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3Grade 3 Standards
Top Mathematicians
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Number
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3.N.1
Say the number sequence 0 to 1000 forward and backward by:
• 5s, 10s or 100s, using any starting point
• 3s, using starting points that are multiples of 3
• 4s, using starting points that are multiples of 4
• 25s, using starting points that are multiples of 25.
• Achievement Indicators:
- 3N1.1 Extend a given skip counting sequence by 5s, 10s or 100s, forward and backward, using a given starting point.
- 3N1.2 Extend a given skip counting sequence by 25s, forward and backward, starting at a given multiple of 25.
- 3N1.3 Identify and correct errors and omissions in a given skip counting sequence.
- 3N1.4 Identify and explain the skip counting pattern for a given number sequence.
- 3N1.5 Determine the value of a given set of coins (nickels, dimes, quarters, loonies) by using skip counting.
- 3N1.6 Extend a given skip counting sequence by 3s, forward and backward, starting at a given multiple of 3.
- 3N1.7 Extend a given skip counting sequence by 4s, forward and backward, starting at a given multiple of 4. -
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3.N.10
Apply mental mathematics strategies and number properties in order to understand and recall basic addition facts and related subtraction facts to 18.
• Achievement Indicators:
- 3N10.1 Explain or demonstrate the mental mathematics strategy that could be used to determine a basic fact, such as:
• using doubles; e.g., for 6 + 8, think 7 + 7
• using doubles plus one, plus two; e.g., for 6 + 7, think 6 + 6 + 1
• using doubles subtract one, subtract two; e.g., for 6 + 7, think 7 + 7 – 1
• making 10; e.g., for 6 + 8, think 6 + 4 + 4 or 8 + 2 + 4
• using addition to subtract; e.g., for 13 – 7, think 7 + ? = 13.
• using commutative property; e.g., for 3 + 9, think 9 + 3
• provide a rule for determining answers when adding and subtracting zero. When you add or subtract 0 to or from a number, the answer is the number you started with.
- 3N10.2 Recall doubles to 18 and related subtraction facts.
- 3N10.3 Recall compatible number pairs for 5 and 10.
- 3N10.4 Recall basic addition facts to 18 and related subtraction facts to solve problems. -
3.N.11
Demonstrate an understanding of multiplication to 5 × 5 by:
• representing and explaining multiplication using equal grouping and arrays
• creating and solving problems in context that involve multiplication
• modelling multiplication using concrete and visual representations, and recording the process symbolically
• relating multiplication to repeated addition
• relating multiplication to division.
• Achievement Indicators:
It is not expected that students achieve instant recall of the basic facts.
- 3N11.1 Identify events from experience that can be described as multiplication.
- 3N11.2 Represent a given story problem, using manipulatives or diagrams, and record the problem in a number sentence.
- 3N11.3 Solve a given multiplication problem.
- 3N11.4 Create and illustrate a story problem for a given number sentence
- 3N11.5 Represent, concretely or pictorially, equal groups for a given number sentence.
- 3N11.6 Represent a given multiplication expression as repeated addition.
- 3N11.7 Represent a given repeated addition as multiplication.
- 3N11.8 Represent a given multiplication expression, using an array.
- 3N11.9 Create an array to model the commutative property of multiplication.
- 3N11.10 Relate multiplication to division by using arrays and writing related number sentences. -
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3.235
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3.2415
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3.2510
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3.2615
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3.2720
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3.N.12
Demonstrate an understanding of division (limited to division related to multiplication facts up to 5 × 5) by:
• representing and explaining division using equal sharing and equal grouping
• creating and solving problems in context that involve equal sharing and equal grouping
• modelling equal sharing and equal grouping using concrete and visual representations, and recording the process symbolically
• relating division to repeated subtraction
• relating division to multiplication.
• Achievement Indicators:
- 3N12.1 Identify events from experience that can be described as equal grouping.
- 3N12.2 Illustrate, with counters or a diagram, a given story problem, presented orally, that involves equal grouping; and solve the problem.
- 3N12.3 Listen to a story problem; represent the numbers, using manipulatives or a drawing; and record the problem with a number sentence.
- 3N12.4 Create and illustrate, with counters, a story problem for a given number sentence; e.g., 6 ÷ 3 = 2.
- 3N12.5 Solve a given problem involving division.
- 3N12.6 Identify events from experience that can be described as equal sharing.
- 3N12.7 Illustrate, with counters or a diagram, a given story problem, presented orally, that involves equal sharing; and solve the problem.
- 3N12.8 Represent a given division expression as repeated subtraction.
- 3N12.9 Represent a given repeated subtraction as a division expression.
- 3N12.10 Relate division to multiplication by using arrays and writing related number sentences. -
3.N.13
Demonstrate an understanding of fractions by:
• explaining that a fraction represents a part of a whole
• describing situations in which fractions are used
• comparing fractions of the same whole that have like denominators.
• Achievement Indicators:
- 3N13.1 Describe everyday situations where fractions are used.
- 3N13.2 Cut or fold a whole into equal parts, or draw a whole in equal parts; demonstrate that the parts are equal; and name the parts.
- 3N13.3 Sort a given set of shaded regions into those that represent equal parts and those that do not, and explain the sorting.
- 3N13.4 Represent a given fraction concretely or pictorially.
- 3N13.5 Identify common characteristics of a given set of fractions.
- 3N13.6 Name and record the fraction represented by the shaded and non-shaded parts of a given region.
- 3N13.7 Identify the numerator and denominator for a given fraction.
- 3N13.8 Model and explain the meaning of numerator and denominator.
- 3N13.9 Compare given fractions with the same denominator, using models. -
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3.295
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3.3020
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3.3120
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3.3220
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3.3315
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3.N.2
Represent and describe numbers to 1000, concretely, pictorially and symbolically.
• Achievement Indicators:
- 3N2.1 Represent a given number pictorially.
- 3N2.2 Read a given number word (0 to 1000).
- 3N2.3 Read a given three-digit numeral without using the word “and”.
- 3N2.4 Represent a given number as an expression; e.g., 300 – 44 for 256 or 20 + 236.
- 3N2.5 Represent a given number, using manipulatives such as base ten materials.
- 3N2.6 Write number words for given multiples of ten to 90.
- 3N2.7 Write number words for given multiples of a hundred to 900. -
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3.110
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3.210
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3.315
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3.N.3
Compare and order numbers to 1000.
• Achievement Indicators:
- 3N3.1 Place a given set of numbers in ascending or descending order, and verify the result by using a hundred chart (e.g., a one hundred chart, a two hundred chart, a three hundred chart), a number line or by making references to place value.
- 3N3.2 Create as many different three-digit numerals as possible, given three different digits. Place the numbers in ascending or descending order.
- 3N3.3 Identify and explain errors in a given ordered sequence to 1000.
- 3N3.4 Identify missing numbers in parts of a given hundred sequence to 1000. -
3.N.4
Estimate quantities less than 1000, using referents.
• Achievement Indicators:
- 3N4.1 Estimate the number of groups of ten in a given quantity, using 10 as a referent (known quantity).
- 3N4.2 Estimate the number of groups of a hundred in a given quantity, using 100 as a referent.
- 3N4.3 Estimate a given quantity by comparing it to a referent.
- 3N4.4 Select an estimate for a given quantity by choosing among three possible choices.
- 3N4.5 Select and justify a referent for determining an estimate for a given quantity. -
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3.N.5
Illustrate, concretely and pictorially, the meaning of place value for numerals to 1000.
• Achievement Indicators:
- 3N5.1 Explain and show, with counters, the meaning of each digit for a given three-digit numeral with all digits the same; e.g., for the numeral 222, the first digit represents two hundreds (two hundred counters) the second digit represents two tens (twenty counters) and the third digit represents two ones (two counters).
- 3N5.2 Explain, using concrete materials, the meaning of zero as a place holder in a given number.
- 3N5.3 Record, in more than one way, the number represented by given proportional materials (e.g., base-ten materials) and non-proportional materials (e.g., money).
- 3N5.4 Represent a given number in different ways, using proportional and non-proportional materials, and explain how the representations are equivalent; e.g., 351 can be represented as three 100s, five 10s and one 1; or two 100s, fifteen 10s and one 1; or three 100s, four 10s and eleven 1s. -
3.N.6
Describe and apply mental mathematics strategies for adding two two-digit numerals.
• Achievement Indicators:
- 3N6.1 Add two given two-digit numerals, using a mental mathematics strategy, and explain or illustrate the strategy.
- 3N6.2 Explain how to use the “adding from left to right” strategy; e.g., to determine the sum of 23 + 46, think 20 + 40 and 3 + 6.
- 3N6.3 Explain how to use the “taking one addend to the nearest multiple of ten and then compensating” strategy; e.g., to determine the sum of 28 + 47, think 30 + 47 – 2 or 50 + 28 – 3.
- 3N6.4 Explain how to use the “using doubles” strategy; e.g., to determine the sum of 24 + 26, think 25 + 25; to determine the sum of 25 + 26, think 25 + 25 + 1 or doubles plus 1.
- 3N6.5 Apply a mental mathematics strategy for adding two given two-digit numerals. -
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3.N.7
Describe and apply mental mathematics strategies for subtracting two two-digit numerals.
• Achievement Indicators:
- 3N7.1 Subtract two given two-digit numerals, using a mental mathematics strategy, and explain or model the strategy used.
- 3N7.2 Explain how to use the “taking the subtrahend to the nearest multiple of ten and then compensating” strategy; e.g., to determine the difference of 48 – 19, think 48 – 20 + 1.
- 3N7.3 Explain how to use the “think addition” strategy; e.g., to determine the difference of 62 – 45, think 45 + 5, then 50 + 12 and then 5 + 12.
- 3N7.4 Explain how to use the “using doubles” strategy; e.g., to determine the difference of 24 – 12, think 12 + 12 = 24.
- 3N7.5 Apply a mental mathematics strategy for subtracting two given two-digit numerals. -
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3.N.8
Apply estimation strategies to predict sums and differences of two two-digit numerals in a problem solving context.
• Achievement Indicators:
- 3N8.1Estimate the solution for a given problem involving the sum of two two-digit numerals; e.g., to estimate the sum of 43 + 56, use 40 + 50 (the sum is close to 90).
- 3N8.2 Estimate the solution for a given problem involving the difference of two two-digit numerals; e.g., to estimate the difference of 56 – 23, use 50 – 20 (the difference is close to 30). -
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3.N.9
Demonstrate an understanding of addition and subtraction of numbers with answers to 1000 (limited to one, two and three digit numerals), concretely, pictorially and symbolically, by:
• using personal strategies for adding and subtracting with and without the support of manipulatives
• creating and solving problems in context that involve addition and subtraction of numbers.
• Achievement Indicators:
- 3N9.1 Model the addition of two or more given numbers, using concrete or visual representations, and record the process symbolically.
- 3N9.2 Create an addition or subtraction story problem for a given solution.
- 3N9.3 Determine the sum of two given numbers, using a personal strategy; e.g., for 326 + 48, record 300 + 60 + 14.
- 3N9.4 Refine personal strategies to increase their efficiency.
- 3N9.5 Solve a given problem involving the sum or difference of two given numbers.
- 3N9.6 Model the subtraction of two given numbers, using concrete or visual representations, and record the process symbolically.
- 3N9.7 Determine the difference of two given numbers, using a personal strategy; e.g., for 127 – 38, record 38 + 2 + 80 + 7 or 127 – 20 – 10 – 8. -
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3.720
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3.820
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3.920
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3.1020
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3.1120
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3.1220
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3.1320
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3.1420
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3.1520
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3.1620
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3.N.1
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Statistics & Probability
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3.SP.1
Collect first-hand data and organize it using:
• tally marks
• line plots
• charts
• lists
to answer questions.
• Achievement Indicators:
- 3SP1.1Record the number of objects in a given set, using tally marks.
- 3SP1.2 Answer questions using collected data.
- 3SP1.3 Organize a given set of data, using tally marks, line plots, charts or lists.
- 3SP1.4 Determine the common attributes of line plots by comparing line plots in a given set.
- 3SP1.5 Collect and organize data, using tally marks, line plots, charts and lists.
- 3SP1.6 Answer questions arising from a given line plot, chart or list. -
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3.5315
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3.545
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3.555
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3.SP.2
Construct, label and interpret bar graphs to solve problems.
• Achievement Indicators:
- 3SP2.1 Determine the common attributes, titles and axes of bar graphs by comparing bar graphs in a given set.
- 3SP2.2 Draw conclusions from a given bar graph to solve problems.
- 3SP2.3 Create a bar graph, labelling the title and axes, to represent a given set of data.
- 3SP2.4 Solve problems by constructing and interpreting a bar graph. -
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3.SP.1
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Patterns and Relations
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3.PR.1
Demonstrate an understanding of increasing patterns by:
• describing
• extending
• comparing
• creating
patterns using manipulatives, diagrams, sounds and actions (numbers to 1000).
• Achievement Indicators:
- 3PR1.1 Describe a given increasing pattern by stating a pattern rule that includes the starting point and a description of how the pattern continues; e.g., for 42, 44, 46 … the pattern rule is start at 42 and add 2 each time.
- 3PR1.2 Identify the pattern rule of a given increasing pattern, and extend the pattern for the next three elements.
- 3PR1.3 Identify and explain errors in a given increasing pattern.
- 3PR1.4 Identify and apply a pattern rule to determine missing elements for a given pattern.
- 3PR1.5 Describe the strategy used to determine missing elements in a given increasing pattern.
- 3PR1.6 Create a concrete, pictorial or symbolic representation of an increasing pattern for a given pattern rule.
- 3PR1.7 Create a concrete, pictorial or symbolic increasing pattern; and describe the relationship, using a pattern rule.
- 3PR1.8 Solve a given problem, using increasing patterns.
- 3PR1.9 Identify and describe increasing patterns in the environment.
- 3PR1.10 Compare numeric patterns of counting by 2s, 5s, 10s, 25s and 100s.
- 3PR1.11 Locate and describe various increasing patterns found on a hundred chart, such as horizontal, vertical and diagonal patterns. -
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3.PR.2
Demonstrate an understanding of decreasing patterns by:
• describing
• extending
• comparing
• creating
patterns using manipulatives, diagrams, sounds and actions (numbers to 1000)..
• Achievement Indicators:
- 3PR2.1 Describe a given decreasing pattern by stating a pattern rule that includes the starting point and a description of how the pattern continues.
- 3PR2.2 Identify the pattern rule of a given decreasing pattern, and extend the pattern for the next three elements.
- 3PR2.3 Solve a given problem, using decreasing patterns.
- 3PR2.4 Identify and describe decreasing patterns in the environment.
- 3PR2.5 Compare decreasing numeric patterns of counting backward by 2s, 5s, 10s, 25s and 100s.
- 3PR2.6 Create a concrete, pictorial or symbolic decreasing pattern for a given pattern rule.
- 3PR2.7 Create a concrete, pictorial or symbolic decreasing pattern; and describe the relationship, using a pattern rule.
- 3PR2.8 Identify and describe various decreasing patterns found on a hundred chart, such as horizontal, vertical and diagonal patterns.
- 3PR2.9 Identify and explain errors in a given decreasing pattern.
- 3PR2.10 Identify and apply a pattern rule to determine missing elements for a given pattern.
- 3PR2.11 Describe the strategy used to determine missing elements in a given decreasing pattern. -
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3.PR.3
Solve one-step addition and subtraction equations involving a symbol to represent an unknown number.
• Achievement Indicators:
- 3PR3.1 Explain the purpose of the symbol in a given addition or subtraction equation with one unknown.
- 3PR3.2 Create an addition or subtraction equation with one unknown to represent a given combining or separating action.
- 3PR3.3 Provide an alternative symbol for the unknown in a given addition or subtraction equation.
- 3PR3.4 Solve a given addition or subtraction equation with one unknown that represents combining or separating actions, using manipulatives.
- 3PR3.5 Solve a given addition or subtraction equation with one unknown, using a variety of strategies, including guess and check.
- 3PR3.6 Solve a given addition or subtraction equation when the unknown is on the left or the right side of the equation.
- 3PR3.7 Explain why the unknown in a given addition or subtraction equation has only one value.
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3.PR.1
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Shape and Space
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3.SS.1
Relate the passage of time to common activities, using nonstandard and standard units (minutes, hours, days, weeks, months, years).
• Achievement Indicators:
- 3SS1.1 Select and use a non-standard unit of measure, such as television shows or pendulum swings, to measure the passage of time, and explain the choice.
- 3SS1.2 Identify activities that can or cannot be accomplished in minutes, hours, days, weeks, months and years.
- 3SS1.3 Provide personal referents for minutes and hours. -
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3.3720
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3.3820
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3.3910
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3.SS.2
Relate the number of seconds to a minute, the number of minutes to an hour and the number of days to a month in a problem solving context.
• Achievement Indicators:
- 3SS2.1 Determine the number of days in any given month, using a calendar.
- 3SS2.2 Solve a given problem involving the number of seconds in a minute, minutes in an hour or days in a given month.
- 3SS2.3 Create a calendar that includes days of the week, dates and personal events. -
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3.405
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3.SS.3
Demonstrate an understanding of measuring length (cm, m) by:
• selecting and justifying referents for the units cm and m
• modelling and describing the relationship between the units cm and m
• estimating length, using referents
• measuring and recording length, width and height.
• Achievement Indicators:
- 3SS3.1 Provide a personal referent for one centimetre, and explain the choice.
- 3SS3.2 Estimate the length of an object, using personal referents.
- 3SS3.3 Draw a line segment of a given length, using a ruler.
- 3SS3.4 Sketch a line segment of a given length without using a ruler.
- 3SS3.5 Provide a personal referent for one metre, and explain the choice.
- 3SS3.6 Match a given standard unit to a given referent.
- 3SS3.7 Show that 100 cm is equivalent to 1 m by using concrete materials.
- 3SS3.8 Determine and record the length and width of a given 2-D shape.
- 3SS3.9 Determine and record the length, width or height of a given 3-D object. -
3.SS.4
Demonstrate an understanding of measuring mass (g, kg) by:
• selecting and justifying referents for the units g and kg
• modelling and describing the relationship between the units g and kg
• estimating mass, using referents
• measuring and recording mass.
• Achievement Indicators:
- 3SS4.1 Provide a personal referent for one kilogram, and explain the choice.
- 3SS4.2 Estimate the mass of a given object, using personal referents.
- 3SS4.3 Provide a personal referent for one gram, and explain the choice.
- 3SS4.4 Match a given standard unit to a given referent.
- 3SS4.5 Explain the relationship between 1000 g and 1 kg, using a model.
- 3SS4.6 Measure, using a scale, and record, using the units g and kg, the mass of given everyday objects.
- 3SS4.7 Provide examples of 3-D objects that have a mass of approximately 1 g, 100 g and 1 kg.
- 3SS4.8 Determine the mass of two given similar objects with different masses, and explain the results.
- 3SS4.9 Determine the mass of an object, change its shape, remeasure its mass, and explain the results. -
3.SS.5
Demonstrate an understanding of perimeter of regular and irregular shapes by:
• estimating perimeter, using referents for cm or m
• measuring and recording perimeter (cm, m)
• constructing different shapes for a given perimeter (cm, m) to demonstrate that many shapes are possible for a perimeter.
• Achievement Indicators:
- 3SS5.1 Measure and record the perimeter of a given regular shape, and explain the strategy used.
- 3SS5.2 Measure and record the perimeter of a given irregular shape, and explain the strategy used.
- 3SS5.3 Construct more than one shape for a given perimeter (cm, m).
- 3SS5.4 Estimate the perimeter of a given shape (cm, m), using personal referents. -
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3.445
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3.455
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3.SS.6
Describe 3-D objects according to the shape of the faces and the number of edges and vertices.
• Achievement Indicators:
- 3SS6.1 Identify the faces, edges and vertices of given 3-D objects, including cubes, spheres, cones, cylinders, pyramids and prisms.
- 3SS6.2 Identify the shape of the faces of a given 3-D object.
- 3SS6.3 Identify 3-D objects as cubes, spheres, cones, cylinders, square pyramids, triangular pyramids, rectangular prisms, or triangular prisms.
- 3SS6.4 Determine the number of faces, curved surfaces, edges and vertices of a given 3-D object.
- 3SS6.5 Sort a given set of 3-D objects according to the number of faces, curved surfaces, edges or vertices.
- 3SS6.6 Construct a skeleton of a given 3-D object, and describe how the skeleton relates to the 3-D object. -
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3.465
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3.475
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3.485
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3.495
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3.505
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3.515
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3.SS.7
Sort regular and irregular polygons, including:
• triangles
• quadrilaterals
• pentagons
• hexagons
• octagons
according to the number of sides.
• Achievement Indicators:
- 3SS7.1 Identify given regular and irregular polygons that have different dimensions.
- 3SS7.2 Identify given regular and irregular polygons that have different orientations.
- 3SS7.3 Classify a given set of regular and irregular polygons according to the number of sides.
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3.SS.1