Students will:

• Create questions that require collecting or acquiring data.
• Determine the data needed to answer a question and collect or acquire existing data (limited to 10 or fewer data points) using different methods (like observations, measurements, and experiments).
• Organize and represent a data set using line graphs with a title and labeled axes with whole number increments, with and without the use of technology tools.
• Analyze data represented in line graphs and communicate results both orally and in writing:
  • Describe the characteristics of the data represented in a line graph and the data as a whole (for example, the time period when the temperature increased the most).
  • Identify parts of the data that have special characteristics and explain the meaning of the greatest, the least, or the same (for example, the highest temperature shows the warmest day).
  • Make inferences about data represented in line graphs.
  • Draw conclusions about the data and make predictions based on the data to answer questions.
  • Solve single-step and multistep addition and subtraction problems using data from line graphs.
• Describe probability as the chance of an outcome happening using terms like impossible, unlikely, equally likely, likely, and certain.
• Model and determine all possible outcomes of a simple event where there are no more than 24 possible outcomes, using various tools (like coins, two-sided counters, number cubes, and spinners).
• Write the probability of a simple event as a fraction between 0 and 1, where there are no more than 24 possible outcomes.
• Determine the likelihood of an event happening and relate it to its whole number or fractional representation (for example, impossible or zero; equally likely; certain or one).
• Create a model or real-life problem to represent a given probability.

Students will:

• Read nine-digit whole numbers presented in standard form and represent the same number in written form.
• Write nine-digit whole numbers in standard form when the numbers are presented orally or in written form.
• Use patterns within the base 10 system to determine and communicate, both orally and in written form, the place and value of each digit in a nine-digit whole number (for example, in 568,165,724, the 8 represents 8 million and its value is 8,000,000).
• Compare two whole numbers up to seven digits each using words (greater than, less than, equal to, not equal to) and/or using symbols (>, <, =, ≠).
• Order up to four whole numbers up to seven digits each from least to greatest or greatest to least.
• Determine and explain whether an estimate or an exact answer is needed when solving real-life problems involving addition and subtraction with whole numbers. Refine estimates by adjusting the final amount, using terms such as closer to, between, and a little more than.
• Use strategies (like rounding to the nearest 100 or 1,000, using compatible numbers, and other number relationships) to estimate a solution for single-step or multistep addition or subtraction problems with whole numbers, where addends or minuends do not exceed 10,000.
• Use strategies (like place value, properties of addition, and other number relationships) and algorithms, including the standard algorithm, to find the sum or difference of two whole numbers, where addends and minuends do not exceed 10,000.
• Estimate, represent, solve, and explain solutions to single-step and multistep real-life problems involving addition and subtraction with whole numbers where addends and minuends do not exceed 1,000,000.
• Identify, describe, extend, and create increasing and decreasing patterns using different representations (like objects, pictures, numbers, number lines, input/output tables, and function machines).
• Analyze an increasing or decreasing single-operation numerical pattern found in lists, input/output tables, or function machines, and figure out the rule to extend the pattern or identify missing terms.
• Given a rule, create increasing and decreasing patterns using numbers and input/output tables (including function machines).
• Solve real-life problems that involve identifying, describing, and extending increasing and decreasing patterns using single-operation input and output rules.

Students will:

• Compare and order up to four fractions (proper or improper) and/or mixed numbers with the same denominators by comparing the number of parts (numerators), using fractions with denominators of 12 or less (for example, 1/5 < 3/5). Explain comparisons orally, in writing, or with a model.
• Compare and order up to four fractions (proper or improper) and/or mixed numbers with the same numerators and different denominators by comparing the size of the parts, using fractions with denominators of 12 or less (for example, 3/8 < 3/5). Explain comparisons orally, in writing, or with a model.
• Use benchmarks (like 0, 1/2, or 1) to compare and order up to four fractions (proper or improper) and/or mixed numbers with the same or different denominators of 12 or less. Explain comparisons orally, in writing, or with a model.
• Compare two fractions (proper or improper) and/or mixed numbers using fractions with denominators of 12 or less, using the symbols >, <, and = (for example, 2/3 > 1/7). Explain comparisons orally, in writing, or with a model.
• Show equivalent fractions with denominators of 12 or less, with and without models.
• Compose and decompose fractions (proper and improper) and/or mixed numbers with denominators of 12 or less, in multiple ways, with and without models.
• Represent the division of two whole numbers as a fraction given a real-life situation and a model (for example, 3/5 means the same as 3 divided by 5 or 3/5 represents the amount of muffin each of five children will receive when sharing three muffins equally).

Students will:

• Determine and explain whether an estimate or an exact answer is needed when solving real-life problems involving multiplication and division of whole numbers. Refine estimates by adjusting the final amount, using terms such as closer to, between, and a little more than. 
• Quickly recall multiplication facts through 12 × 12 and the corresponding division facts.
• Create an equation using addition, subtraction, multiplication, and division to show the relationship between equivalent mathematical expressions (for example, 4 × 3 = 2 × 6; 10 + 8 = 36 ÷ 2; 12 × 4 = 60 − 12).
• Identify and use the appropriate symbol to show whether expressions are equal or not equal, using addition, subtraction, multiplication, and division (for example, 4 × 12 = 8 × 6 and 64 ÷ 8 ≠ 8 × 8).
• Determine all factor pairs for a whole number from 1 to 100, using concrete, pictorial, and numerical representations.
• Find common factors and the greatest common factor of no more than three numbers.
• Use strategies (like rounding, place value, properties of multiplication and/or addition) and algorithms, including the standard algorithm, to estimate and find the product of two whole numbers when given:
  • A two-digit factor and a one-digit factor
  • A three-digit factor and a one-digit factor
• Estimate, represent, solve, and explain solutions to single-step and multistep real-life problems that involve multiplication with whole numbers.
• Use strategies (like rounding, compatible numbers, place value) and algorithms, including the standard algorithm, to estimate and find the quotient of two whole numbers, given a one-digit divisor and a two- or three-digit dividend, with and without remainders.
• Estimate, represent, solve, and explain solutions to single-step real-life problems involving division with whole numbers.
• Interpret the quotient and remainder when solving a real-life problem.
• Identify, describe, extend, and create increasing and decreasing patterns using different representations (like objects, pictures, numbers, number lines, input/output tables, and function machines).
• Analyze an increasing or decreasing single-operation numerical pattern found in lists, input/output tables, or function machines, and figure out the rule to extend the pattern or identify missing terms.
• Given a rule, create increasing and decreasing patterns using numbers and input/output tables (including function machines).
• Solve real-life problems that involve identifying, describing, and extending increasing and decreasing patterns using single-operation input and output rules.

Students will:

• Investigate and describe the ten-to-one place value relationship for decimals through thousandths using concrete models (like place value mats/charts, decimal squares, and base 10 blocks).
• Represent and identify decimals expressed through thousandths using concrete, pictorial, and numerical representations.
• Read and write decimals expressed through thousandths using concrete, pictorial, and numerical representations.
• Identify and explain, both orally and in writing, the place and value of each digit in a decimal through thousandths (for example, in 0.385, the 8 is in the hundredths place and has a value of 0.08).
• Compare using symbols (<, >, =) and/or words (greater than, less than, equal to) and order (from least to greatest and greatest to least) a set of no more than four decimals expressed through thousandths, using multiple strategies (like benchmarks, place value, and number lines). Justify comparisons with a model, orally, and in writing.
• Represent fractions (proper or improper) and/or mixed numbers as decimals through hundredths using multiple representations, limited to halves, fourths, fifths, tenths, and hundredths.
• Identify and model equivalent relationships between fractions (proper or improper) and/or mixed numbers and decimals, using halves, fourths, fifths, tenths, and hundredths.
• Write the decimal and fraction equivalent for a given model (for example, 1/4 = 0.25 or 0.25 = 1/4; 1.25 = 5/4 or 1 1/4; 1.02 = 102/100 or 1 2/100).
• Apply strategies (like rounding to the nearest whole number and using compatible numbers) and algorithms, including the standard algorithm, to estimate and determine the sum or difference of two decimals through the thousandths, with and without models, where:
  • Decimals do not exceed the thousandths
  • Addends, subtrahends, and minuends are limited to four digits
• Estimate, represent, solve, and explain solutions to single-step and multistep real-life problems using addition and subtraction of decimals through the thousandths.

Students will:

• Apply strategies (like rounding, place value, properties of multiplication and/or addition) and algorithms, including the standard algorithm, to estimate and determine the product of two whole numbers when given:
  • A two-digit factor and a two-digit factor
• Estimate, represent, solve, and explain solutions to single-step and multistep real-life problems that involve multiplication with whole numbers.
• Apply strategies (like rounding, compatible numbers, place value) and algorithms, including the standard algorithm, to estimate and determine the quotient of two whole numbers, given a one-digit divisor and a two- or three-digit dividend, with and without remainders.
• Estimate, represent, solve, and explain solutions to single-step real-life problems involving division with whole numbers.
• Interpret the quotient and remainder when solving a real-life problem.
• Identify, describe, extend, and create increasing and decreasing patterns using different representations (like objects, pictures, numbers, number lines, input/output tables, and function machines).
• Analyze an increasing or decreasing single-operation numerical pattern found in lists, input/output tables, or function machines, and figure out the rule to extend the pattern or identify missing terms.
• Given a rule, create increasing and decreasing patterns using numbers and input/output tables (including function machines).
• Solve real-life problems that involve identifying, describing, and extending increasing and decreasing patterns using single-operation input and output rules.

Students will:

• Estimate and determine the sum or difference of two fractions (proper or improper) and/or mixed numbers, having like denominators limited to 2, 3, 4, 5, 6, 8, 10, and 12 (for example, 3/8 + 3/8, 21/5 + 4/5, 7/4 - 5/4) and simplify the resulting fraction. Addition and subtraction with fractions may include regrouping.
• Estimate, represent, solve, and explain solutions to single-step real-life problems using addition and subtraction with fractions (proper or improper) and/or mixed numbers, having like denominators limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fraction. Addition and subtraction with fractions may include regrouping.
• Solve single-step real-life problems involving multiplication of a whole number, limited to 12 or less, and a unit fraction (for example, 6 × 1/3, 1/5 × 8, 2 × 1/10), with models.
• Apply the inverse property of multiplication in models (for example, use a visual fraction model to represent 4/4 or 1 as the product of 4 × 1/4).
• Determine common factors and the greatest common factor of no more than three numbers.
• Describe probability as how likely an outcome is to happen using terms like impossible, unlikely, equally likely, likely, and certain.
• Model and determine all possible outcomes of a simple event with no more than 24 outcomes, using different tools like coins, two-sided counters, number cubes, and spinners.
• Write the probability of a simple event as a fraction between 0 and 1, with no more than 24 possible outcomes.
• Determine the likelihood of an event occurring and relate it to its whole number or fractional representation (for example, impossible or zero; equally likely; certain or one).
• Create a model or real-life problem to represent a given probability.

Students will: 

• Identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices.
• Explain what endpoints and vertices are in relation to lines, line segments, rays, and angles.
• Draw points, line segments, rays, angles, and lines using a ruler or straightedge.
• Identify parallel, perpendicular, and intersecting lines and line segments in both flat (plane) and 3D (solid) figures, including real-life examples.
• Use symbols to name points, lines, line segments, rays, angles, and to describe parallel and perpendicular lines.
• Learn what makes shapes like parallelograms, rectangles, squares, rhombi, and trapezoids unique by exploring their properties and attributes.
• Identify and describe points, line segments, angles, and vertices in four-sided shapes (quadrilaterals).
• Recognize and describe parallel, intersecting, perpendicular, and congruent (equal) sides in quadrilaterals.
• Compare, contrast, and group different quadrilaterals (parallelograms, rectangles, squares, rhombi, and trapezoids) based on their properties, such as:
  • Parallel sides
  • Perpendicular sides
  • Equal sides (congruence)
  • Number of right angles
• Use geometric markings to show the properties of quadrilaterals, such as parallel sides, congruent sides, and right angles.
• Use symbols to name line segments and angles in quadrilaterals.
• Find and recognize models and pictures of solid shapes, like cubes, rectangular boxes, square pyramids, balls (spheres), cones, and cylinders.
• Identify and describe solid shapes (cubes, rectangular boxes, square pyramids, and balls) by looking at their features, such as the number of corners (vertices), edges, and faces, as well as the shapes of the faces.
• Compare and contrast flat shapes (like circles, squares, triangles, rectangles) and solid shapes (like balls, cubes, square pyramids, rectangular boxes) by looking at their features, such as the number of sides, corners (vertices), edges, and the number and shape of their faces.

Students will:

• Determine the appropriate unit of measurement for:
  • Length in U.S. Customary units (inch, foot, yard, mile) and metric units (millimeter, centimeter, meter).
  • Weight/mass in U.S. Customary units (ounce, pound) and metric units (gram, kilogram).
  • Liquid volume in U.S. Customary units (cup, pint, quart, gallon) and metric units (milliliter, liter).
• Estimate and measure:
  • The length of an object to the nearest U.S. Customary unit (1/2 inch, 1/4 inch, 1/8 inch, foot, yard) and nearest metric unit (millimeter, centimeter, meter).
  • The weight/mass of an object to the nearest U.S. Customary unit (ounce, pound) and nearest metric unit (gram, kilogram).
  • The liquid volume to the nearest U.S. Customary unit (cup, pint, quart, gallon) and nearest metric unit (milliliter, liter).
• Compare your estimates of length, weight/mass, or liquid volume with the actual measurements.

• Solve problems by converting between equivalent measures within the U.S. Customary system for:

  • Length (inches and feet, feet and yards, inches and yards).
  • Weight/mass (ounces and pounds).
  • Liquid volume (cups, pints, quarts, and gallons).

Students will:

• Determine the appropriate unit of measurement for:
  • Length in U.S. Customary units (inch, foot, yard, mile) and metric units (millimeter, centimeter, meter).
  • Weight/mass in U.S. Customary units (ounce, pound) and metric units (gram, kilogram).
  • Liquid volume in U.S. Customary units (cup, pint, quart, gallon) and metric units (milliliter, liter).
• Estimate and measure:
  • The length of an object to the nearest U.S. Customary unit (1/2 inch, 1/4 inch, 1/8 inch, foot, yard) and nearest metric unit (millimeter, centimeter, meter).
  • The weight/mass of an object to the nearest U.S. Customary unit (ounce, pound) and nearest metric unit (gram, kilogram).
  • The liquid volume to the nearest U.S. Customary unit (cup, pint, quart, gallon) and nearest metric unit (milliliter, liter).
• Compare your estimates of length, weight/mass, or liquid volume with the actual measurements.

• Solve problems by converting between equivalent measures within the U.S. Customary system for:

  • Length (inches and feet, feet and yards, inches and yards).
  • Weight/mass (ounces and pounds).
  • Liquid volume (cups, pints, quarts, and gallons).