Belle Vernon Area Math Curriculum Guide K 12 2007-2008 School Year 1
Table of Contents: Page 1) Cover page of why and how the checklists were developed. 3 2) User Guide (defining terms found in the checklist). 4 3) Elementary Checklists: a. Kindergarten Mathematics 6 b. First Grade Mathematics 9 c. Second Grade Mathematics 12 d. Third Grade Mathematics 16 e. Fourth Grade Mathematics 20 f. Fifth Grade Mathematics 26 4) Middle School Checklists: a. Sixth Grade Mathematics 31 b. Seventh Grade Mathematics 34 c. Pre- Algebra Mathematics 37 5) High School Checklists: a. Alignment to PSSA Anchors Grid 42 b. Algebra/Geometry Part A 48 c. Algebra/Geometry Part B 51 d. Algebra/Geometry Part C 55 e. Algebra I 58 f. Geometry 61 g. Algebra II 66 h. Algebra III/Trigonometry 68 i. Introduction to Calculus 73 j. Accelerated Geometry 75 k. Accelerated Algebra II 78 l. Honors Pre-Calculus 81 m. Honors Calculus 85 n. AP Calculus 87 o. Statistics 90 p. PSSA Prep 9 th grade 93 q. PSSA Enhancement Grade 11 94 Notes: 1) Every checklist was correlated to the PSSA anchors by the teachers going through the anchors and making sure all of the topics on the 2007 anchors were covered in the checklist. At the high school, a matrix was created due to the fact there are not anchors every single year after grade 8. 2) These checklists are a work in progress. They were completed as of the date of 5/18/2007. 2
Belle Vernon Area School District Math Curriculum Topic Checklists During the 2005-2006 school year a team of math teachers from Kindergarten through 12 th grade came together to review the curriculum at each grade level within the district. Each grade level worked together as a team and created a checklist of the topics to be taught in alignment with the PSSA Assessment anchors, PSSA Standards, and any additional skills needed to be successful in the next math course. Emphasis was placed on creating a seamless K-12 Math Curriculum without gaps or unnecessary repetition. The intentions of these checklists are to: Provide a resource for all staff, parents, and students that shows what is being taught in each course. Insure that all PSSA Anchors, PA Standards, and other necessary skills are being taught when they are needed, so that our students are not taking a standardized test with many items that they have never seen or do not learn until a year after the test. Also, insure that students will have the necessary background skills to be successful in other subject areas. Serve as a guide for any new teacher or long term substitute as to what needs to be taught. Enable communication and collaboration among math teachers Provide a usable document that can be reviewed and updated each year. Serve to strengthen our math department. For each course or grade level a timeline should be established on how long to spend on each topic. Eventually common lesson plans incorporating best teaching practices can be created to help strengthen areas of weakness. Every math teacher and new teacher will be given a copy of this document. Each new teacher should be assigned a Mentor teacher that is familiar with the topic checklists for their course and can assist the new teacher in how to effectively use the checklist to guide instruction. 3
User Guide: Definition of columns used in the topic checklists Content Chapter/Section or lesson Calculator Anchor/Standard Objective Days/Lessons Is the main mathematical or general topic to be covered such as a chapter title like using fractions. Tells where this item can be found in the textbook, workbook, or or other Supplemental Material (listed as SM). The name of the textbook, workbook, and other resources that are used will be listed at the end of the Checklist. For example 1.5 would be Chapter 1 section or lesson 5. In grades K-3 calculators are not used. This column will be used starting with grade 4 and above. C means that a calculator will be allowed on this objective. Displays which PSSA Anchor or PA Standard will be covered. If the objective is not a PSSA Anchor (testable item) then the Pennsylvania Standard that is covered by the objective will be listed. Pennsylvania Standards will have the letters PA in front of them. Some objectives may have neither an Anchor nor PA standard number but still be a required skill needed for the next math course. Clearly states the specific topic to be taught. As an example if the general Content is using fractions the objective may be Adding like fractions. This column lists the suggested number of days/lessons spent teaching this objective. Resources After each Topic Checklist, the textbook name, workbooks, and any additional resources that may be used should be listed such as video, manipulatives, or teacher made worksheets. List all supplemental resources listed in the topic checklist. Assessment Teachers do not have to list all assessments that they use individually, just list the common assessments that all teachers of the same course should administer with some targeted time line. Example: Chapter 1 test, Chapter 2 test, 4sight, Chapter 3 test (end 1 st 9weeks) Chapter 4 test, Chapter 5 test, Chapter 6 then Midterm (end 2 nd 9weeks) 4
Belle Vernon Area Elementary Math Curriculum Guide 5
Content SORTING & CLASSIFYING Chapter/ Section 1.1 1.2 1.3 Kindergarten Mathematics Checklist of Objectives Objective To identify positions top, middle, bottom Compare and identify positions of objects, using before, after, between. Compare and identify positions of objects, using inside and outside. 1.4 Compare and identify positions right and left. 1.5 Compare objects and describe how they are the same or different. 1.6 Identify, sort, and classify objects and shapes by color. 1.7 Identify, sort, and classify objects by size. 1.8 Identify, sort, and classify items by shape. 1.9 Use logical thinking to solve sorting problems. 1.10 Sort objects by shape & color to make real graphs 1.11 Sort & graph coins by kind (pennies, nickels, dimes, quarters) 1.12 Sort objects by various attributes into picture graphs 1.13 Use a graph to gather & interpret data NUMBERS 0-5 3.1 Match objects one to one 3.2 Match & identify equal sets of objects 3.3 Identify sets with more objects 3.4 Identify sets with less objects NUMBERS 6-12 4.1 3.6 Count, recognize, print, and name examples of one and two; identify and read words one and two. 3.7 Count, recognize, print, and name examples of three; identify and read word three. 3.8 Count, recognize, print, and name examples of four; identify and read word four. 3.9 Count, recognize, print, and name examples of five; identify and read word five. 3.10 Count, recognize, print, and name examples of zero; identify and read word zero. 3.11 Count, recognize, print, and name examples of numbers zero through five 3.12 Use ordinal number from first through fifth to show positions 3.13 Solve problems by interpreting graphs using numbers zero though five Count, recognize, print, and name examples of six; identify and read word six. 4.2 Count, recognize, print, and name examples of seven; identify and read word seven. 4.3 Count, recognize, print, and name examples of eight; identify and read word eight. 4.4 Count, recognize, print, and name examples of nine; identify and read word nine. 4.5 Count, recognize, print, and name examples of six through nine 4.6 Count, recognize, print, and name examples of ten; identify and read word ten. 4.7 Count, recognize, print, and name examples of eleven 4.8 Count, recognize, print, and name examples of twelve 6
4.9 Count, recognize, print, and name examples of numbers ten through twelve 4.10 Order numbers for sets of one through twelve objects 4.13 Use more and less to compare sets of objects 4.15 Answer questions about information shown on a picture graph ADDITION 7.2 Add one to the numbers zero through five 7.3 Add one to the numbers six through nine 7.4 Identify plus and equals sign; Add one in a number sentence 7.5 Use a picture to solve and check addition problems 7.6 Add two to the numbers zero through five 7.7 Add two to the numbers six through eight 7.8 Identify and add doubles 7.9 Add numbers in vertical form 7.10 Write number sentences for addition facts through ten 7.11 Use pictures to represent number sentences SUBTRACTION 8.2 Model subtraction of one from one through five and record the results 8.3 Model subtraction of one from six through ten and record the results 8.4 Use number sentences to record subtraction of one 8.5 Act out subtraction stories using concrete objects 8.6 Model and record subtraction of two from numbers two through five 8.7 Model and record subtraction of two from numbers six through ten 8.8 Subtract numbers in vertical form 8.9 Use manipulatives and pictures to model subtraction facts from 10 GREATER NUMBERS 10.1 or less Count & identify teen numbers (overview) 10.2 Identify and write numbers ten through twelve 10.3 Identify and write numbers thirteen through fifteen 10.4 Identify and write numbers sixteen through nineteen 10.6 Order numbers ten through nineteen & identify numbers missing from an order 10.7 Interpret graphs with numbers in the teens 10.8 Count, identify and write number twenty 10.9 Count, identify and write numbers 21 through 25 10.10 Count, identify and write numbers twenty-six through thirty 10.11 Identify and write numbers, in order, to thirty 10.14 Use logical thinking to estimate twenty, more than, and less than twenty CALENDARS 5.1 Identify times of day CLOCKS 5.9 Use analog clocks to tell time to the hour 5.10 Read and match times on digital and analog clocks 5.11 Identify the times on the hour of everyday events 5.12 Determine elapsed time MEASUREMENT 6.1 Compare objects to identify which one is taller, longer or shorter 6.2 Classify objects by length 6.3 Identify which object is longest, tallest or shortest 6.4 Measure length of objects in nonstandard units 6.5 Estimate & measure length in nonstandard units 6.6 Solve a problem by making & using a graph about lengths 6.7 Determine which object is heavier or lighter, using a scale 7
6.8 Compare pictures of objects to determine heaviest & lightest 6.9 Compare capacities of containers & determine which holds more or less 6.10 Determine which container holds the most and least MONEY 6.13 Identify & count pennies 6.14 Identify the nickel and its value and count on from the nickel using pennies 6.15 Identify the dime and its value and count on from the dime using pennies PATTERNS 2.1 Model, describe & extend rhythmic patterns 2.2 Recognize, describe & extend color patterns 2.3 Identify, describe & extend size patterns 2.4 Identify, describe & extend shape patterns 2.6 Identify, describe & extend position patterns 2.9 Identify & extend patterns to solve problems GEOMETRY 9.1 Identify and describe squares & circles 9.2 Identify and describe rectangles and triangles 9.3 Identify and sort plane figures by shapes 9.5 Identify, and describe three -dimensional shapes 9.6 Sort three-dimensional shapes 9.8 Match the surfaces of three-dimensional shapes to plane shapes 9.9 Count & compare numbers of plane & solid shapes FRACTIONS 9.10 Identify symmetry 9.12 Identify & divide pictures in halves Addendum: The listed curriculum must be completed for the kindergarten school year. Any lesson not addressed above should be taught, as applicable, in the remaining time. Resources: Houghton Mifflin Mathematics Grade K Including: Practice Masters Workbook Teacher Created Worksheets and Supplemental Worksheets Assessments: Quick Checks, Chapter Tests, and Teacher Created Tests. (Note: Curriculum tests need to be adapted according to the lessons taught.) 8
First Grade Mathematics Checklist of Objectives Content Chapter/ Section Objective Ch 1 Review number concepts. Comparing and Counting Preview PP. A and B Ch 1 Match the word name with the appropriate whole Counting/Number Preview number. Words PP. C and D Addition concepts Model the concept of addition as increasing. 1.1 Model Addition Model the concept of addition as putting together. 1.2 Use symbols to add 1.3 Solve addition sentences, using + and =. Write Addition Write addition sentences for problem situations. 1.4 Sentences Add with Zero 1.5 Solve addition problems with zero. Problem Solving 1.6 Use models to act out addition problems. Add in any order 1.7 Add numbers in any order.(commutative Property) Ways to make 7 1.8 Write addition sentences with the sum of 7. Ways to make 8 1.9 Write addition sentences that have the sum 8. Algebra Readiness: Write addition sentences with the sum on either side 1.10 the Equals Sign of the equals sign. Add in Vertical Form 1.11 Write addition sentences in vertical format. Problem Solving 1.12 Solve problems by using addition. Subtraction Concepts 2.1 Show the meaning of subtraction. Model Subtraction 2.2 Show the meaning of subtraction by taking away. Symbols to subtract 2.3 Solve subtraction sentences using symbols. Write subtraction Write subtraction sentences with operational symbols. 2.4 sentences Zero in subtraction 2.5 Subtract 0 or find a difference of 0. Problem Solving 2.6 Draw pictures to solve problems. Subtract from 7 or less 2.7 Write number sentences to find the difference. Subtract from 8 or Write subtraction sentences to find the difference. 2.8 less Subtract in vertical Subtract in vertical form. 2.9 form Problem Solving 2.10 Solve problems by choosing the correct operation. Count On to Add 3.1 Write sums to 10 by counting on 1, 2, or 3. Add in Any Order 3.2 Add using the commutative property. Number Line to Add 3.3 Find sums to 10 using a number line. Doubles to Add 3.4 Add using doubles and doubles plus one. Draw a Picture to Add by drawing a picture. 3.5 Add Different Ways to Add using different strategies. 3.6 Add Count Back to Write differences by counting back 1, 2, or 3. 3.7 Subtract Number line To Subtract using a number line. 3.8 Subtract 9
Draw a Picture to Draw a picture to subtract. 3.9 Subtract Subtract to Compare 3.10 Show the meaning of subtraction by comparing. Problem Solving: Subtraction 3.11 Use subtraction to solve problems. Relate Addition and Write and solve number sentences using related 3.12 Subtraction addition and subtraction facts. Fact Families 3.13 Write fact families using related facts. Different Ways to Subtract using different strategies. 3.14 Subtract Problem Solving 3.15 Use number sentences to solve problems. Make A Tally Chart 4.2 Represent data with tally marks on a chart. Read a Picture Read and use a picture graph to compare information. 4.3 Graph Make a Picture Make and use a picture graph to compare and use 4.4 Graph information. Problem Solving 4.5 Use logical reasoning to solve a problem. Read a Bar Graph 4.6 Read a bar graph and use it to compare information Make a Bar Graph 4.7 Make a bar graph and use it to compare information. Different Ways to Show Data 4.8 Problem Solving 4.9 Use a graph to solve a problem. Teen Numbers 5.1 Count, write, and order numbers to 19. Count by Tens 5.2 Count and write decade numbers. Tens and Ones 5.3 Regroup ten ones as one ten. Numbers to 50 5.4 Recognize and write numbers to 50. Numbers to 99 5.5 Identify and write numbers to 99. One Hundred 5.6 Identify and order numbers to 100. Use a tally chart to make a bar graph and compare information. Different Ways to Show two-digit numbers in different ways. 5.7 Show Numbers Count by Twos 5.8 Skip count by twos to 100. Count by fives 5.9 Skip count by fives to 100. Number Patterns 5.10 Identify 1 more, 1 less, 10 more, and 10 less than a given number. Ordinal Numbers 5.11 Identify ordinal numbers from first through tenth. Problem Solving 5.12 Use patterns to solve a problem. Use ten to estimate SM Estimate how many using a group of ten. Compare Numbers 5.14 Compare two numbers, using is greater than and is less than. Use Symbols to Compare two-digit numbers using >, <, and =. 5.15 Compare Numbers Order Numbers 5.16 Compare and order numbers to 100. Value of Coins 7.1 Identify coins-pennies, nickels, and dimes-and their values. Nickels 7.2 Find the value of a group of nickels. Nickels and Pennies 7.3 Find the value of a group of nickels and pennies. Dimes 7.4 Find the value of groups of dimes. Dimes and Pennies 7.5 Find the value of dimes and pennies. Count Coins 7.6 Equal Amounts 7.7 Position Words 8.1 8.2 Find the value of a group of dimes, nickels, and pennies. Find different ways to show the same amount of money. Give and follow directions about position and location of objects in space. 10
Plane Shapes 8.3 Identify and describe attributes of triangles, rectangles, squares and circles. Sorting Shapes 8.4 Classify plane shapes by common attributes. Solid Shapes 8.5 Identify, describe and compare solid shapes. Identify faces of a Identify the faces of a solid shape. 8.6 solid shape. Problem Solving 8.7 Use patterns to solve problems. Symmetry 8.8 Identify symmetric shapes. Equal Parts 8.9 Identify and count equal parts. One Half 8.10 Use fractions to name parts of a whole. Compare Length and Compare lengths and heights of objects. 10.1 Height Nonstandard Units 10.2 Estimate length by using non-standard units. Inches 10.3 Measure an object in inches using a ruler. Compare Weight 10.6 Compare the weights of objects using non-standard Pounds 10.7 units and direct comparison. Compare the weight of an object to one pound by direct comparison. Compare Capacity 10.9 Compare the capacity/volume of containers. Cup, Gallon and Quart SM Identify gallon, cups, and quarts. Order Events 11.1 Order Events. Compare Time 11.2 Compare time. Hour 11.3 Tell time to the hour. Half Hour 11.4 Tell time to the half hour Tell Time 11.5 Write time another way. Digital Clocks 11.6 Tell time on digital clocks. Practice Telling Time 11.7 S M3.E.1.1.2how the time in different ways. Calendar 11.10 Read a calendar. Use a Calendar 11.11 Use a calendar. Do the following at the end of the year if time allows: Count on to Add 6.1 Write sums to 12 by counting on 1, 2, or 3. Sums to 11 6.2 Identify equivalent forms of the same number and write sums to 11. Sums to 12 6.3 Identify equivalent forms of the same number and write sums to 12. Add Three Numbers 6.4 Find the sum of three one-digit numbers. Problem Solving Make a table to solve problems. 6.6 Count Back to Subtract 6.7 Solve subtraction facts. Resources: Houghton Mifflin Mathematics Grade 1 Including: Practice Masters, Spiral Review, Workbook Additional Resources: Math Minutes, Teacher Created Worksheets Assessments: Quick Checks and Chapter Tests; Teacher Created Tests (Note: Curriculum tests need to be adapted according to the lessons taught.) Local Assessments-End of the Year Computation Review-May 11
Second Grade Mathematics Checklist of Objectives Content Addition & Subtraction Facts Numbers and Patterns to 100 Chapter/ Section 1.1 Objective Use the order property to find the sum. 1.2 Use a number line to count on to find the sum. 1.3 Use doubles to find the sum of whole numbers. 1.4 Use doubles and doubles plus one facts to find the sum of whole numbers. 1.5 To find the sum of whole numbers by adding ten to one digit numbers. 1.6 Find the sum of whole numbers by making ten to add seven, eight, or nine. 1.7 Add three addends using the associative rule. 1.8 Use a number line to count back to find the difference of two whole numbers. 1.9 Subtract from numbers to twelve using addition (inverse relationship). 1.10 Subtract from numbers to fifteen using addition (inverse relationship). 1.11 Use the inverse relationship between addition and subtraction to subtract from numbers to twenty. 1.12 Write number sentences to solve problems. 1.13 Model the meaning of subtraction as comparing. 1.14 Identify and write names for numbers. 1.15 Identify and write fact families (inverse relationship). 1.16 Interpret and solve problems involving addition and subtraction. 2.1 Count, read, and write decade numbers. 2.2 Use tens and ones models to show numbers to 100. 2.3 Identify the value of the tens and ones digits of numbers. 2.5 Represent numbers in different forms (words, models, expanded form). 2.6 Identify unnecessary information in a word problem. 2.7 Identify even and odd numbers. Identify patterns on a hundred chart by counting by 2s, 3s, 2.8 and 5s. Data and Graphing 2.9 Compare whole numbers to 100 by using the symbols greater than, less than, and equal to. 2.10 Order whole numbers 2.11 Round numbers to the nearest ten. 2.12 Use patterns to solve problems. 3.1 Record data using tally marks. 3.2 Compare data using tables. 3.3 Read a pictograph. 3.4 Use logical reasoning to solve a problem. 12
Two-Digit Addition Time and Calendar Subtracting 2- Digit Numbers 3.5 Interpret data on a bar graph. 3.6 Represent and compare data from a bar graph and tally chart. 3.7 Find range and mode. 3.8 Use a bar graph to solve a problem. 5.1 Use basic addition facts to add multiples of ten. 5.2 Add numbers without regrouping. 5.3 Demonstrate how to regroup ten ones as one ten. 5.5 Add a 1-digit number to a 2-digit number, with and without regrouping. 5.6 Add 1- and 2- digit numbers with and without regrouping. 5.7 Regroup 10, 11, or 12 ones to add 2-digit numbers. 5.8 Regroup 13, 14, or 15 ones to add 2-digit numbers. 5.9 Regroup 16, 17, or 18 ones to add 2-digit # 5.10 Round to the nearest ten to estimate sums. 5.11 Use guess and check to solve problems. 5.12 Recognize and use different addition methods. 5.13 Rewrite and solve horizontal addition exercises. 5.14 Add money amounts. 5.15 Add three 2-digit numbers. 5.16 Use data from a picture to solve problems. 10.1 Estimate the length of one minute. 10.2 Tell time to the hour. 10.3 Tell time to the half-hour. 10.4 Tell time to the five minutes. 10.5 Tell time to the quarter-hour. 10.6 Determine how much time has passed. (Add supplemental material to cover A.M. and P.M.) 10.7 Solve problems involving elapsed time. 10.8 Read and understand information on a calendar. 10.9 Compare periods of time. 10.10 Use schedules to solve problems. 6.1 Use basic facts to subtract tens. 6.2 Subtract numbers without regrouping. 6.3 Demonstrate how to regroup one ten as ten ones. 6.5 Subtract 1-digit numbers from 2-digit numbers, with and without regrouping. 6.6 Subtract 2-digit numbers from 2-digit numbers, with and without regrouping. 6.7 Use base-ten models to act out and solve problems. 6.8 Subtract 2-digit numbers; practice subtracting from 10 and 11. 6.9 Subtract 2-digit numbers; practice subtracting from 12, 13, and 14. 6.10 Subtract 2-digit numbers; practice subtracting from 15, 16, 17, and 18. 6.11 Estimate differences by rounding to the nearest ten. 6.12 Subtract using different methods. 6.13 Rewrite horizontal subtraction problems in vertical form. 6.14 Add and subtract money amounts less than $1 6.15 Check subtraction by using addition. 13
6.16 Solve problems using data from a table. Money 4.1 Write the value of a group of dimes, nickels, and pennies. 4.2 Identify a quarter and write the value of a group of coins. 4.3 Write the value of a group of coins. 4.4 Show equal amounts with different coin combinations. 4.5 Compare amounts of money. 4.6 Use coins to act out a problem. Geometry, Fractions, and Probability 4.7 Identify a half-dollar and write the value of a group of coins. 4.8 Use coins to show a given amount. 4.9 Use coins to show a given exact amount. 4.10 Identify coin combinations that equal one dollar. 4.11 Count on to make change. 4.12 Solve two step problems using money. 7.1 Identify and classify circles, squares, triangles, and rectangles. 7.2 Identify sides and vertices on plane shapes. 7.3 Identify the number of faces, edges, and vertices for solid shapes. 7.4 Identify congruent shapes. 7.5 Create congruent shapes with pattern blocks. 7.6 Identify and draw lines of symmetry. 7.7 Identify, describe, and extend patterns. 7.8 Identify and write unit fractions. 7.9 Identify and write fractions. 7.10 Identify fractions that show one whole or more than one whole. 7.11 Compare fractions using symbols. 7.12 Identify and write fractions that represent parts of a group or a set. 7.13 Identify fractional parts of a group. 7.14 Predict and record the outcome of an event. 7.15 Solve problems using data from a picture. Measurement 9.1 Estimate and measure length using nonstandard units. 9.2 Compare the measurements of objects with different nonstandard units. Numbers and Patterns to 1,000 9.3 Estimate and measure to the nearest inch or foot. 9.4 Estimate and measure in centimeters and meters. 9.5 Measure centimeters and add to find perimeter. 9.6 Use guess and check to solve problems. 9.7 Estimate the weight of objects using pounds. 9.8 Estimate the mass of objects using kilograms. 9.9 9.10 Use cups, pints, and quarts to measure capacity and identify equivalent measures. Estimate whether containers hold more than, less than, or the same as one liter. 9.11 Read a Fahrenheit thermometer. Choose the best tool and unit to measure distance, weight, 9.12 capacity, temperature. 9.13 Use measurement to solve a problem. Count by 100s and read and write the numbers. 11.1 14
11.2 Use models to count by 100s, tens, and ones and write numbers through 999. 11.3 Count, read, and write numbers through 500. 11.4 Count, read, and write numbers through 1,000. 11.5 Identify place value, represent numbers using expanded form. 11.6 Use models to identify and regroup tens as hundreds. 11.7 Use tables to extend number patterns and solve problems. 11.8 Use words, models, and expanded form to show 3-digit numbers in different ways. 11.9 Compare 3-digit numbers using the symbols less than, 11.10 greater than, and equal to. Identify 3-digit numbers to determine what comes before, after, and between. 11.11 Use place value to order 3-digit numbers. 11.12 Count dollars and coins to determine value. 11.13 Solve problems using combinations of bills and coins. Resources Mathematics by Houghton Mifflin 2002; If time allows and students have mastered necessary skills, teachers may teach Chapter 8 (Multiply and Divide) and Chapter 12 (Add and Subtract 3-digit) at their discretion Assessment Local Assessments at start and end of school year; All Chapter Quick-Checks and Tests 15
Content Chapter/ Section Third Grade Mathematics Checklist of Objectives Objective Numbers Through 999 Round Two- Digit Numbers Round Three Digit Numbers 1.1 1.2 Write numbers to 999 in standard form, expanded form, and word form. Identify the place and value of a digit. Round to the nearest ten or to the nearest ten cents. 1.3 Round to the nearest hundred, dollar, or ten cents. Place Value to Thousands 1.6 Write the numbers to 9,999 in different forms. Identify the place and value of a digit in a number. Compare Numbers Ordering Numbers Round Four Digit Numbers (age 27 only) Problem- Solving Strategy: Find a Pattern Problem- Solving Application: Read a Graph Addition Properties 1.7 1.8 1.9 1.10 1.13 Use inequality symbols to compare numbers through 9,999. Order groups of whole numbers through 9,999. Identifying even and odd numbers. Solve a problem by finding a pattern. Read a graph to solve problems. 3.1 Use the Commutative Property, the Zero Property, and the Associative Property to add. Regroup Ones 3.2 Add by regrouping ten one as one ten. Regroup Ones 3.3 and Tens Add by regrouping both ones and tens. Estimate Sums 3.4 Estimate sums by rounding numbers. Problem Solving Skill: Exact Answer or Estimate 3.5 Column Add Add Greater Numbers Problem Solving Strategy: Guess and Check Subtraction Strategies and 3.6 3.7 3.8 3.9 Decide whether a problem needs an exact answer or an estimate. Add three or more addends. Find the sum of 2 four-digit addends. Use the guess and check strategy to solve. Use properties of subtraction and counting to find 16
Properties differences. Regroup Tens 3.10 Subtract by regrouping 1 ten as 10 ones. Regroup Tens 3.11 and Hundreds Subtract by regrouping tens and hundreds. Estimate Estimate numbers by rounding numbers. 3.12 Differences Problem Solving 3.15 Application: Use addition and subtraction to solve problems. Use Operations Modeling Model multiplication by grouping counters. 5.1 Multiplication Arrays and Multiply numbers in any order. 5.2 Multiplication Multiply with 2 5.3 Learn ways to multiply when 2 is a factor. Multiply with 5 5.4 Learn to find the product of a factor and 5. Problem- Solving Skills: Too Much Information 5.6 Distinguish necessary from extraneous information when solving problems. Multiply with 1 Multiply when a factor is 1 or 0. 5.7 and 0 Multiply with 3 5.8 Learn ways to multiply when 3 is a factor. Multiply with 4 5.10 Learn to find the product of a factor and 4. Line, Line Segments, Rays, and Angles 7.1 Identify and compare lines, line segments, rays, and angles. Plane Figures 7.2 Describe and compare characteristics of plane figures. Quadrilaterals 7.3 Identify the characteristics of quadrilaterals. Triangles 7.4 Identify triangles as equilateral, isosceles, or right. Problem- Solving: Visual Thinking 7.5 Congruent Figures 7.6 Solve visual thinking problems. Develop an understanding and recognition of congruence. Line of Recognize possible lines of symmetry. 7.7 Symmetry Find Area 7.9 Determine the area of a figure. Estimating Area 7.10 Use square units to estimate the area of a figure. Problem- Solving Recognize and complete patterns. 7.11 Strategy: Find a Pattern Solid Figures 7.12 Name and describe the characteristics of solid figures. Estimating Estimate volume by counting unit cubes that fill a box. 7.13 Volume Find Volume 7.14 Determine the volume of a solid figure. Problem- 7.15 Solving Application: Use Determine whether a problem is asking for area or volume and then find the solution. 17
Measurement Value of Money 2.1 Write amounts of money, using dollars, dimes and pennies. Count Coins Write money amounts and count bills and coins. 2.2 and Bill Equivalent Identify equivalent amounts of money. 2.3 Amounts Count Change 2.4 Make change by counting. Choose the Determine whether a problem requires addition or 2.5 Operation subtraction to find the solution. Hour, Half- Hour, Quarter Hour 2.6 Tell time to the hour, half-hour, and quarter hour. Include A.M. and P.M. Time to the Tell time to the minute. 2.8 Minute Elapsed Time 2.10 Find elapsed time shown on clocks. Multiply with 6 6.2 Find the product of a number and 6. Multiply with 8 6.3 Find the product of a number and 8. Problem- Solve problems that have more than one step. Solving Skills: Multi-step Problems 6.4 Multiply with 7 6.5 Find the product of a number and 7. Multiply with 9 6.6 Find the product of a number and 9. Problem- Solving Strategy: 6.7 Decide what strategy to use to solve a problem. Choose a Strategy Multiply Three 6.9 Numbers Problem- Solving Application: Use Operations Measuring Length Measure to the Nearest Half Inch Customary Units of Length Estimating and Measuring Capacity Customary Units of Capacity Customary Units of Weight Strategy: Work Backwards 6.10 4.1 4.2 4.3 Find the product of 3 or more factors. Use operations to solve problems. Estimate and measure lengths of objects to the nearest inch. Measure objects to the nearest half inch. Use customary units to measure the lengths. 4.4 Estimate and measure capacity by using customary units. 4.5 Estimate and choose appropriate units of capacity. 4.6 Measure the weight of objects by using customary units of weight. 4.8 Determine a beginning measurement by working backward from a final measurement. 18
Collecting and Organizing Data Problem- Solving Skills: Use a Bar Graph Make a Bar Graph Problem- Solving Strategy: Make a Table Recording Outcomes Fractions and 10.1 Collect data in the form of a survey and record the results. 10.4 10.5 10.7 10.9 11.1 Regions Fractions and Groups 11.2 Locate and use data from a bar graph. Read and make bar graphs. Solve a problem by organizing data into a table. Experiment with probability and record the data. Read and write fractions. Name equal parts of a group, using fractions. Fractional Parts of a Group Problem- Solving Skills: Multi-Step Problems Add and Subtract Decimals Problem- Solving Application: Use Money Related Multiplication and Division Problem- Solving Application: Use Money Problem- Solving Application: Use Operations 11.8 11.11 Find a fractional part of a group. Determine how to solve problems with more than one step. 11.16 Find the sums and differences of two decimals. 11.18 Solve problems that involve addition and subtraction of money. 8.2 Use multiplication to divide. 9.10 12.15 Solve problems that use money. Determine whether to use addition, subtraction, multiplication, or division to solve problems. Algebraic Concepts Supplement material Determine the missing number or symbol in a number sentence. Resources Mathematics 3 by Houghton Mifflin Houghton Mifflin practice workbook, reteaching masters, challenge masters, refreshers masters, spiral review, fast facts, teaching transparencies, and teaching tools. AssessmentThird grade local assessment (twice a year), Chapter Tests, End of year computation assessment 19
Fourth Grade Mathematics Checklist of Objectives Content Chapter/ Objective Section Place Value Read and write numbers through one-hundred 1.1 through 100,000 thousands Compare and Compare and order numbers through one hundred 1.2 Order Numbers thousands Rounding Estimate a number by rounding it 1.3 Numbers Estimated or Decide whether a number represents an exact 1.4 Exact Amounts amount or an estimate Problem Solving: Solve problems by using logical thinking Use Logical 1.9 Thinking Compare Money Count and compare amounts of money 1.10 Amounts Problem Solving Solve problems involving money Application: Use 1.12 Money Addition Recognize and apply properties of addition 2.1 Properties Add Whole Find whole number sums 2.2 Numbers Subtract Whole Find whole number differences 2.3 Numbers Estimate Sums Round numbers to estimate sums and differences 2.4 and Differences Estimated or Decide whether a problem needs an exact answer 2.5 Exact Answers or an estimate Subtract Across Subtract when some digits are zeros 2.6 Zeros Problem Solving Decide when to use addition or subtraction to Applications: Use 2.7 solve problems Operations Expressions and Simplify and write equations and inequalities 2.8 Equations Write and Write and evaluate expressions containing Evaluate variables 2.9 Algebraic Expressions Write and Solve Write and solve algebraic equations 2.10 Equations Solving Adding Add the same number to or subtract the same 2.11 Equations number from both sides of an equation Equations with Relate equations with two variables to function 2.12 Two Variables tables Problem Solving Use the guess and check strategy to solve Strategy: Guess 2.13 problems and Check 2 Describe, interpret, and/or answer questions based Venn Diagrams p. 101 on a Venn diagram Guess My Rule 2 Determine rule for function table; Guess My Rule 20
Use Doubles to Multiply Multiplication Properties Use Patterns to Multiply Multiples Relate Multiplication and Division Multiply Multiples of 10, 100, and 1,000 p. 147 3.1 p. 104-105 3.2 3.3 3 p. 115 Supplemental Materials 3.4 4.1 p. 164 & 165 Use doubles to multiply when 2,3,4,6,or 8 is a factor Use multiplication properties to find products Use patterns to find products List and identify multiplies of a number where the multiples do not exceed 100 Use known multiplication facts to divide 3 List and identify all factors through 10 of any Factors p. 109 given number Use doubles to Use doubles to divide 3.5 Divide Division Rules 3.6 Apply rules to find quotients Divide by 5, 7, 9, Use related multiplication facts to divide by 5, 7, 3.7 or 10 9, or 10 Division with Find a quotient with remainders 3.8 Remainders Problem Solving Solve multi-step problems Skill: Multi-step 3.9 Problem Problem Solving Use patterns to solve problems Application: 3.12 Using Patterns Two-Step Describe functions with operations and solve for 3.14 Functions one variable when the value is known Use basic facts and patterns of zeros to multiply multiples of 10, 100, or 1,000 1Modeling Multiplication by One-digit Numbers Multiply Two- Digit Numbers by One-digit Numbers Estimate Products 4.2 4.3 4.4 Use base-ten blocks to model multiplication Multiply two-digit numbers by one-digit numbers with one regrouping Estimate products by rounding the factors Problem Solving Strategy: Find a Pattern 4.5 Solve a problem by finding a pattern 21
Multiply Three- Digit Numbers by One-Digit Numbers Multiply Greater Numbers Multiply with Zeros Choose the Operation Multiply Multiples of 10 and 100 Multiply Two 2- Digit Numbers Multiply Three- Digit Numbers by Two-Digit Numbers Problem Solving Application: Use a Pictograph 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 Multiply three-digit numbers by one-digit numbers with regrouping Multiply four-digit numbers by one-digit numbers with regrouping Multiply three-and four digit factors with zeros Decide what operation is necessary to solve a given problem Multiply mentally when both factors are multiples of 10 or 100 Multiply by two-digit numbers when regrouping Multiply three-digit numbers by two-digit numbers with regrouping Use a pictograph to solve problems Modeling Division Two-Digit Quotients Regrouping in Division Interpreting Remainders Mental Math: Divide Multiples of 10, 100, and 1,000 Three-digit Quotients Place the First Digit of the Quotient 5.1 p. 216-217 5.2 5.3 5.4 5.5 5.6 5.7 Model regrouping in division Divide two-digit dividends by one-digit divisors, with and without remainders (no regrouping) Divide two-digit dividends by one-digit divisors, with and without remainders when regrouping is necessary Determine a reasonable answer by interpreting remainders when solving division problems Divide mentally using basic facts and patterns Divide three-digit dividends by one digit divisors (three-digit quotients with and without remainders. Divide three-digit dividends by one-digit divisors (two-digit quotients with and without remainders) Divide Money 5.8 Divide money amounts by whole numbers Zeros in the Divide three-digit dividends by one-digit divisors 5.9 Quotient (zeros in the quotient) Solve problems by working backward Problem Solving Strategy: 5.10 Work Backward Divisibility Rules 5.11 Identify numbers divisible by 2,5, or 10 Prime and 5.12 Identify a number as prime or composite Composite Add p. 161 22
Problem Solving Applications: Use Operations Represent Fractions Fractional Parts of a Number Compare Fractions with Like Denominators Write Mixed Numbers Add with Like Denominators Subtract with Like Denominators Fractions and Decimals Mixed Numbers and Decimals Fraction and Decimal Equivalents Compare and Order Decimals Problem Solving Strategy: Find a Pattern Add and Subtract Decimals Problem Solving Applications: Use Decimals Inch, Half Inch, and Quarter Inch Customary Units of Capacity and Weight Centimeter and Millimeter Metric Units of Capacity and Mass Problem Solving Strategy: Make a Table 5.17 7.1 p. 322-323 7.2 Refer to 7.6 p. 339 Supplemental Materials 7.7 7.9 7.10 8.1 p. 370-371 8.2 8.3 Supplemental Materials 8.4 p. 380 Supplemental Materials 8.6 8.7 Add p. 377 8.8 6.1 p. 276-277 6.3 6.5 6.7 6.8 Supplemental Materials Solve problems by choosing an operation Write a fraction for a part of a region or a part of a group Find the fractional part of a number, using models or computation Locate and identify fractions on a number line ONLY fractions with like denominators Write equivalent improper fractions and mixed numbers Add fractions and mixed numbers with like denominators Subtract fractions an mixed numbers with like denominators Demonstrate the relationship between fractions and decimals Read, write, and model decimals greater than one Write equivalent fractions and decimals thru 10ths Compare and order decimals on a number line thru 10ths Recognize and use patterns to solve problems Find sums and differences of decimals Solve problems by finding decimal sums and differences; Measure to the nearest inch, half inch, and quarter inch Change customary units of capacity and weight Measure, using centimeters and millimeters Change metric units of capacity and mass Solve a problem by organizing information in a table 23
Digital and Analog Time Identify Time Determine Elapsed Time Collect and Organize Data 6 Supplemental Materials 6 Supplemental Materials 6 Supplemental Materials 9.1 Use a Bar Graph 9.3 Problem Solving Skill: Interpret a Line Graph Read and Understand Line Graphs Problem Solving: Choose a Strategy Probability and Outcomes 9.4 9.5 9.6 9.7 Match/construct analog time (a picture of a clock), to the same time written in digital Identify time(analog or digital) as the amount of minutes before and/or after the hour Determine the beginning or ending time, given the elapsed time (limited to 2 adjacent hours) Conduct a survey and collect and organize information; Vocabulary data, bar graph, line plot Read and interpret bar graphs and double gar graphs Interpret line graph data Read and interpret a line graph Choose a strategy to solve problems Describe the probability of an event Find Probability 9.8 Write the probability of an event Making Use probability to make predictions 9.9 Predictions Problem Solving Use data and probability to solve problems Applications: Use Data and 9.11 Probability Create a Graph 9 Supplement Materials Graph data or complete a graph given the data (bar graph, or pictograph grid is provided) Interpret Data from a Graph Points, Lines, and Line Segments 9 Supplement Materials 10.1 p. 458-549 Translate information based on data or chance (data my be shown in tables, charts, line graphs, bar graphs or pictographs) Name and describe the characteristics of points, lines, line segments, parallel, perpendicular lines Name and describe the characteristics of rays and Rays and Angles 10.2 angles Polygons and Name and describe the characteristics of polygons 10.3 Quadrilaterals and quadrilaterals Classify Name and classify triangles: right, obtuse, and 10.4 Triangles acute 10.5 Identify parts of a circle and turns about the center Circles of a circle Symmetry Identify line and rotational symmetry 10.7 Problem Solving 10.12 Solve problems that require visual thinking 24
Skill: Analyze Visual Problems Solid Figures (No Nets) Locate Points on a Grid Using Whole Numbers Graph Ordered Pairs Supplemental Materials 10.13 11.1 p. 522-523 11.2 Name and identify the characteristics of solid figures: cube, sphere, rectangular prism, pyramid Name points on a grid, using ordered pairs Plot points on a graph, using ordered pairs Resources: Houghton Mifflin Mathematics Book 4 Including: Practice Masters, Spiral Review, Workbook Additional Resources: Math Minutes Teacher Created Worksheets Assessments: Quick Checks, Chapter Tests, and Teacher Created Tests (Note: Curriculum tests need to be adapted according to the lessons taught.) Local Assessments September & January End of Year Computation Review - May 25
Fifth Grade Mathematics Checklist of Objectives *Topic is taught without the use of a calculator at first and then the students are shown how to solve problems with a calculator Content Whole Numbers Decimals and Integers 1.1 1.2 1.3 1.3 Chapter/ Section Objective Use expanded notation to represent whole numbers and decimals. Identify the place value of a digit. Read and write numbers through hundred thousands with exponents Compare whole numbers through 9 digits using >, <, = Round whole numbers through millions and decimals through hundredths. 1.4 Solve problems involving whole numbers and decimals using estimation. 1.5 Use expanded notations to represent whole numbers and decimals. 1.5 Identify the place value of a digit. 1.6 Round whole numbers through millions and decimals through hundredths. Read and write decimals in standard and word forms. 1.8 Identify the place value of a digit 1.9 1.10 Compare whole numbers through 9 digits and decimals through hundredths using <, >, = Round whole numbers through millions and decimals through hundredths. 1.11 1.12 Compare whole numbers through 9 digits and decimals through hundredths using <, >, = Locate integers on a number line (greater than or equal to -20) Addition Subtraction and Equations Supplemental 2.1 Identify negative numbers on a thermometer Addition of whole numbers 2.2 Subtraction of whole numbers 2.4 Addition of decimals to thousandths 2.5 Subtraction of decimals to thousandths 2.6 Solve problems by working backwards 2.9 Solve for a missing number in an equation single operation (whole numbers) 2.10 Solve addition and subtraction equations using a function table 26
Multiplication 3.2 Multiply by a one digit number 3.3 Multiplying numbers that contain zeros by a one-digit number 3.4 Using estimation to solve problems involving whole numbers and decimals 3.5 Use patterns or mental math to multiply by multiples of 10, 100, 1000 Division and Equations Measurement and Integers 3.6 Multiply by multiples of 10 3.8 Multiply by two digit numbers 3.9 Choose an operation to solve a problem 4.1 Use place value to divide by one-digit divisors 4.2 Problems with zeros in the quotient 4.3 Using basic multiplication facts to estimate quotients 4.4 Calculate the mean, median and range of a set of data 6.5 Identify the mode of a set of a data Calculate the mean, median and range of a set of data 4.13 Write and solve multiplication and division equations 4.14 Use counters to solve equations Solve equations involving multiplication and division 4.15 using function tables 4.16 Write equations to solve word problems Measure to the nearest fraction of an inch. 5.1 Use a ruler to measure to the nearest 1/8 inch or centimeter Select appropriate unit for calculating perimeter and area. 5.2 Calculate and label perimeter and area of a square or rectangle Select appropriate unit for measuring weight and capacity 5.3 Converting capacity and weight measurements in customary and metric Solve problems of weight, length and capacity 5.4 Solve problems involving more than one step Measure in metric units and make conversions Number Theory and Addition and Subtraction of Fractions 5.5 5.6 5.7 7.1 Use a ruler to measure to the nearest 1/8 inch or centimeter Change from one metric unit of capacity or mass to another Conversion of metric units of mass and capacity Solving problems of metric units of weight, mass and capacity Use addition and subtraction to solve problems involving times and schedules Identify prime and composite numbers 27
Data, Statistics and Probability Multiplication and Division of Decimals Geometry and Measurement 7.2 Write the prime factorization of a number 7.3 Determine when 2, 3, 4, 5, 9, or 10 is a factor of a number 7.4 Find common factors and the greatest common factors of 2 or more numbers 7.5 Find common multiples and the least common multiple 7.7 Write a fraction to represent some part of a whole amount or a part of a group of objects 7.8 Use multiplication to find equivalent fractions 7.9 Using division or prime factorization to write fractions in simplest form 7.10 Compare fractions, mixed numbers and decimals 7.11 Compare unlike fractions 7.13 Add and subtract fractions with like denominators 7.14 Add fractions with unlike denominators 7.15 Use the least common denominator to add fractions with unlike denominators 7.16 Add mixed numbers having like or unlike denominators 7.17 Rename mixed numbers to find differences 7.18 Subtract fractions and mixed numbers with unlike denominators 7.19 Use renaming to subtract mixed numbers 7.20 Use patterns to solve fraction problems 6.2 Compare data sets by using a double bar graph 6.3 Make and interpret a histogram 6.4 Analyze data from graphs to solve word problems Use a line plot to find the mean, median and mode of a 6.6 set of data 6.7 Analyze line graphs without numbers 6.8 Interpret and make line and double line graphs 6.9 Choose an appropriate graph according to the data given 6.10 Solve a problem by using a table 6.12 Predict an determine outcomes 6.13 Use fractions to find probability 6.14 Use data to make predictions Find the product of a whole number and a decimal 9.1 9.2 Use rounding to estimate products of decimal factors 9.3 Find the product of two decimal factors 9.4 Write zeros in the product of decimal factors when needed 9.5 Recognize and apply patterns to solve problems 10.1 Identify and draw points, lines, line segment and rays 10.5 Classify quadrilaterals and find missing angle measures 10.6 Solve problems by thinking about a simpler problem 10.10 Identify rotational and line symmetry 28
Integers and the Coordinate Plane Division and Equations Multiplication and Division of Fractions Ratio and Percent 10.16 12.1 4.5 Identify solid figures from different perspectives and find surface area of rectangular prisms and cubes (faces, vertices, edges) Identify transformations such as translations, reflections and rotations After PSSA Interpret remainders 4.7 Divide by a two digit number 4.8 Estimated quotient is too large 4.9 Estimated quotient is too small Multiply Fractions 8.2 8.3 Multiply Fractions and Mixed Numbers 8.4 Use the Operation 8.8 Divide by a Fraction 8.5 Divide by a Unit Fraction 8.6 Divide by a Counting Number 8.7 Solve a Simpler Problem 8.9 Divide with Mixed Numbers 8.10 Use Circle Graphs 11.1 Meaning of Ratios 11.2 Equivalent Ratios 11.3 Rates 11.6 Understand Percent 11.7 Ratio and Percent 11.8 Decimals and Percents 11.9 Use Fractions, Decimals, and Percents for Comparisons 11.10 Choose a Strategy 11.12 Percent of a Number 11.13 Compare Data Sets 11.14 Use Percent Resources Mathematics 5 by Houghton Mifflin Houghton Mifflin practice workbook, reteaching masters, challenge masters, refresher masters, spiral review and teaching tools PSSA Coach Assessment Fifth grade local assessment (twice a year) End of year computation assessment 29
Belle Vernon Area Middle School Math Curriculum Guide 30
Content Chapter/ Section Sixth Grade Mathematics Checklist of Objectives Calculator Place Value 1.1 NC Ordering numbers Rounding numbers Compute Decimals and Whole numbers 1.2 NC 1.3 NC 1.5 NC Objective Learn how to read, write, and understand whole number and decimal place value. Compare/Order numbers and decimals from millions to hundred thousandths using a number line Round whole numbers and decimals by using place value Add and subtract decimals and whole numbers 1.7-1.9 NC Multiply whole numbers and decimals 1.11-1.13 NC Divide whole numbers and decimals 3.13 NC Divide with terminating or repeating quotients Estimation SUP NC Estimate and compute value of whole numbers and decimals. (up to 2-digit divisors) Exponents 3.2/1.15 NC Comprehension of exponential value and powers of 10 3.2 NC Computation of exponents Number Theory 3.4 NC Use and know the divisibility rules for 2, 3, 5, 10 3.1 NC 3.3 NC Understand the difference between prime and composite numbers and factoring. Compute prime factorization 3.5 NC Find the greatest common factor of numbers up to 3 3.6 NC Find the least common multiple of numbers up to 3 Data Analysis 2.1 C Definition analysis and application of mean, median, mode, range. 2.2 NC Analyze and comprehend single and double bar graphs. 2.3 NC Analyze and comprehend frequency tables and histograms. 2.4 NC Analyze and comprehend single and double line graphs and line plots. SUP NC Analyze and comprehend circle graphs using percents. (center point and tic marks) SUP NC Choose the appropriate representation for a specific set of data from the same type of graph. Fractions 3.8 NC Understand the value of fractions and compare their equivalency. 3.9 NC Reduce the value to its simplest form 3.10 NC Compare and order the differences in value of fractions SUP NC Conversion of mixed numbers to improper and vice versa 4.1-4.2 NC Add fractions and mixed numbers 4.3 NC Subtract fractions and mixed numbers 4.5-4.6 NC Multiply fractions and mixed numbers 4.7-4.10 NC Divide fractions and mixed numbers (reciprocal) Measurement SUP NC Use or read a ruler to measure to the nearest 1/16 in. SUP NC Use or read a ruler to measure to the nearest 31