5th Grade - Chapter 1 - Place Value

Transcription

1 5th Grade - Chapter 1 - Place Value and Operations in Base Ten 12 days + 1 day Benchmark #1 Math Benchmark #1 Place Value Through Compare and Order Millions Whole Number Activity Through Millions Model Fractions and Decimals Represent Decimals Understand Place Value Place Value Through Thousandths Compare Decimals Order Whole and Decimals 2 Use the Four-Step Plan 3 Chapter 1 - Vocabulary Understand the place value system. 1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 3. Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = (1/10) + 9 (1/100) + 2 (1/1000). place-value chart period place place value standard form expanded form decimal decimal point equivalent decimals b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Chapter 1 Learning Stations Use Activity After 2 Graphic Novel Popular Pet 2 Activity Music Countdown 6 RWPS Reader Our Nation s 50 States 7 Game Decimal War 8 Graphic Novel Greenhouse Shopping Spree! 8 Problem Solving Continents Read and write whole numbers through the millions. Compare and order whole numbers through the millions. Use models to relate decimals to fractions. Represent fractions that name tenths, hundredths and thousandths as decimals. Understand place value in decimal numbers. Read and write decimals in standard form, expanded form and word form. Compare decimals. Order whole numbers and decimals. Standards Covered in Chapter 1- #1, 2, 3, 4, 5, 6, 8 7) Look for and make use of structure. 8) Look for and express regularity in repeated reasoning. *

2 5th Grade - Chapter 2 - Multiply Whole and Operations in Base Ten 13 days Prime Factorization Prime Factorization Patterns Powers and Exponents Multiplication Patterns Make a Table Use Partial Products and the Distributive Property The Distributive Property Estiamte Products Multiply by One-Digit 0 Multiply by Two-Digit 2 3 Chapter 2 - Vocabulary Understand the place value system. 2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Perform operations with multi-digit whole numbers and with decimals to hundredths. 5. Fluently multiply multi-digit whole numbers using the standard algorithm. prime factorization exponent base power squared cubed powers of 10 property Distributive Property compatible numbers Chapter 2 Learning Stations 9 Graphic Novel Pizza Party! 10 Game What s The Difference? 10 Problem Solving The Bone Bank 10 Activity What Can You Buy? Find the prime factorization of numbers. Explore patterns in prime factorization. Use powers and exponents in expressions. Use basic facts and patterns to multiply multiples of 10, 100 and 1000 mentally. Explore multiplication by using area models. Use the Distributive Property to multiply mentally. Estimate products by using rounding and compatible numbers. Multiply up to a three-digit number by a one or twodigit number. Standards Covered in Chapter 2- #1, 2, 3, 4, 5, 6, 7, 8 8) Look for and express regularity in repeated reasoning. *

3 5th Grade - Chapter 3 - Divide by a One-Digit Divisor and Operations in Base Ten Activity Relate Division to Multiplication 16 days Division Models Two-Digit Dividends Division Patterns Estimate Quotients Division Models with Greater Distributive Property and Partial Quotients Divide Three- and Four Digit Dividends Place the First Digit 0 Quotients with Zeros 2 1 Use Models to Interpret the Remainder 3 2 Interpret the Remainder 4 3 Determine Extra of Missing Information 5 6 Chapter 3 - Vocabulary Perform operations with multi-digit whole numbers and with decimals to hundredths. 6. Find whole-number quotients of whole numbers with up to fourdigit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. fact family unknown variable dividend divisor quotient remainder partial quotients Chapter 3 Learning Stations 9 Activity 10 Graphic Novel Way Down Upon the Suwannee River! Man, Oh Manatee! Understand how division and multiplication are related. Carry out divsion with and without remainders. Use basic facts and patterns to divide multiples of 10, 100 and 1000 mentally. Estimate quotients by using rounding and compatible numbers. Divide using the Distributive Property and partial quotients. Divide up to a four-digit number by a one-digit number. Understand how to place the first digit in a quotient. Solve division problems that result in quotients that have zeros. Interpret the remainder in a division problem. Standards Covered in Chapter 3- #1, 2, 3, 4, 5, 6 7) Look for and make use of structure. 8) Look for and express regularity in repeated reasoning.

4 5th Grade - Chapter 4 - Divide by a Two-Digit Divisor and Operations in Base Ten Activity Estimate Quotients 9 days Divide Using Base-Ten Blocks Divide by a Two-Digit Divisor Adjust Quotients Divide Greater Solve a Simpler Problem Chapter 4 - Vocabulary Perform operations with multi-digit whole numbers and with decimals to hundredths. 6. Find whole-number quotients of whole numbers with up to fourdigit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (No New Vocabulary- review terms) dividend quotient divisor Chapter 4 Learning Stations 3 Graphic A Big Book Novel 3 Game Lowest Number Wins! 3 Problem Solving The Statue of Liberty Estiamte quotients with two-digit divisors. Divide up to a three-digit number by a two-digit divisor. Adjust the quotient when the estimated digit is too high or too low. Divide greater numbers by multi-digit divisors. Standards Covered in Chapter 4- #1, 2, 3, 4, 5, 7 6) Attend to precision. 8) Look for and express regularity in repeated reasoning.

5 5th Grade - Chapter 5 - Add and Subtract Decimals and Operations in Base Ten Round Decimals 13 days Estimate Sums and Differences Estimate or Exact Answer Add Decimals Using Base-Ten Blocks Add Decimals Using Models Add Decimals Addition Properties Subtract Decimals Using Base- Ten Blocks Subtract Decimals Using Models 0 Subtract Decimals 2 3 Understand the place value system. 4. Use place value understanding to round decimals to any place. Perform operations with multi-digit whole numbers and with decimals to hundredths. 7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Chapter 5 - Vocabulary Commutative Property of Addition Associative Property of Addition Identity Property of Addition inverse operations Chapter 5 Learning Stations 1 Game Match Up 6 Game Find the Least Sum 6 Activity Music Counts 10 Graphic Ride Riddle Novel 10 Graphic novel Filling a Phone Round decimals. Estimate sums and differences by rounding. Explore adding decimals using base-ten blocks and models. Add decimals. Use the Associative, Commutative and Identity Properties to add whole numbers and decimals mentally. Explore subtracting decimals using base-ten blocks and models. Subtract decimals. Standards Covered in Chapter 5- #1, 2, 3, 4, 5, 6, 7 8) Look for and express regularity in repeated reasoning.

6 5th Grade - Chapter 6 - Multiply and Divide Decimals and Operations in Base Ten Multiply Decimals Estimate Products of Whole and Decimals Multiply Decimals By Powers of Ten 17 days Use Models to Multiply Problem Solving: Look for a Pattern Multiply Decimals by Whole Multiplication Properties Use Models to Multiply Decimals Estimate Quotients 0 Divide Decimals Divide Decimals by Whole 7 3 Lesson 12 Use Models to Divde 4 3 Divide Decimals 5 4 Divide Decimals by Powers of Ten Understand the place value system. 2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Chapter 6 - Vocabulary Commutative Property of Multiplication Associative Property of Multiplication Identity Property of Multiplication 4. Use place value understanding to round decimals to any place. Perform operations with multi-digit whole numbers and with decimals to hundredths. 5. Fluently multiply multi-digit whole numbers using the standard algorithm. 7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Chapter 6 Learning Stations 6 RWPS Reader Early American Settlements 11 Graphic Mowing Money Novel 14 Game Estimation Roll Off 14 Activity Decimal Fairy Tales Estimate products of whole numbers and decimals. Multiply decimals by whole numbers. Multiply decimals by decimals. Use the Associative, Commutative and Identity Properties to multiply decimals mentally. Exstimate and find quotients of decimals and whole numbers. Divide decimals by decimals. Divide decimals by powers of ten. Standards Covered in Chapter 6- #1, 2, 3, 4, 5, 6, 8 3) Construct viable arguments and critique the reasoning of others. * 7) Look for and make use of structure. 8) Look for and express regularity in repeated reasoning. *

7 5th Grade - Chapter 7 - Expressions and Patterns Operations and Algebraic Thinking 12 days Numerical Expressions Order of Write Numerical Operations Expressions Work Backward Generate Patterns Patterns Hands On: Map Locations Ordered Pairs Graph Patterns 2 Operations and Algebraic Thinking Write and interpret numerical expressions. 1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Analyze patterns and relationships. 3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. Geometry Graph points on the coordinate plane to solve realworld and mathematical problems. 1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Chapter 7 - Vocabulary numerical expression evaluate order of operations sequence term coordinate plane origin ordered pairs x-coordinate y-coordinate Chapter 7 Learning Stations 1 Game Expression Race 7 Problem Solving What s Your Latitude? 8 Game Where s My Line? 9 Activity Mystery Story 2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Write and evaluate numerical expressions using order of operations. Use numbers and operation symbols to write verbal phrases as numerical expressions. Generate/extend numerical patterns and identify pattern relationships. Plot points on a grid to solve real-world problems. Graph points (ordered pairs) on a coordinate plane to solve real-world problems, mathematical problems and problems involving two numerical patterns. Standards Covered in Chapter 7- #1, 2, 3, 4, 5, 6, 7, 8 8) Look for and express regularity in repeated reasoning. *

8 Least Common Multiple 5th Grade - Chapter 8- Fractions and Decimals Fractions and Decimals and Operations - Fractions Fractions and Decimals Compare Fractions 11 days Greatest Common Factor Use Models to Write Fractions as Decimals Simplest Form Write Fractions as Decimals Guess, Check and Revise Perform operations with multi-digit whole numbers and with decimals to hundredths. 5. Fluently multiply multi-digit whole numbers using the standard algorithm. Number and Operations Fractions Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 3. Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 5. Interpret multiplication as scaling (resizing), by: b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by 1. Chapter 8 - Vocabulary fraction numerator denominator common factors greatest common factor (GCF) simplest form equivalent fractions multiple common multiples least common multiple (LCM) least common denominator (LCD) Chapter 8 Learning Stations 2 Graphic Novel Sandwich Slice Sizes! 5 Activity Preparing for a Party Solve word problems by interpreting a fraction as division of the numerator by the denominator. Determine the common factors and the greatest common factor of a set of numbers. Generate equivalent fractions by writing a fraction in simplest form. Determine the common multiples and the least common multiple of a set of numbers. Compare fractions by using the least common denominator. Use fraction equivalence to write fractions as decimals. Standards Covered in Chapter 8- #1, 2, 3, 4, 5, 6 7) Look for and make use of structure. 8) Look for and express regularity in repeated reasoning.

9 5th Grade - Chapter 9 - Add and Subtract Fractions and Operations - Fractions Round Fractions 15 days Add Like Fractions Subtract Like Fractions Use Models to Add Unlike Fractions Add Unlike Fractions Use Models to Subtract Unlike Fractions Subtract Unlike Fractions Determine Reasonable Answers Estimate Sums and Differences 0 Use Models to Add Mixed 2 1 Add Mixed 2 Subtract Mixed 3 3 Subtract with Renaming 4 5 Number and Operations Fractions Use equivalent fractions as a strategy to add and subtract fractions. 1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Chapter 9 - Vocabulary like fractions unlike fractions 2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Chapter 9 Learning Stations 7 Game Fraction Subtraction 11 Problem Solving Making Mixtures 13 Graphic Novel Happy Trails 15 RWPS Reader Life in Colonial America Use number lines and benchmark fractions, such as 1/2, to round fractions. Add like fractions and solve word problems involving the addition of like fractions. Subtract like fractions and solve word problems involving the subtraction of like fractions. Add unlike fractions and solve word problems involving the addition of unlike fractions. Subtract unlike fractions and solve word problems involving the subtraction of unlike fractions. Use number sense and benchmark fractions to estimate sums and differences. Standards Covered in Chapter 9- #1, 2, 3, 4, 5, 6 7) Look for and make use of structure. 8) Look for and express regularity in repeated reasoning.

10 5th Grade - Chapter 10 - Multiply and Divide Fractions and Operations - Fractions Part of a Number 15 days Estimate Products of Fractions Model Fraction Multiplication Multiply Whole and Fractions Use Models to Multiply 0 Divide Whole by Unit Fractions Multiply Fractions 2 1 Divide Unit Fractions by Whole Multiply Mixed 3 2 Draw a Diagram Multiplication as Scaling 4 Division with Unit Fractions 5 Number and Operations - Fractions Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. Chapter 10 - Vocabulary scaling unit fraction b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 5. Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Chapter 10 Learning Stations b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. 4 RWPS Reader 5 Activity Nature s Delicate Balance All About Me b. Interpret division of a whole number by a unit fraction, and compute such quotients. c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Explore how to find part of a number. Estimate products of fractions using compatible numbers and rounding. Multiply whole numbers, mixed numbers and fractions. Divide whole numbers by unit fractions using models. Use bar diagrams to divide whole numbers by unit fractions and divide unit fractions by whole numbers. Standards Covered in Chapter 10- #1, 2, 3, 4, 5, 6, 7 8) Look for and express regularity in repeated reasoning.

11 5th Grade - Chapter 11 -Measurement Measurement Convert Customary Units of Weight 0 Convert Metric Units of Length 6 Measure with a Ruler Estimate and Measure Capacity 2 1 Estimate and Measure Metric Mass Measurement and Data Convert like measurement units within a given measurement system. 1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Represent and interpret data. 2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. 16 days Convert Customary Units of Length Convert Customary Units of Capacity 3 2 Convert Metric Units of Mass Use Logical Reasoning Display Measurement Data on a Line Plot 4 3 Convert Metric Units of Capacity Estimate and Measure Weight Metric Rulers 5 Chapter 11 - Vocabulary Length inch foot yard mile customary system convert weight capacity ounces pound ton fluid ounce pints cups quarts gallons fair share metric system centimeter millimeter meter kilometer mass milligram kilogram liter milliliter Chapter 11 Learning Stations Use After Activity 2 RWPS Reader City Planning 5 Problem Solving Soccer Rules! 13 Game Metric Pairs! 13 RWPS Reader How Big is the Solar System? 13 Problem-Solving The Wright Measurements Measure length to the nearest half inch and quarter inch. Convert measurements of length, weight and capacity within the customary system. Estimate the weight or mass of objects and use a balance to measure the weight or mass of the object. Estimate and measure the capacity of liquids. Display measurement data in fractions of a unit on a line plot and solve real-world problems. Measure the length of objects to the nearest centimeter and millimeter. Convert measurements of length, mass and capacity within the metric system. Standards Covered in Chapter 11- #1, 2, 3, 4, 5, 6, 7, 8 8) Look for and express regularity in repeated reasoning. *

12 5th Grade - Chapter 12 - Geometry Geometry Polygons 15 days Sides and Angles of Triangles Classify Triangles Sides and Angles of Quadrilaterals Classify Quadrilaterals Use Models to Find Volume Three-Dimensional Figures Use Models to Find Volume Volume of Prisms 0 Build Composite Figures 2 1 Volume of Composite Figures 3 2 Make a Model 4 5 Geometry Classify two-dimensional figures into categories based on their properties. 3. Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. 4. Classify two-dimensional figures in a hierarchy based on properties. Measurement and Data Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas V=l w h and V=b h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. c. Recognize volume as additive. Find volumes of solid figures composed of two non- overlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems. Chapter 12 - Vocabulary polygon regular polygon pentagon, hexagon, octagon congruent sides congruent angles attribute congruent figures Types of triangles: equilateral, acute, isosceles, obtuse, scalene, right Types of quadrilaterals: square, rectangle, parallelogram, rhombus, trapezoid Three-dimensional figures: cube, rectangular prism, triangular prism face, edge, base, vertex volume unit cube cubic unit composite figure Chapter 12 Learning Stations 5 RWPS Reader Flags: Shaping History 7 Activity 3-D Constructions 9 Graphic Novel A Carrier for Kitty 9 Problem Birdseye View Solving 9 RWPS Reader Exploring the World by Sea Classify two-dimensional figures based on properties. Classify triangles based on attributes, such as side measures and angle measures. Measure the sides and angles of quadrilaterals. Use this information to find congruent sides, parallel sides and right angles; and classify the quadrilaterals. Build nets and describe the properties of threedimensional figures. Use volume formulas to find the volume rectangular prisms. Find the volume of composite figures by relating Standards Covered in Chapter 12- #1, 2, 3, 4, 5, 6, 7, 8 8) Look for and express regularity in repeated reasoning. *