and Similarity

• Identify congruent figures (using “same size and shape” terminology)
• Identify figures that are similar, have the same shape

New Vocabulary in this Range: shape, circle, same as

New Signs and Symbols: none

RIT scores between 161 and 170

Shapes and Figures, 2- and 3-dimensional

· Identify and name solid figures: can (cylinder) and cone

• Relate and compare plane figures to solid figures
• Identify sides and corners (vertices) on solid figures
• Contrast open and closed figures
• Identify cylinder (can) attributes

Congruency and Similarity

• Identify congruent figures

New Vocabulary in this Range: matches, triangle, square, corners, cone, closed, inside

New Signs and Symbols: none

RIT scores between 171 and 180

Shapes and Figures, 2- and 3-dimensional

• Classify and sort solid figures

Congruency and Similarity

• Identify congruent figures using terminology

Symmetry and Transformations

• Recognize transformations of plane figures (slides, flips, and turns) by identifying the figure that will fit in a certain space

New Vocabulary in this Range: congruent, figure

New Signs and Symbols: none

RIT scores between 181 and 190

Shapes and Figures, 2- and 3-dimensional

• Identify and name the plane figures: circle, triangle, square, and rectangle
• Recognize solid figures: cube (box)
• Identify characteristics of plane figures (sides and corners)

Congruency and Similarity

• Identify congruent figures, angles, and line segments
• Identify similar figures (same shape, may or may not be same size)

Symmetry and Transformations

• Identify figures with line symmetry
• Recognize transformations of plane figures (slides, flips, and turns)
• Identify types of transformations (slides, flips, and turns)

Line Properties and Terminology

• Identify points on a line
• Identify the correct label for a line

New Vocabulary in this Range: symmetry, point, sides, rectangle, cube, straight, line segment, shortest

New Signs and Symbols: line AB (with double arrow over AB), line segment AB (with segment line over AB)

RIT scores between 191 and 200

Shapes and Figures, 2- and 3-dimensional

• Recognize solid figures: sphere (ball)
• Identify and name solid figures: cube, cylinder, cone, rectangular prism, and sphere
• Identify characteristics of plane figures (sides and corners)

Symmetry and Transformations

• Identify figures with line symmetry and symmetrical parts

Geometric Properties and Terminology

· Identify position concepts: (over, under, inside, outside, in front, behind, top, middle, bottom)

• Describe and measure right angles
• Identify right angles
• Identify intersecting, parallel lines
• Identify the diagonal of a circle

New Vocabulary in this Range: symmetrical, parallel, intersecting, diagonal, pair, angle, cylinder, outside, inside, sphere, faces, corresponding, point, intersect, outside, axis of symmetry, line segment, pentagon

New Signs and Symbols: symbol for parallel lines

RIT scores between 201 and 210

Shapes and Figures, 2- and 3-dimensional

• Identify faces, edges, and corners (vertices) on solid figures
• Identify polygons: triangle, quadrilateral, pentagon, and octagon
• Identify quadrilaterals: square, rectangle, and parallelogram

· Identify, name, and analyze solid figures: cube, cylinder, triangular pyramid and square pyramid (faces, edges, and vertices)

Symmetry and Transformations

• Identify mirror-images

Congruency and Similarity

• Identify congruent figures, angles and line segments

Geometric Properties and Terminology

• Identify points, lines, line segments, rays, planes, and angles
• Identify the diameter of a circle
• Identify intersecting, parallel, and perpendicular lines

New Vocabulary in this Range: intersection, quadrilaterals, octagon, parallelogram, pyramid, isosceles, right angle, diameter, right angle, geometric, perpendicular, plane

New Signs and Symbols: D for triangle, angle symbol

RIT scores between 211 and 220

Shapes and Figures, 2- and 3-dimensional

• Identify faces, edges, and corners (vertices) on solid figures

· Contrast open and closed figures

· Identify polygons: triangle, quadrilateral, pentagon, hexagon, and octagon

· Identify quadrilaterals: square, rectangle, parallelogram, trapezoid, rhombus

· Analyze solid figures: triangular pyramid and rectangular pyramid (faces, edges, and vertices)

Congruency and Similarity

· Identify similar figures (same shape, may or may not be the same size)

• Identify congruent polygons and their corresponding sides and angles

Symmetry and Transformations

• Identify types of transformations (rotation)

Geometric Properties and Terminology

• Identify points, lines, line segments, rays, and angles

· Identify angles: right, obtuse, and acute

· Identify when two intersecting lines are perpendicular

• Identify properties of similar figures

New Vocabulary in this Range: symmetrical, perpendicular, ray, vertex, rotation, triangular prism, corresponding parts, supplementary, acute angle, transformation

New Signs and Symbols: @ - congruent symbol, « - double arrow symbol for similarity, p - pi symbol, DABC - to label triangle

RIT scores between 221 and 230

Shapes and Figures, 2- and 3-dimensional

· Analyze solid figures: rectangular prism, triangular prism, triangular pyramid, square, pyramid (faces, edges and vertices)

• Classify polygons by sides and angles

Congruency and Similarity

• Identify congruent triangles according to corresponding parts (SSS, SAS, ASA)

Geometric Properties and Terminology

• Identify the center, radius and diameter of a circle
• Measure angles using a protractor
• Classify angles: supplementary and complementary
• Classify angles: adjacent, vertical, corresponding, and supplementary

New Vocabulary in this Range: radius, polygon, circumference, trapezoid, rectangular box, equilateral, similar, obtuse angle, straight angle, slide

New Signs and Symbols: angle symbol, label for line – L₁

RIT scores between 231 and 240

Symmetry and Transformations

· Understand meaning and representation of a dilation

Geometric Properties and Terminology

• Classify triangles by sides (equilateral, isosceles, and scalene) and angles (acute, obtuse, and right)

• Classify polygons by sides and angles

• Identify and discriminate between regular and irregular polygons
• Find the missing angle measurement in a triangle when two angles are known
• Solve word problems involving similar polygons
• Identify the base angles of a triangle
• Know the definition of the hypotenuse of a triangle

New Vocabulary in this Range: transformation, hypotenuse, edge, isosceles, scalene triangle, similar trapezoids, alternate interior angles, sum of angles in triangle

New Signs and Symbols: none

RIT scores between 241 and 250

Congruency and Similarity

· Construct congruent segments and angles

Symmetry and Transformations

• Identify symmetry of a sphere

Geometric Properties and Terminology

• Identify properties of parallel lines
• Construct angle bisectors
• Use the Pythagorean theorem to calculate the measure of one side of a right triangle when the other two sides are known
• Identify angle bisectors
• Solve problems regarding relationships among chords of a circle

New Vocabulary in this Range: symmetrical halves, diameter, radius, angle bisector, tangent, corresponding parts of congruent triangles, Pythagorean theorem, corresponding angles, complementary angles, construction

New Signs and Symbols: sign for parallel lines

RIT scores between 251 and 260

Congruency and Similarity

· Solve problems involving properties of similar triangles

Symmetry and Transformations

· Solve problems involving rotations (turns) and reflections (flips)

Geometric Properties and Terminology

• Identify properties and slope of lines
• Identify plane
• Identify midpoint and endpoint
• Identify perpendicular bisector
• Identify properties of polygons (rhombus, parallelogram)

New Vocabulary in this Range: slope, non-vertical and non-horizontal, midpoint, endpoint, rotational symmetry, reflected, perpendicular bisector, similar triangles, similar trapezoids, similar cylinders, conditional, counterexample, conclusion of in-then statement, interior of angle, exterior angle of regular polygon, interior angle of regular polygon, sum of angles in triangle equals 180 degrees, congruent angles, adjacent angles, vertical angles

New Signs and Symbols: none

RIT scores between 261 and 270

Geometric Properties and Terminology

• Identify the correct definition of a postulate
• Solve problems using two chord power theorem
• Identify and solve problems involving right triangles using the trigonometric functions and the Pythagorean Theorem
• Use of distance formula to determine type of triangle using coordinates
• Solve problems regarding relationships among chords, secants, tangents, inscribed angles, central angle, arc, and inscribed and circumscribed polygons of circles
• Measure and compare angles in degrees
• Solve problems involving the perimeter, circumference, area, volume, and surface area of common geometric figures
• Determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids
• Find and use measures of sides and interior and exterior angles to identify figures and solve problems involving polygons
• Know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections

New Vocabulary in this Range: postulate

New Signs and Symbols: none

RIT scores between 271 and 280

Congruency and Similarity

· Prove that triangles and other polygons are congruent or similar using algebraic, coordinate, and deductive proofs

Geometric Properties and Terminology

• Identify number of diagonals of regular polygons
• Informally prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles

New Vocabulary in this Range: HL

New Signs and Symbols: none

RIT scores between 281 and 290

Symmetry and Transformations

· Solve problems involving volume with rotational transformation

New Vocabulary in this Range: none

New Signs and Symbols: none

Math Goal 4: Measurement

– includes customary and metric units of measure around time, money, size, temperature, and weight, and the use of them in both calculating and estimating measurements.

RIT scores between 151 and 160

Length, Weight, Volume

• Compare objects by shape, size, height or length (larger, smaller, taller, shorter, longer)
• Measure length with metric measures using a graphic of a ruler(centimeters)

Time, Temperature

· Choose the appropriate tool: clock to measure time, calendar to measure days and months, thermometer to measure temperature, ruler to measure length

• Measure temperature with customary measures

New Vocabulary in this Range: longest, shortest, how tall, kilometer, meter, time

New Signs and Symbols: C for Celsius, cm for centimeter

RIT scores between 161 and 170

Time, Temperature

• Order periods of time (days of the week, months of the year, etc.)
• Tell and write time to the hour and half hour using analog and digital clocks
• Identify and interpret a calendar
• Read a Fahrenheit and Celsius thermometer to the nearest degree

Money

• Identify value of a penny, nickel, dime, and quarter

New Vocabulary in this Range: how long, names of days of week, next, names of months, pennies, centimeter, inches

New Signs and Symbols: degree symbol, : for time – 1:00, face of quarter, dime, penny, and nickel

RIT scores between 171 and 180

Length, Weight, Volume

• Determine more capacity or less capacity
• Measure length with customary measures (inch)
• Measure weight with customary measure (pounds)
• Measure capacity to the nearest cup, pint, quart, and gallon and do appropriate conversions between these units

· Estimate and measure the length of an object to the nearest metric and customary measure using a picture of a ruler

Area, Perimeter, Circumference

• Find the perimeter of a figure using units
• Estimate and verify the area of a figure using square units (counting)

Time, Temperature

• Tell time to the quarter hour using analog and digital clocks
• Tell time to the nearest 5 minutes using analog and digital clocks

· Compute simple conversions among units of time: seconds, minutes, hours, days, weeks, months, years

Money

• Identify value of a one dollar bill

· Determine if a collection of coins is enough to purchase an object up to and including $1.00

New Vocabulary in this Range: line segment, area, square units, perimeter, days, week, set, coins, thermometer, temperature, pounds, ounces, pints, quarts

New Signs and Symbols: $, decimal point for cents, F = Fahrenheit, lb = pounds, sq = square units, cent sign, recognize back of penny, nickel, dime, and quarter

RIT scores between 181 and 190

Length, Weight, Volume

• Measure weight with metric measures with units provided (grams)

· Measure length to the nearest inch, foot, and yard and do appropriate conversions between these units

Area, Perimeter, Circumference

• Develop area readiness by counting squares and blocks
• Estimate and verify the area of a figure using square units (counting)
• Find the perimeter of a polygon with 5 or less sides (no formula)

Time, Temperature

• Tell time to the nearest one minute on analog and digital clocks
• Compute word problems with time and calendars
• Determine elapsed clock time (no remaining with addition and subtraction)
• Determine elapsed clock time (any operation with renaming)

Money

• Identify the coins: pennies, nickels, and dimes
• Identify the value of a penny, nickel, dime, quarter, and one dollar bill

· Combine and identify the value of a collection of coins and bills up to and including $1.00

• Combine and identify equivalent values of coins and bills up to and including $1.00
• Make change to $1.00 by “counting on” or subtracting

· Compute simple addition or subtraction problems involving monetary amounts up to $10.00

New Vocabulary in this Range: about, length, estimate, perimeter, change, quarter, dollars, dozen, units, feet, yard, grams, meters, cups, gallons, nickel, pennies, dime, tablespoon, hours, minutes, degree

New Signs and Symbols: m = meters, g = grams

RIT scores between 191 and 200

Length, Weight, Volume

• Measure length to the nearest millimeter, centimeter, meter, and kilometer
• Select the appropriate metric and customary unit to measure an object or distance

· Perform conversions between linear units in the customary system; also as necessary in addition or subtraction problems

· Perform conversions between units of capacity in the customary system; also as necessary in addition or subtraction problems

Area, Perimeter, Circumference

• Estimate and verify the area of a figure using square units (counting)
• Find the area of irregular shapes; using square units
• Find the perimeter of polygons

Time, Temperature

· Identify time relationships: minutes in an hour, hours in a day, days in a week, weeks in a year

Money

· Combine and identify the value of a collection of coins and bills up to and including $10.00

· Compute simple addition or subtraction problems involving monetary amounts up to $10.00

• Compute and count change up to and including $100.00
• Compute and count change greater than $20.00

New Vocabulary in this Range: height, width, parallelogram, square, rectangle, triangle, year, ton, seconds, kilogram, distance, miles, liter

New Signs and Symbols: mm = millimeter, a.m. and p.m., hr = hours, min = minutes

RIT scores between 201 and 210

Length, Weight, Volume

• Find the volume of a figure using cubic units

· Perform conversions between units of mass in the metric system; also as necessary in addition or subtraction problems

• Select appropriate unit of measure for length and area
• Find the volume of rectangular solids using the formula

Area, Perimeter, Circumference

• Find the perimeter of a square or rectangle using the formula

· Solve practical word problems involving perimeter and area of a square, rectangle or triangle

• Calculate the area of a triangle
• Calculate the surface area of a rectangular prism

Time, Temperature

• Compute basic operations with units of time (include basic concept of time zones)

Angle Identification and Measure

• Identify angles according to their measure: right, obtuse, and acute

Money

• Compute and count change up to and including $5.00 (addition and subtraction only)
• Solve written word problems involving the addition or subtraction of monetary amounts

New Vocabulary in this Range: right angle, circumference, minutes, decades, milligrams, gram, cubic feet, volume, liters, length, weight, kilometers, millimeters, mass

New Signs and Symbols: ft for feet, mL = milliliters, right angle symbol, symbol for line segment, p

RIT scores between 211 and 220

Length, Weight, Volume

• Measure length to the nearest millimeter, centimeter, meter, and kilometer

Area, Perimeter, Circumference

• Calculate the area of irregular shapes
• Understand the effects of changing dimensions on perimeter and area

Angle Measure

• Measure angles using a protractor

Money

• Compute basic operations with monetary amounts up to and including $20.00

New Vocabulary in this Range: yards, measure of angle, degrees, protractor, centuries, below zero, Celsius, rectangular solid, rectangular prism, decades, ounces

New Signs and Symbols: ” = inches, yd = yards, b = base, h = height, r = radius, s = side, angle symbol, - for negative, + for positive, d = distance, tsp = teaspoon, pt = pint, gal = gallon, qt = quart, c = cup

RIT scores between 221 and 230

Length, Weight, Volume

• Measure length with metric measures (centimeter)
• Measure length with customary measures (inch)

• Select the appropriate unit of measure for length, area, and volume

Area, Perimeter, Circumference

• Analyze circles: center, chord, diameter, radius, arc, semicircle, and circumference
• Find the missing angle measurement in a triangle when two angles are known

New Vocabulary in this Range: reasonable, formula, segment BC, pi, radius squared, diameter, metric units, quarts, gallons, rectangular box, base, rate

New Signs and Symbols: oz = ounces, C = circumference

RIT scores between 231 and 240

Length, Weight, Volume

• Find the volume of a pyramid

Area, Perimeter, Circumference

• Find the perimeter of a square or rectangle using the formula
• Find the perimeter of polygons
• Calculate the area of a parallelogram and rectangle
• Calculate the area of a triangle
• Calculate the circumference of a circle using the formula

Time, Temperature

• Convert from Celsius to Fahrenheit
• Subtract Fahrenheit temperatures

Money

• Find commission and total pay

• Compute and count change greater than $20.00

New Vocabulary in this Range: rectangular house, height and base, algebraic expression, rows and columns, checking account, car purchase, commission, simple interest

New Signs and Symbols: F = 9/5 C + 32, formula for finding volume of a pyramid

RIT scores between 241 and 250

Area, Perimeter, Circumference

• Calculate the area of a parallelogram and rectangle using algebra tiles
• Understand the effects of changing dimensions on perimeter, area, and volume
• Calculate the surface area of a rectangular prism and cylinder

New Vocabulary in this Range: doubled and tripled, rectangular solid, cylindrical tank, algebra tiles, inscribed, time-and-a-half, sales tax, discount

New Signs and Symbols: none

RIT scores between 251 and 260

Length, Weight, Volume

• Find volume of cones and rectangular prisms and cylinders

Area, Perimeter, Circumference

• Find area of inscribed figure by using midpoints and endpoints

Angle Identification and Measure

• Relationship of size of angles and corresponding sides of a triangle

New Vocabulary in this Range: circumscribed, distance formula

New Signs and Symbols: formula for finding volume of a cone, formula for volume of a cube, formula for finding volume of a rectangular solid

RIT scores between 261 and 270

Area, Perimeter, Circumference

• Understand that area of a square equals side squared
• Find the surface area of a polyhedron and cylinder
• Find the diameters when given the area of a circle
• Find the perimeter with use of variables

New Vocabulary in this Range: none

New Signs and Symbols: none

RIT scores between 271 and 280

Length, Weight, Volume

• Find volume of cylinder using knowledge of radius versus diameter

Money

• Solve problem given two discounts

New Vocabulary in this Range: rate of interest, successive discounts

New Signs and Symbols: none

RIT scores between 281 and 300

Area, Perimeter, Circumference

• Solve problem using ratio of rectangular areas

New Vocabulary in this Range: none

New Signs and Symbols: none

Math Goal 5: Statistics/Probability and Graphing

– Students determine the mathematical probability of events, calculate measures of central tendency, and work with combinations and permutations. Interpret and predict information from charts, graphs, and tables.

RIT scores between 151 and 160

Graphing

• Use pictographs or bar graphs to compare quantities

New Vocabulary in this Range: none

New Signs and Symbols: none

RIT scores between 161 and 170

Probability and Prediction

• Determine an outcome and make a prediction (single event)

Graphing

• Understand the concept of addition using concrete objects
• Represent and compare data (e.g. largest, smallest, most often, least often) by using picture graphs, pictures, or simple bar graphs

New Vocabulary in this Range: probability

New Signs and Symbols: none

RIT scores between 171 and 180

Probability and Prediction

• Interpret a table and make predictions (chance)
• Predict the likely number of times a condition will occur based on an analysis of data

Graphing

• Complete and interpret simple picture graphs, bar graphs, line graphs or tables using the key to indicate the quantity represented by each symbol
• Graph ordered pairs in the first quadrant
• Identify least and greatest values represented in bar graphs and pictographs

New Vocabulary in this Range: chance

New Signs and Symbols: none

RIT scores between 181 and 190

Probability

· Predict whether common events are certain, likely, unlikely, possible, impossible, fair or unfair

· Investigate experimental probability of an event using a coin or spinner

Graphing

• Solve simple word problems based on data from picture and bar graphs

New Vocabulary in this Range: most often

New Signs and Symbols: none

RIT scores between 191 and 200

Probability and Prediction

• Develop concept of chance and make predictions for events (ex. rolling a number dice)

Statistics

• Use tallies to record data
• Compute averages with a given set of data

Combinations and Permutations

• Solve problems involving combinations or permutations

Graphing

• Use a number line to write number sentences using subtraction
• Solve problems using information from a bar graph
• Solve multi-step word problems with pictographs, bar graphs, or line graphs
• Construct, and solve word problems involving line graphs
• Construct and solve word problems involving circle graphs
• Read and interpret dual bar graphs and dual broken-line graphs

New Vocabulary in this Range: average, bar graph, percentage

New Signs and Symbols: %

RIT scores between 201 and 210

Probability and Prediction

• Compute simple probability outcomes
• Determine the probability of an outcome (multiple events)
• Use the counting principle to determine probability

Statistics

• Solve practical problems involving the mean (average) of a set of numbers

Graphing

· Solve problems using information from a picture graph (symbol may represent more than one)

• Interpret data given in percent form on a circle graph and broken line graph

New Vocabulary in this Range: least often, how many ways, ordered pairs, coordinates, distance formula

New Signs and Symbols: none

RIT scores between 211 and 220

Graphing

• Identify and order decimal and fractional coordinates on a number line
• Order integers on a number line

New Vocabulary in this Range: dice, arranged, highest mean

New Signs and Symbols: none

RIT scores between 221 and 230

Probability and Prediction

• Investigate experimental probability of an event using a coin or spinner

Statistics

• Know the concepts of mode, median, and mean; compute and compare them in simple examples to demonstrate that these measures of central tendency may differ for a given set of data

Combinations and Permutations

• Use a tree diagram to determine the number of possible outcomes of an event

Graphing

• Interpret data given in horizontal and vertical bar graphs to solve problems
• Graph ordered pairs in all four quadrants (coordinate geometry)

New Vocabulary in this Range: even numbers, mean, median, integer, intersection, table, frequency, origin, quadrant

New Signs and Symbols: none

RIT scores between 231 and 240

Statistics

• Calculate range, mode, median, and mean

Graphing

• Find location of coordinates on a number line
• Place numbers in correct order on a number line
• Locate the vertex on a coordinate grid
• Create a table of (x, y) values for the given linear equation and graph the function

New Vocabulary in this Range: vertex, fractional part, amount of sales, translation, matrix, possibility, mean salary, coordinates of points

New Signs and Symbols: none

RIT scores between 241 and 250

Probability and Prediction

• Predict outcomes using a six-sided cube

Combinations and Permutations

• Find how many different ways a set can be ordered

Graphing

• Use a graph to predict some future point in time
• Determine endpoints and midpoint of a line on a coordinate graph

New Vocabulary in this Range: coordinate, Venn diagram, greatest decrease, endpoints, midpoint

New Signs and Symbols: none

RIT scores between 251 and 260

Probability and Prediction

• Calculate basic probability theoretically and use results to make predictions

Graphing

• Derive linear equations by using the point-slope formula
• Derive and solve problems involving use of ordered pairs to determine area of a figure
• Know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections
• Determine the axis of symmetry of a linear graph

New Vocabulary in this Range: none

New Signs and Symbols: none

RIT scores between 261 and 300

Combinations and Permutations

• Perform complex combinations in problem solving situations

Graphing

• Determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids

New Vocabulary in this Range: none

New Signs and Symbols: none

Math Goal 6: Algebraic Concepts

– includes patterns, functions, solving equations, order of operations, properties, simplifying expressions and continues up through more difficult skills in Algebra specific content

RIT score between 151 and 160

Patterns, Sequences, Functions

• Find and extend patterns
• Recognize and extend a pattern: shape, color and size

Solving Equations and Inequalities, Simplifying Expressions, Order of Operations

• Determine what operation is needed to solve a word problem (addition and subtraction)

New Vocabulary in this Range: none

New Signs and Symbols: € for answer to equation

RIT score between 161 and 170

Solving Equations, Simplifying Expressions, Order of Operations

· Solve for missing numbers in an addition or subtraction sentence

• Determine what operation is needed to solve a word problem (any operation)

New Vocabulary in this Range: none

New Signs and Symbols: ( ) used in equations

RIT score between 171 and 180

Solving Equations and Inequalities, Simplifying Expressions, Order of Operations

• Solve for missing factors in a multiplication or division sentence
• Evaluate a numerical equation involving more than one operation

Properties

• Demonstrate the associative, commutative, and zero property of addition

New Vocabulary in this Range: none

New Signs and Symbols: <, > symbols

RIT score between 181 and 190

Patterns, Sequences, Functions

• Find and extend patterns, both increasing and decreasing
• Complete a table according to a rule

· Choose and apply an appropriate problem solving strategy: Find a pattern

Solving Equations and Inequalities, Simplifying Expressions, Order of Operations

• Use inverse operations to find missing equation
• Write number sentences using addition
• Identify missing elements in number sentences

Properties

• Identify the associative, commutative, identity and zero property of multiplication

Ordered Pairs

• Graph ordered pairs in the first quadrant

New Vocabulary in this Range: sign

New Signs and Symbols: - used as negative

RIT score between 191 and 200

Patterns, Sequences, Functions

• Count and write by 4’s

Solving Equations and Inequalities, Simplifying Expressions, Order of Operations

• Use symbols of inequality, < and > to write and complete number sentences
• Solve simple addition problems with “n” as an addend or sum
• Solve simple multiplication problems with “n” as a multiple or product
• Solve simple division problems with “n” as a quotient or divisor

• Identify the base and the exponent of a given numerical expression and calculate its value
• Evaluate numerical expressions using the order of operations

• Solve whole number equations with any operation

New Vocabulary in this Range: if-then, product, sum

New Signs and Symbols: variables, exponents

RIT scores between 201 and 210

Patterns, Sequences, Functions

• Use of a function “machine” to determine input and output

Solving Equations and Inequalities, Simplifying Expressions, Order of Operations

• Evaluate an expression involving more than one operation (order of operations)
• Use the basic properties of multiplication to write an algebraic expression that is equivalent to a given algebraic expression

• Solve equations