MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE UNIT 1: SOLVE MULTIPLICATION AND DIVISION WORD PROBLEMS
Resources: Math Expressions (teach all lessons)
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.)
Mathematical Reasoning & Connections:
● Use models, words, properties, etc to explain the validity of mathematical conclusions. (Show and explain conclusions.)
● Use appropriate language when describing relationships between mathematical ideas.
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.
MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE UNIT 2: Quadrilaterals
Resources: Math Expressions (teach all lessons)
Estimated Timeframe: 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.
Mathematical Reasoning & Connections:
● Use models, words, properties, etc to explain the validity of mathematical conclusions. (Show and explain conclusions.)
● Use appropriate language when describing relationships between mathematical ideas.
MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE UNIT 3: PLACE VALUE AND MULTI-­‐DIGIT ADDITION & SUBTRACTION
Resources: Math Expressions (teach all lessons except 3.2)
Estimated Timeframe: 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.
Mathematical Reasoning & Connections:
● Use models, words, properties, etc to explain the validity of mathematical conclusions. (Show and explain conclusions.)
● Use appropriate language when describing relationships between mathematical ideas.
Statistics & Data Analysis:
MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE ●
Describe, interpret, and/or answer questions based on data shown in tables, charts, bar graphs, line plots, and pictographs.
MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE UNIT 4: ANGLES & POLYGONS
Resources: Math Expressions (teach all lessons)
Estimated Timeframe: 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.
Mathematical Reasoning & Connections:
● Use models, words, properties, etc to explain the validity of mathematical conclusions. (Show and explain conclusions.)
● Use appropriate language when describing relationships between mathematical ideas.
MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE UNIT 5: MULTI-­‐DIGIT MULTIPLICATION
Resources: Math Expressions (teach all lessons)
Estimated Timeframe: 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). Mathematical Reasoning & Connections:
● Use models, words, properties, etc to explain the validity of mathematical conclusions. (Show and explain conclusions.)
● Use appropriate language when describing relationships between mathematical ideas.
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
MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE UNIT 6: THE METRIC MEASURMENT SYSTEM
Resources: Math Expressions (teach all lessons)
Estimated Timeframe: 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.
Mathematical Reasoning & Connections:
● Use models, words, properties, etc to explain the validity of mathematical conclusions. (Show and explain conclusions.)
● Use appropriate language when describing relationships between mathematical ideas.
MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE UNIT 7: MULTI-­‐DIGIT DIVISION
Resources: Math Expressions (teach all lessons)
Estimated Timeframe: 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). Mathematical Reasoning & Connections:
● Use models, words, properties, etc to explain the validity of mathematical conclusions. (Show and explain conclusions.)
● Use appropriate language when describing relationships between mathematical ideas.
Statistics & Data Analysis:
● Recognize and calculate the range, median, mode, and mean of a set of data.
MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE UNIT 8: PATTERNS, FUNCTIONS, AND GRAPHS
Resources: 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
Estimated Timeframe: 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. Mathematical Reasoning & Connections:
● Use models, words, properties, etc to explain the validity of mathematical conclusions. (Show and explain conclusions.)
● Use appropriate language when describing relationships between mathematical ideas.
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.
MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE UNIT 9: FRACTIONS
Resources: Math Expressions (teach all lessons)
Estimated Timeframe: 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).
Mathematical Reasoning & Connections:
● Use models, words, properties, etc to explain the validity of mathematical conclusions. (Show and explain conclusions.)
● Use appropriate language when describing relationships between mathematical ideas.
MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE 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.
MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE UNIT 10: THREE-­‐DIMENSIONAL FIGURES
Resources: Math Expressions (teach all lessons)
Estimated Timeframe: 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. Mathematical Reasoning & Connections:
● Use models, words, properties, etc to explain the validity of mathematical conclusions. (Show and explain conclusions.)
● Use appropriate language when describing relationships between mathematical ideas.
MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE UNIT 11: DECIMAL NUMBERS
Resources: Math Expressions (teach all lessons)
Estimated Timeframe: 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
Mathematical Reasoning & Connections:
● Use models, words, properties, etc to explain the validity of mathematical conclusions. (Show and explain conclusions.)
● Use appropriate language when describing relationships between mathematical ideas.
MATH EXPRESSIONS GRADE 4 – SCOPE AND SEQUENCE UNIT 12: THE U.S. CUSTOMARY SYSTEM
Resources: Math Expressions (teach all lessons)
Estimated Timeframe: 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.
Mathematical Reasoning & Connections:
● Use models, words, properties, etc to explain the validity of mathematical conclusions. (Show and explain conclusions.)
● Use appropriate language when describing relationships between mathematical ideas.