Northwest Arkansas Instructional Alignment Fifth Grade Mathematics

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1 1 NO Develop and use a variety of algorithms with computational fluency to perform whole number operations using addition and subtraction (up to fivedigit numbers), multiplication (up to three-digit x twodigit), division (up to two-digit divisor) interpreting remainders, including real-world problems A. Develop and use a variety of algorithms with computational fluency to perform whole number operations using addition and subtractions (up to fivedigit numbers) including real-world problems B. Develop and use a variety of algorithms with computational fluency to perform whole number operations using multiplication (up to three-digit times two-digit) including real-world problems C. Develop and use a variety of algorithms with computational fluency to perform whole number operations using division (up to two-digit divisor) interpreting remainders, including real-world problems *apply rules of regrouping and renaming *compose real-world problems using addition and subtraction *demonstrate a variety of algorithms *apply two-digit multiplication *illustrate correct alignment of digits *compose real-world problems with multiplication *demonstrate a variety of algorithms *divide with one and two-digit divisors *practice a variety of division algorithms *compose problems involving real-world situations in which remainders affect the outcome. *solve problems in real-world situations in which the remainder affects the outcome addend sum difference quotient divisor dividend remainder product factor congruent FIRST NINE WEEKS 1. Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: problem solving is important, takes significant time and repeated efforts, and requires reflection. 1 Essential Question - How are the four basic operations related to one another? 1 Essential Question - What are the specific strategies that have wide application in attacking problems and can help in problem solving? 2 NO Solve, with and without appropriate technology, twostep problems using a variety of methods and tools Solve two-step problems, with and without appropriate technology, using a variety of methods and tools *identify key information within the context of the problem *select and apply problem-solving strategies *determine steps necessary to solve problems *solve two-step problems with or without a calculator C.5.3 C Enduring Understanding - Choices in data collection and representation affect their interpretation and use. 2 Essential Question - What data display is appropriate for a given set of data? DAP Develop appropriate questions for surveys DAP Collect numerical and categorical data using surveys, observations and experiments that would result in bar graphs, line graphs, line plots and stem-and-leaf plots Develop appropriate questions for surveys Collect numerical and categorical data using surveys, observations and experiments that would result in bar graphs, line graphs, line plots and stem-and-leaf plots *select appropriate survey topic survey *write questions with limited answer choices to develop data surveys *collect numerical and categorical data using surveys, observations or experiments *determine the appropriate graph for data data bar graph line graph line plot stem-and-leaf plots data 1 of 9

2 C DAP Construct and interpret frequency tables, charts, line plots, stem-and-leaf plots and bar graphs A. Construct frequency tables, charts, line plots, stemand-leaf plots and bar graphs B. Interpret frequency tables, charts, line plots, stemand-leaf plots and bar graphs intervals *draw an axis and choose proper increments or increments intervals increase *find appropriate labels for both axis (x-axis and y-axis) decrease *construct a frequency table relationship *select an appropriate title interpret *make a key (legend) key *construct line plots legend *construct stem-and-leaf plots frequency table *construct bar graphs *interpret graphs and use information to draw appropriate conclusions C DAP Interpret graphs such as line graphs, double bar graphs, and circle graphs C DAP Make predictions and justify conclusions based on data Interpret graphs such as line graphs, double bar graphs and circle graphs Predict and justify conclusions based on data *utilize information to draw conclusions (change over time, comparisons, part of a whole) *make predictions based on data *justify conclusions based on data line graph double bar graphs circle graphs prediction justify data conclusion 3. Enduring Understanding - Statistical measures provide a numeric picture of the shape of dat 3 Essential Question - How can the mean, median, mode, and range be used to describe the shape of the data? C DAP Determine, with and without appropriate technology, the range, mean, median and mode (whole number data sets) and explain what each indicates about the set of data 2 NO Develop and use strategies to estimate the results of whole number computations and to judge the reasonableness of such results A. Determine, with and without appropriate technology, the range, mean, median and mode B. Explain what the range, mean, median and mode indicates about the set of data Develop and use strategies to estimate the results of whole number computations and to judge the reasonableness of the answer *apply algorithms with and without technology *solve problems in relation to real-world problems *differentiate among range, mean, median, and mode 4. Enduring Understanding - Computational estimation produce approximate results. 4 Essential Question - What is the purpose of estimation and what determines a reasonable estimation for a situation? NO Use divisibility rules to determine if a number is a factor of another number (2, 3, 5, 10) Use divisibility rules to determine if a number is a factor of another number *use a variety of estimation strategies to solve realworld problems *acknowledge that more than one answer is possible depending on the method of estimation 5. Enduring Understanding - Fractions,, and percents express a relationship between two numbers. 5 Essential Question - When is it appropriate to use percents? Decimals? Fractions? FP NO Use models and visual representations to develop the concepts of the following: Fractions: parts of unit wholes parts of a collection locations on number lines locations on ruler (benchmark fractions) divisions of whole numbers Ratios: part-to-part (2 boys to 3 girls) part-to-whole (2 boys to 5 people) Percents: part-to-100 A. Model concepts of fractions using manipulatives and B. Model concept of ratios using manipulatives and C. Model concept of percents using manipulatives and *apply divisibility rules of 2, 5 and 10 *apply the divisibility rule for 3 *use divisibility rules to determine if a number is a factor of another number Use models to develop concepts of fractions: *parts of unit wholes *parts of a collection (set) *locations on number lines *locations on ruler *divisions of whole numbers Use models to develop concepts of ratio: *part-to-part (2 boys to 3 girls) *part-to-whole (2 boys to 5 people) *part-to-100 Use models to develop concepts of percent: *use hundreds grid, links, counters *connect percents to and fractions range mean median mode average estimate reasonableness divisibility rules factor prime composite fraction ratio percent equivalent numerator denominator 2 of 9

3 ; FP 5.2 NO Use factors of numbers: to introduce exponents 36= 6 x 6 or 6² to find common factors of two numbers to simplify fractions to the lowest terms Note: Only the bolded part of this SLE at this point in the curriculum. A. Use factors of numbers to introduce exponents B. Use factors of numbers to find common factors of two numbers C. Use factors of numbers to simplify fractions to the lowest terms *recognize that exponents represent repeated multiplication of a single factor *apply exponential notation representation 512 = 8³ = 8x8x8) *list all of the factors of a number *identify common factors *identify greatest common factor (GCF) *use (GCF) or repeated division to simplify fractions exponents base factors common factor simplify greatest common factor FP.5.2 NO Identify decimal and percent equivalents for benchmark fractions FP NO Use models of benchmark fractions and their equivalent forms: to analyze the size of fractions to determine that simplification does not change the value of the fraction to convert between mixed numbers and improper fractions Given a benchmark fraction identify decimal and percent equivalents 5 Essential Question - How are fractions and ordered and compared? A. Analyze the size of fractions by using models of benchmark fractions and their equivalent forms B. Demonstrate that simplification does not change the value of the fraction C. Demonstrate ability to convert between mixed numbers and improper p fractions *identify benchmark fractions 0, 1/4, 1/2, 3/4, 1 and their percent and decimal equivalents 1/4 =.25 = 25% *identify benchmark fractions *use a variety of shapes to represent 1 whole *show that models being compared must be equivalent forms *draw benchmark fractions *determine whether the fraction is closer to 0 or 1 whole *analyze the size of fractions by using models of benchmark fractions and their equivalent forms *use models and grid paper to compare fractions *demonstrate that simplification does not change the value of the fraction *model proper, improper and mixed numbers with manipulatives *demonstrate the ability to convert between mixed numbers and improper fractions benchmark fractions equivalent congruent improper fraction mixed number FP.5.2 FP.5.2 NO Develop understanding of decimal place value using models NO Round and compare to a given place value (whole number, tenths, hundredths) Model decimal place value using manipulatives and A. Round decimal numbers to a given place value B. Compare to a given place value (whole number, tenths, hundredths) *identify that a decimal is part of a whole number *identify tenths and hundredths using models (place value chart, base ten blocks, et) *use manipulatives to model decimal equivalencies (0.4 = 0.40, 0.42 = ) *apply rules for rounding *identify place value through thousandths *round to a specific place value *identify place value through hundredths *use comparison symbols (,, =) *compare to the hundredths place decimal tenths hundredths place value thousandths (greater than) (less than) = (equal to) 6. Enduring Understanding - Operation strategies with fractions and are similar to those used with whole numbers. 6 Essential Question - What strategies can be developed to show computation with fractions and? 3 of 9

4 FP.5.2 NO Model addition, subtraction, and multiplication of fractions with like and unlike denominators and A. Model addition, subtraction, and multiplication of fractions with like and unlike denominators and B. Model addition, subtraction and multiplication of *use manipulatives to add, subtract and multiply fractions with like denominators. *use manipulatives to convert fractions with unlike denominators prior to adding or subtracting *model addition, subtraction, and multiplication of fractions with like and unlike denominators and *model using manipulatives (money, grid paper, base ten blocks, et) *model addition, subtraction and multiplication of least common multiple common denominator FP NO Develop and use algorithms: to add and subtract numbers containing (up to thousandths place) to multiply (hundredths x tenths) to divide by whole number divisors to add and subtract fractions with like denominators A. Develop and use algorithms to add and subtract numbers containing (up to thousandths place) B. Develop and use algorithms to multiply (hundredths times tenths) C. Develop and use algorithms to divide by whole number divisors D. Develop and use algorithms to add and subtract fractions with like denominators *apply place value (including NO.1.5.2) *model an understanding of addition and subtraction of using manipulatives *add and subtract using algorithms *model multiplying using manipulatives or *apply place value to understand that multiplying can result in a larger or smaller product *multiply using algorithms *model dividing by whole numbers using manipulatives or *apply place value to understand where the decimal point should be placed in the quotient *divide by whole number divisors using algorithms d. *model adding fractions with like denominators using manipulatives or *know that the denominator stays the same and represents congruent pieces *add and subtract fractions with like denominators SECOND NINE WEEKS 1. Enduring Understanding - Mathematical properties of our number system aid in computation. 1 Essential Question - How do number properties assist in computation? 1 NO Apply rules (conventions) for order of operations to Apply rules for order of operations to whole numbers where the left to right computations are modified only whole numbers where the left to right computations are by the use of parentheses modified only by the use of parentheses *identify that order of operations solves from left to right (do not teach ALL of order of operations at this level) *when parenthesis are present, do that operation first, otherwise, solve from left to right *solve inside parenthesis first *understand when using parenthesis everything inside reads left to right *apply rules for order of operations to whole numbers where the left to right computations are modified only by the use of parentheses order of operations parenthesis 4 of 9

5 1 A Write expressions containing one variable (a letter representing an unknown quantity) using rules for addition and subtraction Apply rules for subtraction and addition to write expressions containing one variable using rules for addition and subtraction *state the difference between an expression and an equation *identify that a variable represents an unknown value *apply expressions to real-world situations *write expressions containing one variable expression variable NO Identify commutative and associative properties NO Identify the Distributive Property by using physical models to solve computation and real-world problems Identify commutative and associative properties Identify the Distributive Property by using physical models to solve computation and real-world problems *identify that these properties only apply to addition and multiplication *practice to identify property *distinguish between the two *identify commutative and associative properties *use physical models to demonstrate that Distributive Property is used to break down numbers to make a problem easier to solve in your head *use the Distributive Property to show different representations of the same value *solve problems using Distributive Property Commutative Property Associative Property Distributive Property 2. Enduring Understanding - Powers and roots are related. 2 Essential Question - How are powers and roots related? ; FP NO Use factors of numbers: to introduce exponents 36= 6 x 6 or 6² to find common factors of two numbers to simplify fractions to the lowest terms Note: Only the bolded part of this SLE at this point in the curriculum. A. Use factors of numbers to introduce exponents B. Use factors of numbers to find common factors of two numbers C. Use factors of numbers to simplify fractions to the lowest terms *recognize that exponents represent repeated multiplication of a single factor *apply exponential notation ti representation ti 512 = 8³ = 8x8x8 *list all of the factors of a number *identify common factors *identify greatest common factor (GCF) *use (GCF) or repeated division to simplify fractions exponents base factors common factor simplify greatest common factor NO Use models to differentiate between perfect squares up to 100 and other numbers A Select, write and evaluate algebraic expressions with one variable by substitution Evaluate x+4 if x=7 C A Interpret and write a rule for a one-operation function table adding 3 Differentiate between perfect squares up to 100 and other numbers using models Select, write and evaluate algebraic expressions with one variable by substitution evaluate x + 4 if x=7 Interpret and write a rule for a one-operation function table *identify perfect squares *use models to differentiate between perfect squares and other numbers 3. Enduring Understanding - A numeric or algebraic expression represents a quantity. 3 Essential Question - When are algebraic and numeric expressions used? *select algebraic expressions to match a real-world situation *write algebraic expressions using one variable *solve the unknown variable by replacing with a given value *recognize the relationship of the paired numbers in a function table *determine correct operation *write a rule for a one-operation function table square perfect square 4. Enduring Understanding - Algebraic representations using patterns and relationships can be represented graphically, numerically, symbolically, and verbally to solve real-world problems. 4 Essential Question - How are graphs, tables, and symbols used to represent relationships? function table 5 of 9

6 C.5.3 A Draw conclusions and make predictions, with and without appropriate technology, from models, tables and line graphs Draw conclusions and make predictions, with and without appropriate technology, from models, tables and line graphs *identify parts of data collection tools table, chart, graph *interpret meaning of data to make predictions and draw conclusions with and without technology table line graph prediction T-chart relationship C A Solve problems by finding the next term or missing term in a pattern or function table using real-world situations C.5.1; C Essential Question - How can patterns be identified using mathematical rules to solve real-world problems? A Model and describe quantities that change using realworld situations age and height Solve problems by finding the next term or missing term in a pattern or function table using real-world situations Use real-world situations to model and describe change (rate of change) 4 Essential Question - Why are equations useful? 2 A Use manipulatives and appropriate technology to Model and solve simple equations by informal methods model and solve simple equations using manipulatives and appropriate technology *identify what a function table is (input and/or output, what's my rule) *use appropriate operation to find the missing term or terms *apply patterns to real-world situations *identify things that change over time *identify relationships of change (increase or decrease) *identify that an equation is balanced on both sides of the equal sign *solve simple equations for unknowns using manipulatives and technology THIRD NINE WEEKS 1. Enduring Understanding - Points, lines, and planes are the foundations of geometry. 1 Essential Question - How are properties used to classify and construct geometric figures? 1 G Identify and model regular and irregular polygons including decagon Note: There is a gap here because three-dimensional properties are discussed in fourth grade and sixth grade, but is ignored in fifth grade. It would seem 3-D objects are higher level than 2-D. Identify and model regular and irregular polygons including decagon *identify the characteristics of regular and irregular polygons *measure lengths of sides and degrees of angles to identify regular and irregular polygons *identify regular and irregular polygons *relationships among polygons *parallel lines function table term increase decrease relationship proportional rate rate of change equation equality inequality polygon regular polygon irregular polygon angle side triangle, quadrilateral, pentagon, hexagon, octagon, decagon relationships parallel lines 1 G Identify and draw congruent, adjacent, obtuse, acute, right and straight angles (Label parts of an angle: vertex, rays, interior and exterior) Note: There is a gap here because in grade 5-7 perpendicular angles and intersecting lines are not mentioned until 8th grade (G ). In 4th grade, G , intersecting, perpendicular, and parallel lines are mentioned in problem solving context. Characteristics (G.8.5.1) of polygons are mentioned concerning polygon which would include parallel lines, but not necessarily the other two. A. Identify and draw congruent, adjacent, obtuse, acute, right and straight angles B. Label the parts of an angle (vertex, rays, interior and exterior) Note: There is a tremendous gap concerning intersecting and perpendicular line segments from 5-7 grades. *use a protractor to measure and draw angles *identify acute, obtuse, right and straight angles from their measurements *compare angle measures to determine congruence *identify adjacent angles *identify interior and exterior points of an angle *label the parts of an angle congruent adjacent angle obtuse angle acute angle right angle straight angle vertex ray interior exterior point 1 Essential Question - How are angles measured? 6 of 9

7 M Use benchmark angles to estimate the measure of angles 45 degrees, 90 degrees, 120 degrees, 180 degrees G Model and identify circle, radius, diameter, center, circumference and chord 4 G Predict and describe the results of translation (slide), reflection (flip), rotation (turn), showing that the transformed shape remains unchanged Use benchmark angles to estimate the measure of angles 1 Essential Question - What are the properties of a circle? Model and identify circle, radius, diameter, center, circumference and chord Predict and describe the results of translation (slide), reflection (flip), rotation (turn), showing that the transformed shape remains unchanged *identify benchmark angles 45, 90, 120, and 180 *estimate angle measures using benchmark angles *label the parts of a circle *distinguish among radius, chord and diameter *model circumference using real-world objects string, tape measure *show that a transformation can take place over a horizontal or vertical axis *know a rotation occurs around a vertex *use formal and informal vocabulary translation =slide *recognize that the transformed shape remains unchanged *predict and describe the results of a given transformation benchmark angles 45, 90, 120, and 180 right angle obtuse angle acute angle straight angle circle radius diameter center circumference chord 2. Enduring Understanding - Geometric figures can change position and maintain the same attributes on a coordinate plane. 2 Essential Question - How does the movement of a geometric figure affect its attributes? translation (slide) reflection (flip) rotation (turn) transformation mirror image G Model and identify the properties of congruent figures Identify and model the properties of congruent figures *G *Identify and model the properties of congruent figures congruent G Use geometric vocabulary to describe the location and Use geometric vocabulary (horizontal/x-axis, vertical/ y- plot points in quadrant 1 axis, ordered pairs) to describe the location and plot points in quadrant I (same as G ) 1 G Using grid paper, draw and identify two-dimensional patterns (nets) for cubes Note: G talks about three dimensional models, which is a higher level than two dimensional models. Also, they have to construct a 3-D model. A. Use grid paper to draw two-dimensional patterns (nets) for cubes B. Identify two-dimensional patterns (nets) for cubes *use vertical and horizontal number lines that include positive numbers *show that the first number is the horizontal axis and the second number is the vertical axis in an ordered pair *locate horizontal/x-axis and vertical/y-axis *use geometric vocabulary to describe the location and plot points in quadrant 1 *know there are several patterns for a cube *use manipulatives to form cubes *using grid paper, draw and identify two-dimensional patterns (nets) for cubes horizontal axis x-axis vertical axis y-axis ordered pair quadrant 1 plot point 3. Enduring Understanding - Geometric relationships exist between two-dimensional and three-dimensional figures. 3 Essential Question - How are two- dimensional and three-dimensional figures related? two-dimensional cube net 3 Essential Question - What is the relationship between linear measures and area and volume? M Model the differences between covering the faces (surface area/nets) and filling the interior (volume of cubes) Use manipulatives to model the differences between covering the faces and filling the interior *use manipulatives to model surface area by covering faces an object interior *use manipulatives to model volume by filling an object net 7 of 9

8 M Understand when to use linear units to describe perimeter, square units to describe area or surface area, and cubic units to describe volume in real-world situations 3 M Develop and use strategies to solve real-world problems involving perimeter and area of rectangles Use real-world situations to recognize when to use linear units to describe perimeter, square units to describe area or surface area, and cubic units to describe volume Develop and use strategies to solve real-world problems involving perimeter and area of rectangles *use manipulatives to clarify linear units, square units, and cubic units *identify the measurement/unit that is needed for a given situation 3 Essential Question - How are problems involving two-dimensional measures solved? *demonstrate the difference between perimeter and area *identify real-world applications that would involve measurement of perimeter or area *know and use formulas for finding perimeter and area *use strategies to solve real-world problems involving perimeter and area of rectangles linear unit perimeter square unit area area surface area cubic unit volume perimeter area rectangle FOURTH NINE WEEKS 1. Enduring Understanding - Selection of standard measurement tools and units depend on the real-world situation. 1 Essential Question - Why are specific tools and units used to measure different attributes? M Identify and select appropriate units and tools to measure angles with degrees, distance with feet Identify and select appropriate units and tools to measure angles with degrees, distance with feet *identify units/tools of measurements *recognize that a protractor is the appropriate tool to measure angles *recognize that a ruler, yard stick, meter stick, tape measure, et are used for linear measure *select appropriate unit for measurement *thermometer for temperature protractor angle ruler yard stick tape measure meter stick Celsius Fahrenheit thermometer M Draw and measure distance to the nearest cm and ¼ inch accurately A. Draw distance to the nearest centimeter and 1/4 inch accurately B. Measure distance to the nearest centimeter and 1/4 inch accurately M A. Count the distance between two points on a Count the distance between two points on a horizontal horizontal or vertical line or vertical line and compare the lengths of the paths on B. Compare the lengths on a grid between two points a grid (shortest path, paths of equal length) shortest path, paths of equal length, et 2 M Determine which unit of measure or measurement tool matches the context for a problem situation Recognize which unit of measurement or measurement tool matches the context for a problem situation *distinguish between metric and customary measurements on a ruler *identify the benchmark fractions on a ruler *identify where measurement begins on a ruler *count the distance between two points on a line or a grid *determine the length of a path on a grid *compare the lengths of paths on a grid *identify the necessary unit and then measurement tool to solve problems horizontal vertical interval 4 M Make conversions within the customary measurement system in real-world problems hours to minutes, feet to inches, quarts to gallons, et Use real-world situations to make conversions within the customary measurement system (hours to minutes, feet to inches, quarts to gallons) *identify the necessary unit of measurement to solve problems *select correct operation for computation *utilize labels for conversions *convert between customary units of measurement conversion convert customary M Establish through experience benchmark prefixes of milli-, centi-, and kilo- Recognize the value of the benchmark prefixes milli-, centi-, and kilobenchmark prefixes: milli-, centi-, kilometric system 8 of 9

9 C.5.2 C.5.3 M Solve real-world problems involving one elapsed time, counting forward (calendar and clock) A. Solve real-world problems involving one elapsed time, counting forward on a calendar B. Solve real-world problems involving one elapsed time, counting forward on a clock *read consecutive months on a calendar elapsed time *demonstrate that passing 12 o'clock changes time from am to pm or pm to am *solve real-world problems involving one elapsed time, counting forward (calendar and clock) 2. Enduring Understanding - The expected outcome of an event is a prediction of what might actually happen in the long run. 2 Essential Question - How is the probability of an event determined and described? DAP List and explain all possible outcomes in a given situation List and explain all possible outcomes in a given situation *identify all possible outcomes *explain why outcomes are possible 2 Essential Question - How are predictions made based on the outcomes of a probability experiment? C DAP Identify and predict the probability of events within a simple experiment Identify and predict the probability of events within a simple experiment (marbles, dice, spinners, cards, et) *identify the probability of events occurring within a simple experiment *predict the results of events occurring within a simple experiment outcomes combinations conclusion probability possible outcomes experiment conclusion 9 of 9