Students will: 

• Ask questions that require collecting or finding data.
• Figure out what data is needed to answer a question and collect or find the data (limited to 30 or fewer data points for no more than eight categories) using various methods (like polls, observations, tallies).
• Organize and represent a data set using pictographs that include an appropriate title, labeled axes, and a key. Each pictograph symbol should represent 1, 2, 5, or 10 data points.
• Organize and represent a data set using bar graphs with a title and labeled axes, with and without the use of technology tools. Choose and use an appropriate scale (increments limited to multiples of 1, 2, 5, or 10).
• Analyze data represented in pictographs and bar graphs, and communicate results orally and in writing:
  • Describe the categories of data and the data as a whole (for example, data collected on preferred ways to cook or prepare eggs - scrambled, fried, hard boiled, and egg salad).
  • Identify parts of the data that have special characteristics, including categories with the most, least, or the same amount (for example, most students prefer scrambled eggs).
  • Make inferences about data represented in pictographs and bar graphs.
  • Use characteristics of the data to draw conclusions and make predictions (for example, it is unlikely that a third grader would like hard boiled eggs).
  • Solve one- and two-step addition and subtraction problems using data from pictographs and bar graphs.
• When given an incorrect bar graph or pictograph, explain why the interpretation is or correct and explain why.
• Ask questions that require collecting or finding data.
• Figure out what data is needed to answer a question and collect or find the data (limited to 10 or fewer data points) using various 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 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 multi-step addition and subtraction problems using data from line graphs.

Students will: 

• Read and write six-digit whole numbers in standard form, expanded form, and word form.
• Use patterns within the base 10 system to determine and explain, both orally and in writing, the place and value of each digit in a six-digit number (for example, in 165,724, the 5 represents 5 thousands and its value is 5,000).
• Break down and build up numbers up to 9,999 in multiple ways according to place value (for example, 256 can be 1 hundred, 14 tens, 16 ones, or 25 tens, 6 ones), with and without models.
• Compare two whole numbers, each 9,999 or less, using symbols (>, <, =, ≠) and/or words (greater than, less than, equal to, not equal to), with and without models.
• Order up to three whole numbers, each 9,999 or less, from least to greatest and greatest to least, with and wDecide and explain whether an estimate or an exact answer is needed when solving single-step and multistep real-life problems involving addition and subtraction, where the numbers do not exceed 1,000.
• Use strategies (like rounding to the nearest 10 or 100, using compatible numbers, and other number relationships) to estimate the answer for single-step or multistep addition or subtraction problems, including real-life situations, where the numbers do not exceed 1,000.
• 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 the numbers do not exceed 1,000.
• Identify and use the appropriate symbol to show if expressions are equal or not equal (for example, 256 - 13 = 220 + 23; 457 + 100 ≠ 557 + 100).
• Show, solve, and explain solutions to single-step and multistep real-life problems involving addition and subtraction with whole numbers where the numbers do not exceed 1,000 without models.
• Identify and describe increasing and decreasing patterns using different representations (like objects, pictures, numbers, and number lines).
• Look at an increasing or decreasing pattern, figure out the change, and continue the pattern or find missing terms using different representations.
• Solve real-life problems that involve identifying, describing, and extending patterns.
• Create increasing and decreasing patterns using objects, pictures, numbers, and number lines.
• Explore and explain the connection between two different representations of the same increasing or decreasing pattern.
• Given a real-life problem involving addition and/or subtraction of whole numbers 9,999 or less and a solution with or without a mathematical explanation, evaluate if the solution and/or explanation makes sense using mental math and estimation strategies, including rounding.
• When given a solution to an increasing or decreasing pattern, students will be able to analyze the solution for errors and justify their thinking.
• Read nine-digit whole numbers presented in standard form and write the same number in words.
• 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 explain, both orally and in writing, the place and value of each digit in a nine-digit number (for example, in 568,165,724, the 8 represents 8 millions 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 symbols (>, <, =, ≠).
• Order up to four whole numbers up to seven digits each, from least to greatest or greatest to least

Students will: 

• Show multiplication and division of whole numbers through 10 × 10, including in real-life situations, using different approaches and models (like repeated addition/subtraction, equal-sized groups/sharing, arrays, equal jumps on a number line, and skip counting).
• Use inverse relationships to write related facts connected to a given model for multiplication and division of whole numbers through 10 × 10.
• Use strategies (like place value, the properties of multiplication, and/or addition) when multiplying and dividing whole numbers.
• Show fluency with multiplication facts through 10 × 10 by using reasoning strategies (like doubling, adding a group, subtracting a group, near squares, and inverse relationships).
• Show, solve, and explain solutions to single-step real-life problems that involve multiplication and division of whole numbers through 10 × 10.
• Quickly recall multiplication facts through 10 × 10 and the corresponding division facts.
• Create an equation to represent the mathematical relationship between equivalent expressions using multiplication and/or division facts through 10 × 10 (for example, 4 × 3 = 14 - 2, 35 ÷ 5 = 1 × 7).
• Describe and explain the multiplicative relationship between two factors and the resulting product using five different representations: visual, symbolic, verbal, contextual, and physical.

Students will: 

• Describe a polygon as a closed plane figure made of at least three line segments that do not cross.
• Classify figures as polygons or not polygons and explain your reasoning.
• Identify and describe triangles, quadrilaterals, pentagons, hexagons, and octagons in different orientations, with and without real-life examples.
• Identify and name examples of polygons (triangles, quadrilaterals, pentagons, hexagons, octagons) in the environment.
• Classify and compare different polygons (triangles, quadrilaterals, pentagons, hexagons, octagons).
  Combine up to three polygons, each having three or four sides, and name the resulting polygon (triangles, quadrilaterals, pentagons, hexagons, octagons).
• Subdivide a three-sided or four-sided polygon into up to three parts and name the resulting polygons.
• Identify and describe points, lines, line segments, rays, and angles, including their 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 and solid shapes, including real-life examples.
• Use symbolic notation to name points, lines, line segments, rays, angles, and to describe parallel and perpendicular lines.
• Develop definitions for parallelograms, rectangles, squares, rhombi, and trapezoids by exploring their properties and attributes.
• Identify and describe points, line segments, angles, and vertices in quadrilaterals.
• Identify and describe parallel, intersecting, perpendicular, and congruent sides in quadrilaterals.
• Compare, contrast, and classify quadrilaterals (parallelograms, rectangles, squares, rhombi, and trapezoids) based on the following properties and attributes:
  • Parallel sides
  • Perpendicular sides
  • Congruence of sides
  • Number of right angles
• Use geometric markings to show the properties of quadrilaterals and identify parallel sides, congruent sides, and right angles.
• Use symbolic notation to name line segments and angles in quadrilaterals.

Students will: 

• Represent, name, and write a given fraction (proper or improper) or mixed number with denominators of 2, 3, 4, 5, 6, 8, and 10 using:
  • Region/area models (like pie pieces, pattern blocks, geoboards)
  • Length models (like paper fraction strips, fraction bars, rods, number lines)
  • Set models (like chips, counters, cubes)
• Identify a fraction represented by a model as the sum of unit fractions.
• Use a model of a fraction greater than one to count the fractional parts to name and write it as an improper fraction and as a mixed number (for example, 1/4, 2/4, 3/4, 4/4, 5/4 = 1 1/4).
• Compose and decompose fractions (proper and improper) with denominators of 2, 3, 4, 5, 6, 8, and 10 in multiple ways (for example, 7/4 = 4/4 + 3/4 or 4/6 = 3/6 + 1/6 = 2/6 + 2/6) using models.
• Create a real-life situation that involves comparing two fractions (proper, improper, or mixed numbers) and explain why the solution makes sense by showing the numbers in a visual, verbal, and/or symbolic form. In your explanation, use the relative size of each fractional part in relation to the whole.

Students will: 

• Show multiplication and division of whole numbers through 10 × 10, including in real-life situations, using different approaches and models (like repeated addition/subtraction, equal-sized groups/sharing, arrays, equal jumps on a number line, and skip counting).
• Use inverse relationships to write related facts connected to a given model for multiplication and division of whole numbers through 10 × 10.
• Use strategies (like place value, the properties of multiplication, and/or addition) when multiplying and dividing whole numbers.
• Show fluency with multiplication facts through 10 × 10 by using reasoning strategies (like doubling, adding a group, subtracting a group, near squares, and inverse relationships).
• Show, solve, and explain solutions to single-step real-life problems that involve multiplication and division of whole numbers through 10 × 10.
• Quickly recall multiplication facts through 10 × 10 and the corresponding division facts.
• Create an equation to represent the mathematical relationship between equivalent expressions using multiplication and/or division facts through 10 × 10 (for example, 4 × 3 = 14 - 2, 35 ÷ 5 = 1 × 7).
• Describe and explain the multiplicative relationship between two factors and the resulting product using five different representations: visual, symbolic, verbal, contextual, and physical.
• When given a solution to an increasing or decreasing pattern, students will be able to analyze the solution for errors and explain their reasoning.
• 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 multi-step real-life problems that involve multiplication with whole numbers.
• Estimate, represent, solve, and explain solutions to single-step real-life problems involving division with whole numbers.
• 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: 

• Read and write six-digit whole numbers in standard form, expanded form, and word form.
• Use patterns within the base 10 system to determine and explain, both orally and in writing, the place and value of each digit in a six-digit number (for example, in 165,724, the 5 represents 5 thousands and its value is 5,000).
  Break down and build up numbers up to 9,999 in multiple ways according to place value (for example, 256 can be 1 hundred, 14 tens, 16 ones, or 25 tens, 6 ones), with and without models.
• Decide and explain whether an estimate or an exact answer is needed when solving single-step and multistep real-life problems involving addition and subtraction, where the numbers do not exceed 1,000.
• Use strategies (like rounding to the nearest 10 or 100, using compatible numbers, and other number relationships) to estimate the answer for single-step or multistep addition or subtraction problems, including real-life situations, where the numbers do not exceed 1,000.
• 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 the numbers do not exceed 1,000.
• Identify and use the appropriate symbol to show if expressions are equal or not equal (for example, 256 - 13 = 220 + 23; 457 + 100 ≠ 557 + 100).
• Show, solve, and explain solutions to single-step and multistep real-life problems involving addition and subtraction with whole numbers where the numbers do not exceed 1,000.
• Identify and describe increasing and decreasing patterns using different representations (like objects, pictures, numbers, and number lines).
• Look at an increasing or decreasing pattern, figure out the change, and continue the pattern or find missing terms using different representations.
• Solve real-life problems that involve identifying, describing, and extending patterns.
• Create increasing and decreasing patterns using objects, pictures, numbers, and number lines.
• Explore and explain the connection between two different representations of the same increasing or decreasing pattern.
• Given a real-life problem involving addition and/or subtraction of whole numbers 9,999 or less and a solution with or without a mathematical explanation, evaluate if the solution and/or explanation makes sense using mental math and estimation strategies, including rounding.
• When given a solution to an increasing or decreasing pattern, students will be able to analyze the solution for errors and explain their thinking.
• Read nine-digit whole numbers presented in standard form and write the same number in words.
• 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 explain, both orally and in writing, the place and value of each digit in a nine-digit number (for example, in 568,165,724, the 8 represents 8 millions and its value is 8,000,000).
• Decide 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 like "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 the answer for single-step or multi-step addition or subtraction problems with whole numbers, where the numbers 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 the numbers do not exceed 10,000.
• Estimate, represent, solve, and explain solutions to single-step and multi-step real-life problems involving addition and subtraction with whole numbers where the numbers do not exceed 1,000,000.

Students will: 

• Explain whether an estimate or an exact measurement is needed for a real-life situation and choose the appropriate unit.
• Estimate and measure:
  • The length of an object to the nearest U.S. Customary unit (½ inch, inch, foot, yard) and metric unit (centimeter, meter).
  • The weight/mass of an object to the nearest U.S. Customary unit (pound) and metric unit (kilogram).
    The liquid volume to the nearest U.S. Customary unit (cup, pint, quart, gallon) and metric unit (liter).
    Compare your estimates of length, weight/mass, or liquid volume with the actual measurements.
• Solve problems, including real-life situations, involving area:
  • Describe and give examples of area as a measurement in real-life situations.
  • Estimate and determine the area of a given surface by counting the number of square units, describe the measurement (using the number and unit), and explain why the measurement is correct.
• Solve problems, including real-life situations, involving perimeter:
  • Describe and give examples of perimeter as a measurement in real-life situations.
  • Estimate and measure the distance around a polygon (with no more than six sides) to determine the perimeter and explain why the measurement is correct.
  • Given the lengths of all sides of a polygon, determine the perimeter.
• Describe a polygon as a closed plane figure made of at least three line segments that do not cross.
• Classify figures as polygons or not polygons and explain your reasoning.
• Identify and describe triangles, quadrilaterals, pentagons, hexagons, and octagons in different orientations, with and without real-life examples.
• Identify and name examples of polygons (triangles, quadrilaterals, pentagons, hexagons, octagons) in the environment.
• Classify and compare different polygons (triangles, quadrilaterals, pentagons, hexagons, octagons).
• Combine up to three polygons, each having three or four sides, and name the resulting polygon (triangles, quadrilaterals, pentagons, hexagons, octagons).
• Subdivide a three-sided or four-sided polygon into up to three parts and name the resulting polygons.
• Determine an appropriate unit of measure to use when measuring:
  • Length in both U.S. Customary units (inch, foot, yard, mile) and metric units (millimeter, centimeter, meter).
  • Weight/mass in both U.S. Customary units (ounce, pound) and metric units (gram, kilogram).
  • Liquid volume in both 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 (½ inch, ¼ inch, ⅛ inch, foot, yard) and nearest metric unit (millimeter, centimeter, or 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.
• Given the equivalent measure of one unit, solve problems, including real-life situations, by determining the 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).
• Use concrete materials and pictorial models to develop a formula for the area and perimeter of a rectangle (including a square).
• Use concrete materials and pictorial models to explore the relationship between the area and perimeter of rectangles.
• Identify and represent rectangles with the same perimeter but different areas, or with the same area but different perimeters.

Students will: 

• Show multiplication and division of whole numbers through 10 × 10, including in real-life situations, using different approaches and models (like repeated addition/subtraction, equal-sized groups/sharing, arrays, equal jumps on a number line, and skip counting).
• Use inverse relationships to write related facts connected to a given model for multiplication and division of whole numbers through 10 × 10.
• Use strategies (like place value and the properties of multiplication and/or addition) when multiplying and dividing whole numbers.
• Show fluency with multiplication facts through 10 × 10 by using reasoning strategies (like doubling, adding a group, subtracting a group, near squares, and inverse relationships).
• Show, solve, and explain solutions to single-step real-life problems that involve multiplication and division of whole numbers through 10 × 10.
• Quickly recall multiplication facts through 10 × 10 and the corresponding division facts.
• Create an equation to represent the mathematical relationship between equivalent expressions using multiplication and/or division facts through 10 × 10 (for example, 4 × 3 = 14 - 2, 35 ÷ 5 = 1 × 7).
• Describe and explain the multiplicative relationship between two factors and the resulting product using five different representations: visual, symbolic, verbal, contextual, and physical.
• 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 a fraction, less than or equal to one, to the benchmarks of 0, 1/2, and 1 using area/region models, length models, and without models.
• Compare two fractions (proper or improper) and/or mixed numbers with like numerators of 2, 3, 4, 5, 6, 8, and 10 (for example, 2/3 > 2/8) using words (greater than, less than, equal to) and/or symbols (>, <, =), using area/region models, length models, and without models.
• Compare two fractions (proper or improper) and/or mixed numbers with like denominators of 2, 3, 4, 5, 6, 8, and 10 (for example, 3/6 < 4/6) using words (greater than, less than, equal to) and/or symbols (>, <, =), using area/region models, length models, and without models.
• Show equivalent fractions with denominators of 2, 3, 4, 5, 6, 8, or 10 using region/area models and length models.
• Create a real-life situation that involves comparing two fractions (proper, improper, or mixed numbers) and explain why the solution makes sense by showing the numbers in a visual, verbal, and/or symbolic form. In your explanation, use the relative size of each fractional part in relation to the whole.

Students will: 

• Tell and write time to the nearest minute using analog and digital clocks. 
• Match a written time (for example, 4:38, 7:09, 12:51) to the time shown on analog and digital clocks to the nearest minute.
• Solve single-step real-life problems involving elapsed time in one-hour increments within a 12-hour period (within a.m. or within p.m.) when given:
  • The starting time and the ending time, determine the amount of time that has passed.
  • The starting time and the amount of elapsed time in one-hour increments, determine the ending time.
  • The ending time and the amount of elapsed time in one-hour increments, determine the starting time.
• Determine the value of a collection of bills and coins whose total is $5.00 or less.
• Construct a set of bills and coins to total a given amount of money whose value is $5.00 or less.
• Compare the values of two sets of coins or two sets of bills and coins, up to $5.00, using words (greater than, less than, equal to) and/or symbols (>, <, =) with concrete or pictorial models.
• Solve real-life problems to make change from $5.00 or less by using counting on or counting back strategies with concrete or pictorial models.
• Solve single-step and multi-step real-life problems involving elapsed time in hours and minutes within a 12-hour period (within a.m., within p.m., and across a.m. and p.m.) when given:
  • The starting time and the ending time, determine the amount of time that has passed in hours and minutes.
  • The starting time and the amount of elapsed time in hours and minutes, determine the ending time.
  • The ending time and the amount of elapsed time in hours and minutes, determine the starting time.

Students will: 

• Show multiplication and division of whole numbers through 10 × 10, including in real-life situations, using different approaches and models (like repeated addition/subtraction, equal-sized groups/sharing, arrays, equal jumps on a number line, and skip counting).
• Use inverse relationships to write related facts connected to a given model for multiplication and division of whole numbers through 10 × 10.
• Use strategies (like place value and the properties of multiplication and/or addition) when multiplying and dividing whole numbers.
• Show fluency with multiplication facts through 10 × 10 by using reasoning strategies (like doubling, adding a group, subtracting a group, near squares, and inverse relationships).
• Show, solve, and explain solutions to single-step real-life problems that involve multiplication and division of whole numbers through 10 × 10.
• Quickly recall multiplication facts through 10 × 10 and the corresponding division facts.
• Create an equation to represent the mathematical relationship between equivalent expressions using multiplication and/or division facts through 10 × 10 (for example, 4 × 3 = 12 + 0, 35 ÷ 5 = 7).
• Describe and explain the multiplicative relationship between two factors and the resulting product using five different representations: visual, symbolic, verbal, contextual, and physical. 
• Identify and use the appropriate symbol to show if expressions are equal or not equal, using addition, subtraction, multiplication, and division (for example, 4 × 12 = 8 × 6 and 64 ÷ 8 ≠ 8 × 8). 
• 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 multi-step real-life problems that involve multiplication with whole numbers. 
• Estimate, represent, solve, and explain solutions to single-step real-life problems involving division with whole numbers.
• 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.

In this unit, teachers will provide differentiated opportunities for students to explore content at a deeper level.