MATH EXPRESSIONS GRADE 4 SCOPE AND SEQUENCE

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Reynard Campbell
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1 UNIT 1: SOLVE MULTIPLICATION AND DIVISION WORD PROBLEMS Estimated time frame: 12 days (9 lessons + assessment) Algebra & Functions: Correlate story situations with expressions or equations (may use numbers and one operation +, -, or x). Solve for a missing number in an equation (using estimation, guess & check, etc.). Create or match a story problem to an equation. Correlate story situations with expressions or equations (may use numbers and one operation +, -, or x; no variables). Computation & Estimation: Solve problems involving multiplication facts through 12 x 12. Solve problems involving division facts through 9 x 9. Number, Number Systems, And Number Relationships: Find/list/identify all factors through 10 of any given number. Identify factors of numbers to 100. Find/list/identify multiples of a number, where the multiples do not exceed 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-50 is prime or composite. Mathematical Problem Solving And Communication: Choose an appropriate strategy and correct operation to solve a problem with 1 or 2 steps/operations. Choose and explain the mathematical tools (graphs, vocabulary, and symbols, etc.) necessary to solve a problem through written and spoken language. (See PSSA Assessment Anchor Glossary.) Statistics & Data Analysis: Collect and organize data in tables properly labeled with title and headings. Graph data or complete a graph given the data (bar graph, line plot, or pictograph, grid is provided) Translate information from one type of display to another (table, chart, bar graph, line plot, or pictograph) Describe, interpret, and/or answer questions based on data shown in tables, charts, bar graphs, line plots, and pictographs. Determine reasonableness of conclusions drawn based on data in a graph.

2 UNIT 2: Quadrilaterals 10 days (6 lessons + assessment) Geometry: Identify and draw congruent, non- congruent, and similar shapes. Identify, classify, and/or compare two- dimensional figures (circle, triangle, square, parallelogram, trapezoid, rhombus, rectangle, pentagon, hexagon, and octagon). Identify points, lines, line segments, and rays. Identify parallel and perpendicular lines. Identify or create figures that have one, two, or no lines of symmetry. Recognize mirror/rotational symmetry. Measurement & Estimation: Apply the area and perimeter formulas for rectangles to real world and mathematical problems. Recognize that polygons with the same area can have a different perimeter and polygons with the same perimeter can have a difference area.

3 UNIT 3: PLACE VALUE AND MULTI- DIGIT ADDITION & SUBTRACTION Math Expressions (teach all lessons except 3.2) 28 days (20 lessons + assessment) Algebra & Functions: Solve equations using multiplication and addition properties (identity, associative, and commutative), using concrete objects to demonstrate equality between the two number expressions (e.g., using cubes on a balance). Correlate story situations with expressions or equations (may use numbers and one operation +, -, or x). Solve for a missing number in an equation (using estimation, guess & check, etc.). Create or match a story problem to an equation. Identify the missing symbol (+, -, x,, <, >, =) that makes a number sentence true. Calculus: Compare whole numbers, up through 6 digits, and fractions using <, >, or = (may use number lines or manipulatives). Computation & Estimation: Solve problems involving multiplication facts through 12 x 12. Solve problems involving division facts through 9 x 9. Round whole numbers to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. Estimate the answer to addition, subtraction, and multiplication problems using whole numbers through six digits (for multiplication, no more than 2 digits times 1 digit excluding powers of 10). *Round amounts of money to the nearest dollar. Number, Number Systems, And Number Relationships: Understand and use vocabulary terms: addend, sum, difference Compare two multi- digit numbers based on meanings of the digits in each place, using >, =, and < through six digits. Write and read whole numbers in expanded, standard, and /or word form through 6 digits. Order a set of whole numbers from least to greatest or greatest to least up through 6 digits. Demonstrate the inverse relationship between addition and subtraction and multiplication and division using fact families. Solve problems involving addition and subtraction with decimals through the hundredths, or money to the cent and/or explain the solutions. Limit to two- step problems. Statistics & Data Analysis:

4 Describe, interpret, and/or answer questions based on data shown in tables, charts, bar graphs, line plots, and pictographs.

5 UNIT 4: ANGLES & POLYGONS 9 days (7 lessons + assessment) Geometry: Identify and draw congruent, non- congruent, and similar shapes. Identify, classify, and/or compare two- dimensional figures (circle, triangle, square, parallelogram, trapezoid, rhombus, rectangle, pentagon, hexagon, and octagon). Identify or create figures that have one, two, or no lines of symmetry. Recognize mirror/rotational symmetry. Measurement & Estimation: Recognize that polygons with the same area can have a different perimeter and polygons with the same perimeter can have a difference area. Recognize the differences in angle measurements, i.e. acute, obtuse, right.

6 UNIT 5: MULTI- DIGIT MULTIPLICATION 26 days (17 lessons + assessment) Algebra & Functions: Correlate story situations with expressions or equations (may use numbers and one operation +, -, or x). Computation & Estimation: Demonstrate fluency in using the following U.S. algorithms: 2-, 3-, & 4- digit x 1- digit Multiplication with regrouping 2- digit x 2- digit Multiplication with regrouping Round whole numbers to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. Estimate the answer to addition, subtraction, and multiplication problems using whole numbers through six digits (for multiplication, no more than 2 digits times 1 digit excluding powers of 10). Statistics & Data Analysis: Translate information from one type of display to another (table, chart, bar graph, line plot, or pictograph). Describe, interpret, and/or answer questions based on data shown in tables, charts, bar graphs, line plots, and pictographs

7 UNIT 6: THE METRIC MEASURMENT SYSTEM 8 days (5 lessons + assessment) Measurement & Estimation: Know relative sizes of measurement units within one system of units, including km, m, cm, kg, g, lb, oz, l, ml, hr, min, and sec. Use or read a ruler to measure to the nearest ¼ inch or centimeter. Select and use appropriate tools for measuring time, weight, temperature and capacity. Make reasonable estimates of weights, lengths, and capacities of familiar objects (measurements in the same system). Apply the area and perimeter formulas for rectangles to real world and mathematical problems. Continue to develop estimation and measurement skills for liquid volume to the nearest half gallon, gallon, and liter; temperature to the nearest degree in Fahrenheit and Celsius; and time to the nearest minute.

8 UNIT 7: MULTI- DIGIT DIVISION 21 days (14 lessons + assessment) Algebra & Functions: Solve for a missing number in an equation (using estimation, guess & check, etc.). Correlate story situations with expressions or equations (may use numbers and one operation +, -, or x). Identify the missing symbol (+, -, x,, <, >, =) that makes a number sentence true. Calculus: Compare whole numbers, up through 6 digits, and fractions using <, >, or = (may use number lines or manipulatives). Computation & Estimation: Demonstrate fluency in using the following U.S. algorithms: 2- digit & 3- digit x 1- digit Division Multiply & Divide decimals by 1- digit whole number (through hundredths) Geometry: Identify or create figures that have one, two, or no lines of symmetry. Recognize mirror/rotational symmetry. Measurement & Estimation: Match/construct time (a picture of a clock), to the same time written in digital. Select and use appropriate tools for measuring time, weight, temperature and capacity. Calculate the elapsed time to the minute in a given situation, limited to two adjacent hours. Determine the beginning or ending time, given the elapsed time, limited to two adjacent hours. Number, Number Systems, And Number Relationships: Understand and use vocabulary terms: addend, sum, difference, factor, product, divisor, quotient, and dividend Solve problems involving all operations with whole numbers and/or explain the solution (limit to two- step problems, e.g., multiply then add, single digit multipliers and divisors). Statistics & Data Analysis: Recognize and calculate the range, median, mode, and mean of a set of data.

10 UNIT 8: PATTERNS, FUNCTIONS, AND GRAPHS Math Expressions (teach all lessons except 8.5- the tables are confusing- x/y are switched) Coordinate Grid activities from Investigations I and Coordinate Grid Resource books 8 days (5 lessons + assessment) Algebra & Functions: Extend or find a missing element in a numerical or geometric pattern (+, -, or x may be used; whole numbers). Identify/describe the rule for a numerical or geometric pattern shown (+, -, or x may be used; patterns must be whole numbers). Create or replicate a numerical or geometric pattern showing 3 repetitions (+, -, or x may be used; whole numbers or money). Determine the missing elements in a function table (functions may use +, -, or x and whole numbers). Determine the rule for a function given a table (functions may use +, -, or x and whole numbers). Geometry: Match or plot the ordered pair with the appropriate point (or object) on a simple grid. Statistics & Data Analysis: Collect and organize data in tables properly labeled with title and headings. Describe, interpret, and/or answer questions based on data shown in tables, charts, bar graphs, line plots, and pictographs Trigonometry: Recognize the differences in angle measurements, i.e. acute, obtuse, right.

11 UNIT 9: FRACTIONS 27 days (22 lessons + assessment) Geometry: Identify, classify, and/or compare two- dimensional figures (circle, triangle, square, parallelogram, trapezoid, rhombus, rectangle, pentagon, hexagon, and octagon). Number, Number Systems, And Number Relationships: Locate/identify fractions or decimals on a number line (decimals and fractions through the hundredths- do not mix fractions and decimals- *fractions through twelfths. Compare fractions and decimals using greater than (>), less than (<), and equal to (=). Compare two fractions with different numerators and different denominators by using strategies such as comparing to a benchmark fraction (1/2), using a visual model, or creating common denominators. Write the fractional decimal including mixed numbers, which corresponds to a drawing or set- no simplification. Create a drawing or set that represents a given fraction or decimal, including mixed numbers through the tenths place. Explain why a fraction is equivalent to another fraction using pictures, manipulatives or words Demonstrate fractional parts using drawings, diagrams, or models (e.g., using number lines, manipulatives, and simple drawings). Use drawings, diagrams, and models to represent fractions as division of a whole number by a whole number. Probability & Predictions: Make a prediction based on data or chance (data may be shown in tables, charts, line graphs, bar graphs, line plots, and pictographs). Describe, interpret and/or answer questions based on data or chance. Determine the probability of events recurring (by studying past data). Identify an event as certain, more likely, less likely, equally likely, or impossible. Show fraction equivalencies for events based on the likelihood line with zero being impossible, certain being one, and maybe being one- half (1/2). Describe possible outcomes for events that can be predicted with more than six trials using data from an experiment. Recognize the variable(s) that created the difference between prediction and outcome (by formulating questions about data and/or collecting, organizing, analyzing and displaying data).

12 Statistics & Data Analysis: Graph data or complete a graph given the data (bar graph, line plot, or pictograph, grid is provided). Translate information from one type of display to another (table, chart, bar graph, line plot, or pictograph). Describe, interpret, and/or answer questions based on data shown in tables, charts, bar graphs, line plots, and pictographs Determine reasonableness of conclusions drawn based on data in a graph.

13 UNIT 10: THREE- DIMENSIONAL FIGURES 5 days (3 lessons + assessment) Geometry: Identify, classify, and/or compare two- dimensional figures (circle, triangle, square, parallelogram, trapezoid, rhombus, rectangle, pentagon, hexagon, and octagon). Identify or classify three- dimensional figures (cube, sphere, rectangular prism, and pyramid). Measurement & Estimation: Apply the area and perimeter formulas for rectangles to real world and mathematical problems.

14 UNIT 11: DECIMAL NUMBERS 15 days (15 lessons + assessment) Computation & Estimation: Solve addition or subtraction problems involving decimals through hundredths (decimal numbers must have the same number of places). Round amounts of money to the nearest dollar. Number, Number Systems, And Number Relationships: Compare and/or order whole numbers through 6 digits and amounts of money to $100. Locate/identify fractions or decimals on a number line (decimals and fractions through the hundredths- do not mix fractions and decimals). fractions through twelfths. Compare fractions and decimals using greater than (>), less than (<), and equal to (=). Match the standard number form to the word form of decimal numbers through the hundredths place. Write the fractional decimal including mixed numbers, which corresponds to a drawing or set- no simplification. Create a drawing or set that represents a given fraction or decimal, including mixed numbers through the tenths place. Write the fractional decimal including mixed numbers, which corresponds to a drawing or set- no simplification. Create a drawing or set that represents a given fraction or decimal, including mixed numbers through the tenths place. Solve problems involving addition and subtraction with decimals through the hundredths, or money to the cent and/or explain the solutions. Limit to two- step problems

15 UNIT 12: THE U.S. CUSTOMARY SYSTEM 8 days (5 lessons + assessment) Measurement & Estimation: Match/construct time (a picture of a clock), to the same time written in digital. Know relative sizes of measurement units within one system of units, including km, m, cm, kg, g, lb, oz, l, ml, hr, min, sec. Use or read a ruler to measure to the nearest ¼ inch or centimeter. Select and use appropriate tools for measuring time, weight, temperature and capacity. Calculate the elapsed time to the minute in a given situation, limited to two adjacent hours. Determine the beginning or ending time, given the elapsed time, limited to two adjacent hours. Use a table to convert feet/mile, inches/foot, feet/yard, inches/yard, ounces, cups, pints, and quarts to other designated units; milliliters/liters, grams/kilograms, meters/centimeters. Make reasonable estimates of weights, lengths, and capacities of familiar objects (measurements in the same system). Continue to develop estimation and measurement skills for liquid volume to the nearest half gallon, gallon, and liter; temperature to the nearest degree in Fahrenheit and Celsius; and time to the nearest minute.

MATH EXPRESSIONS GRADE 5 SCOPE AND SEQUENCE

MATH EXPRESSIONS GRADE 5 SCOPE AND SEQUENCE UNIT 1: MULTIPLICATION AND DIVISION WORD PROBLEMS Math Expressions (teach all lessons) 10 --- 15 days (assuming a 60 minute lesson) Algebra & Functions: Solve for a missing number (blank, question mark,