Mathematics Curriculum

Quick Access links: Grades 3-5 & Grades 6-8

K - 2

Skill Area:	The student will be able to:
	Kindergarten	Grade 1	Grade 2
1. Number and Operations	Explore and identify the number of objects in a set Explore and identify equal and unequal sets of objects Count pictorial representations of objects up to 20 Count concrete objects up to 20 Explore the order relation of whole numbers on a number line Identify numerals 0 – 20 Explore the use of numbers and numerals in daily life Develop the skills of recognizing half an object and half a set of objects Tell which objects in a line are first, second, or last Match two sets of objects with 1 to 1 correspondence Identify number words 0 – 10 Given sets of 0 – 20, write the correct numeral	Count by ones to 100 Count objects to 100 grouping by 10’s and 1’s Read and write numerals to 100 Know place value of tens and ones Identify whole objects, one-half, one-fourth, and one-third of an object Recognize and use symbols of ½, ¼, and 1/3. Match numerals and number words 0 – 20 Count by 2’s to 20 Count by 5’s and 10’s to 100 Use +, -, and = symbols Add to 18 using manipulatives Know addition facts to 10 Add three single digit numbers Subtract from numbers to 10 with manipulatives	Count, read and write 0 – 1000 Identify a numeral 0 – 1000 out of sequence Know place value to hundreds Indicate ordinal number to 20 Recognize and use less than, greater than and equal to Rewrite numerals into words and words into numerals 0 – 99 Recognize and use symbols ½, 1/3, ¼, 2/3, ¾ Identify dozen and half dozen Count by 2’s, 5’, and 10’s to 100 Recognize even and odd numbers Know additions facts to 18

Skill Area:	The student will be able to:
	Kindergarten	Grade 1	Grade 2
1. Number and Operations (continued)	Given a numeral 0 – 20, match a set with that number of elements Write the numerals 0 – 20 in numerical order Using concrete objects, explore the process of joining and separating sets Explore joining a set of zero to a set of objects Using sets of concrete objects, explore addition and subtraction Solve one step word problems involving addition and subtraction Count by 10’s to 100 Divide a group of objects into 2 equal sets Identify penny, nickel, dime, and quarter Count up to 10 pennies and designate value Count dimes to one dollar	Add two-digit numbers without regrouping Solve word problems with oral explanation given Divide a group of objects into 2 or more equal sets Name and assign value to penny, nickel, dime, and quarter Choose coins equal to a given value up to 50¢ Solve one step word problems using money with oral explanation given Apply the commutative property to addition	Add three digits vertically and horizontally (column and math sentences) Add 2 and 3 digit numbers with regrouping Solve number sentences with missing addends Know subtractions facts to 10 Subtract from numbers to 18 Subtract 2 and 3 digit numbers, no regrouping Subtract two digit numbers with regrouping Solve written word problems with work shown and explanation given Understand situations that require multiplication and division
Skill Area:	The student will be able to:
	Kindergarten	Grade 1	Grade 2
1. Number and Operations (continued)			Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators Name and assign value to all coins and one dollar Use ¢, $, and decimal point correctly Know equivalent value of all coins 10¢ = 2 nickels, 2 quarters = half dollar, etc. Count values of any combination of coins to 99¢ Addition/subtraction of decimals with dollar signs Solve word problems involving money with work shown and explanation given Apply the commutative property of addition
Skill Area:	The student will be able to:
	Kindergarten	Grade 1	Grade 2
2. Algebra	Given a simple pattern be able to reproduce the same Classify by size, color, and shape Sort, classify and order by one attribute, such as size, color or shape Use concrete, pictoral, and verbal representations to develop an understanding, using objects, pictures and symbols Demonstrate the addition and subtraction of whole numbers, using objects, pictures and symbols	Classify by size, color, and shape Identify and copy simple patterns Recognize and extend patterns Use concrete, pictoral, and verbal representations to develop an understanding, using objects, pictures, and symbols Demonstrate the addition and subtraction of whole numbers, using objects, pictures, and symbols	Identify and continue complex numeric and geometric patterns Analyze and identify different types of patterns including repeating and growing patterns Use concrete, pictoral, and verbal representations to develop and understanding, using objects, pictures, and symbols Demonstrate the addition and subtraction of whole numbers, using objects, pictures, and symbols
3. Geometry	Recognize plane shapes – circle, triangle, square, and rectangle Recognize similar shapes in the environment	Identify number of sides in a basic plane shape Recognize similar shapes in the environment Expand use of positional words to include left and right	Recognize basic solid figures – cubes, cylinders, pyramids, spheres, rectangular solids, and cone Recognize symmetric figures
Skill Area:	The student will be able to:
	Kindergarten	Grade 1	Grade 2
3. Geometry	Draw shapes – circle, triangle, square, and rectangle Classify by size, color, and shape Use positional words to describe the relationship of two or more objects (over, under, beside, etc.)		Identify number of angles/sides in basic plane shapes in the environment Recognize similar shapes in the environment Recognize rotated shapes Explore symmetry through paper folding & cutting Investigate and predict the results of combining, dividing, and changing 2 dimensional shapes Further expand use of positional words to include: to the left of, to the right of, vertical, horizontal, etc. Explore concept of area, perimeter, and volume using non-standard measures

Skill Area:	The student will be able to:
	Kindergarten	Grade 1	Grade 2
4. Measurement	Explore the reasons for measuring objects Measure with non-standard unit of measure (length, weight) Use the terms morning, afternoon and night correctly Read clocks to the hour – analog & digital Read calendars to identify current month, day, date, and year	Read a ruler to nearest whole inch Measure length and height with non-standard and customary units (inches) Weigh with non-customary units Choose appropriate measuring tools Read clocks to hour and half hour – analog & digital Expand use of calendars to include yesterday, today and tomorrow	Measure in inches, feet and centimeters Estimate length to the nearest whole inch or foot Read balance scales Read thermometers (F) Understand second, minute, hour, day, week, month, season, and year as unit of time Tell time to five-minute intervals – analog and digital Expand the use of calendars to identify dates in the recent future and past Weigh using pounds and grams Measure using cups, pints, quarts, and liters Choose appropriate units of measure Understand 60 minutes in an hour and 30 minutes in half hour

Skill Area:	The student will be able to:
	Kindergarten	Grade 1	Grade 2
5. Data Analysis and Probability	Read charts Interpret simple charts Read simple pictograph using key Draw conclusions from graphs Read and interpret bar graphs Use concepts of chance to predict and record outcomes of simple events	Read charts Interpret simple charts Read simple pictograph using key Draw conclusions from graphs Read and interpret bar graphs Use concepts of chance to predict and record outcomes of simple events	Read charts Interpret simple charts Read simple pictograph using key Draw conclusions from graphs Read and interpret bar graphs Collect and organize data to make a graph include tallies, check marks and pictoral representations Use concepts of chance to predict and record outcomes of simple events
6. Problem Solving	Tell the number sentence that could be used to solve the word problem	Write the number sentence that could be used to solve a word problem Use the best operation for solving a problem Explain orally how you solved the problem	Design a picture that represents a problem Choose the best strategy to solve a problem Choose the best strategy to solve a problem; solve the problem with work shown and explanation given; and label the solution appropriately
Skill Area:	The student will be able to:
	Kindergarten	Grade 1	Grade 2
7. Reasoning and Proof	Understand estimation is a reasonable guess Visually estimate number of objects (guessing jar, comparing objects) Check work to see if the solution is reasonable	Use estimation skills to compare number, length, and weight Check work to see if the solution is reasonable	Use estimation skills to include estimate of number, height, weight, and length of time Check work to see if the solution is reasonable
8. Communication	Communicate his/her mathematical thinking coherently and clearly to others, in a grade appropriate manner	Communicate his/her mathematical thinking coherently and clearly to others, in a grade appropriate manner	Communicate his/her mathematical thinking coherently and clearly to others, in a grade appropriate manner
9. Connections	Recognize and use connections among mathematical ideas Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Recognize and apply mathematics in contexts outside of mathematics	Recognize and use connections among mathematical ideas Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Recognize and apply mathematics in contexts outside of mathematics	Recognize and use connections among mathematical ideas Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Recognize and apply mathematics in contexts outside of mathematics

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Grades 3 - 5

Skill Area:	The student will be able to:
	Grade 3	Grade 4	Grade 5
1. Number and Operations	Know place value to thousands Write in expanded notation Read and write numbers through thousands Round off numbers to tens and hundreds Rewrite numerals into words and words into numerals to 999 Recognize any even and odd number Recognize and use ( ) Add/subtract up to 3 digit numbers with or without regrouping Solve written word problems with work shown and explanation given Know multiplication facts 0 – 5 Multiply two or three digit numbers by a one digit number Divide a 2 digit number by a 1 digit number with or without remainders Know subtract facts through 18	Know place value to 1 million Write number in expanded notation through hundred thousand Round off numbers to thousands Add/subtract multi-digit numbers with and without regrouping Know multiplication facts up to the tens Multiply two-digit numbers by two digit numbers Divide any number by one digit with or without a remainder Solve word problems with work shown and explanation given Create equivalent fractions Add/subtract fractions with like denominators	Round off numbers to ten thousand Read number line including decimal numbers Determine greatest common factor Determine least common multiple Name and use the divisibility rules for 2, 3, 5, and 10 Explore exponents Add and subtract any whole numbers fluently Multiply three digit number by two digit numbers Divide by one digit and two digit divisors Demonstrate order of operations using parentheses and explain order of operations (M, D, A, S) Add or subtract fractions with like and unlike denominators

Skill Area:	The student will be able to:
	Grade 3	Grade 4		Grade 5
1. Number and Operations (continued)	Recognize and use equivalent fractions Add and subtract fractions with like denominators Recognize shaded areas as fractional parts Make change up to $1.00 using fewest possible coins Add/subtract decimals with dollar signs Solve one and two step word problems involving money with work shown and explanation given Add decimal numbers Estimate total cost of several items with prices given	Understand the concept of mixed numbers Add, subtract and multiply decimals with dollar signs Solve one and two step word problems involving money with work shown and explanation given Estimate total cost of several items with prices given Make change up to $5.00 using the fewest possible coins and bill Add/subtract decimal numbers		Add and subtract mixed numbers Calculate the fractional part of a whole number Discuss and solve routine one and two step word problems requiring addition and subtraction of fractions with work shown and explanation given Order fractions Add or subtract numbers with varying numbers of decimal places Solve routine word problems involving decimals Compare decimals to the thousandths place Recognize and generate equivalent forms of commonly used fractions, decimals, and percents Describe classes of #’s according to characteristics
Skill Area:	The student will be able to:
	Grade 3		Grade 4	Grade 5
1. Number and Operations (continued)				Explore ratios and proportions of whole numbers

Skill Area:	The student will be able to:
	Grade 3	Grade 4	Grade 5
2. Algebra	Find replacements for variables that make single operation number sentences true Investigate how a change in one variable relates to a change in another variable Represent the idea of a variable as an unknown quantity using letters or symbols Identify and continue complex numeric and geometric patterns Identify and use commutative property to compute with whole numbers Express mathematical relationship using equations Represent and analyze patterns and functions using words Use representations such as graphs, tables, and equations to draw conclusions Identify and describe situations with constant or varying rates of change and compare them	Find replacements for variables that make dual operation number sentences true Investigate how a change in one variable relates to a change in a second variable Represent the idea of a variable as an unknown quantity using a letter or symbol Identify and use the commutative and associative properties to compute with whole numbers Express mathematical relationships using equations Identify and continue complex numeric and geometric patterns Represent and analyze patterns and functions using words and tables Use representations such as graphs, tables, and equations to draw conclusions Identify and describe situations with constant or varying rates of change and compare them (students should have opportunities to study situations that display different patterns of change – constant such as someone walking at a constant speed; rate change (increase or decrease) such as plants growing)	Find replacements for variables that make multiple operation number sentences true Investigate how to change in one variable relates to a change in a second variable Represent variables as a letter or symbol Identify and use the commutative, associative and distributive properties Express mathematical relationships using equations Identify and continue complex numeric and geometric patterns Represent and analyze patterns and functions using words, tables, and graphs Use representations such as words, tables, and graphs Identify and describe situations with constant or varying rates of change and compare them

Skill Area:	The student will be able to:
	Grade 3	Grade 4	Grade 5
3. Geometry	Recognize number of angles/sides in basic plane figure Identify basic plane figures/polygons Identify, compare, and analyze attributes of two dimensional shapes Put together needed blocks to complete larger blocks Recognize result of cutting solid shapes (solid/cross sections) Recognize rotating two dimensional figures Identify congruent and symmetrical figures Experiment with paper folding cutting/symmetry Build and/or draw geometric objects Use the properties of shapes and figures to describe the physical world Use geometric models to solve problems in other areas of mathematics, such as number and measurement	Identify number of angles/sides in basic plane figure Identify basic plane figures/polygons Identify and build a three dimensional representation of a two dimensional object Predict and describe the results of rotating two dimension figures Recognize and describe line of symmetry in two dimensional figures Use geometric models to solve problems in other areas of mathematics, such as number and measurement Use the properties of shapes and figures to describe the physical world	Identify basic plane figures/polygons Identify types of quadrilaterals Identify basic solid shapes Know there are 360 degrees in a circle Estimate the size of an angle Use properties of circles Find the coordinates of a point Identify and describe congruent, similar, and symmetric figures Identify and build two dimensional representation of a three dimension object Discuss and define the properties of triangles Identify the different types of triangles Predict and describe the results of sliding, flipping, and turning two dimensional shapes and designs Identify and describe line and rotational symmetry in two dimensional and three dimensional shapes and designs
Skill Area:	The student will be able to:
	Grade 3	Grade 4	Grade 5
3. Geometry (continued)	Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life		Use geometric models to solve problems in other areas of mathematics, such as number and measurement Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life

Skill Area:	The student will be able to:
	Grade 3	Grade 4	Grade 5
4. Measurement	Compute perimeter of a rectangle Compute the area of a rectangle using blocks Tell time to the minute-analog and digital Know concept of a.m. and p.m. Read thermometers Read scales Read and use calendars Estimate and measure to nearest inch, centimeter, foot, yard, and meter Convert cups, pints, quarts and gallons using a visual aid Estimate and weigh using 16 oz. Read map scales Convert minutes after hour to minutes before hour Estimate distance on a map using key Choose appropriate units and tools of measurement	Compute perimeter of any polygon Compute area of a rectangle using formula: length times width Determine the surface areas and volumes of rectangular solids Read map scales Estimate distance on a map using a scale Measure to the ¼ inch Read thermometers Read clock Convert minutes after hour to minutes before next hour Convert inches to feet and feet to inches Estimate and measure to nearest meter Convert feet to yards and yards to feet Convert ounces to pounds and pounds to ounces Choose appropriate units and tools of measurement	Compute the area of a rectangle, triangle, and parallelogram Read protractors Read rulers to the nearest quarter inch Read thermometers Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes Convert unit equivalents within the metric system Convert unit equivalents with the English system Experiment with the selection of the appropriate metric unit of measuring a particular linear distance Choose appropriate units and tools of measurement
Skill Area:	The student will be able to:
	Grade 3	Grade 4	Grade 5
4. Measurement (continued)	Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of units for measuring each attribute Understand that measurements are approximations and understand how differences in units affect precision	Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute Understand that measurements are approximations and understand how differences in units affect precision	Understand that measurement are approximations and understand how differences in units affect precision Explore what happens to measurements of a two dimensional shape such as its perimeter and area when the shape is changed in some way

Skill Area:	The student will be able to:
	Grade 3	Grade 4	Grade 5
5. Data Analysis and Probability	Collect and organize data using observations, surveys, and experiments Represent data using various types of graphs, charts, and tables Represent data using bar graphs, line graphs, pictographs, and tables Use concepts of chance to predict the probability of outcomes and test the predictions Compare different representations of the same data and evaluate how well each representation shows important aspects of the data	Collect and organize data using observations, surveys, and experiments Read and interpret various types of graphs, charts, and tables Draw conclusions from graphs Represent data using bar graphs, pictographs, and tables Use concepts of chance to predict the probability of outcomes and test the predictions	Collect data using observations, surveys, and experiments Represent data using bar graphs, pictographs, circle graphs, and tables Use concepts of chance to predict the probability of outcomes and test the predictions Compare different representations of the same data and evaluate how well each representation shows important aspects of the data Organize and analyze data using mean, median, mode, and range

Skill Area:	The student will be able to:
	Grade 3	Grade 4	Grade 5
6. Problem Solving	Restate a problem Choose the best strategy to solve a single or multi-step problem: i.e., picture, graph, table, number sentence, etc. Solve the problem with work shown and explanation given Determine essential information to solve a problem	Restate a problem Choose the best strategy to solve a single or multi-step problem: i.e., picture, graph, table, number sentence, etc. Solve the problem with work shown and explanation given Determine essential information to solve a problem	Restate a problem Choose the best strategy to solve a single or multi-step problem: i.e., picture, graph, table, number sentence, etc. Solve the problem with work shown and explanation given Determine essential information to solve a problem Interpret and solve non routine word problems

Skill Area:	The student will be able to:
	Grade 3	Grade 4	Grade 5
7. Reasoning and Proof	Using estimation skills to make and investigate mathematical conjectures Check work to see if the answer is reasonable	Using estimation skills to make and investigate mathematical conjectures Check work to see if the answer is reasonable	Using estimation skills to make and investigate mathematical conjectures Check work to see if the answer is reasonable
8. Communication	Communicate their mathematical thinking coherently and clearly to others, in a grade appropriate manner	Communicate their mathematical thinking coherently and clearly to others, in a grade appropriate manner	Communicate their mathematical thinking coherently and clearly to others, in a grade appropriate manner
9. Connections	Recognize and use connections among mathematical ideas Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Recognize and apply mathematics in contexts outside of mathematics (use simple tables and graphs to communicate ideas and information in a concise and clear manner)	Recognize and use connections among mathematical ideas Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Recognize and apply mathematics in contexts outside of mathematics	Recognize and use connections among mathematical ideas Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Recognize and apply mathematics in contexts outside of mathematics

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Grades 6 - 8

Data Analysis and Probability
STANDARD	EXPECTATION
Instructional Programs from grade 6-8 should enable students to-	In grade 6 all students should-	In grade 7 all students should-	In grade 8 all students should-
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them	collect data about a characteristic shared by two populations or different characteristics within one population	collect data about a characteristic shared by two populations or different characteristics within one population	formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population
	select, create, and use appropriate graphical representations of data, including line, bar, pie pictograph, line plots, stem and leaf and circle graphs	create, and use appropriate graphical representations of data, including, but not limited to, histograms, box plots, and scatterplots	select, create, and use appropriate graphical representations of data, including, but not limited to, histograms, box plots, and scatterplots
Select and use appropriate statistical methods to analyze data	find measures of center and spread (to include median and mode) including mean, median, mode and range		use and interpret measures of center and spread (to include median and mode) including mean and interquartile range
			discuss and understand the correspondence between data sets and their graphical representations,especially histograms, stem-and-leaf plots, box plots, and scatterplots
Develop and evaluate inferences and predictions that are based on data	use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken