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.

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.

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).

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.

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.

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).

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.

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.

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).

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.

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.

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).

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