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4Grade 4 Standards
Top Mathematicians
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Patterns and Relations
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4.PR.1
Identify and describe patterns found in tables and charts, including a multiplication chart.
• Achievement Indicators:
- 4PR1.1 Describe the pattern found in a given table or chart.
- 4PR1.2 Determine the missing element(s) in a given table or chart.
- 4PR1.3 Identify the error(s) in a given table or chart.
- 4PR1.4 Identify and describe a variety of patterns in a multiplication chart. -
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4.4720
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4.7220
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4.7315
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4.7415
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4.755
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4.7620
-
4.7720
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4.7820
-
4.7915
-
4.8015
-
4.8115
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-
4.PR.2
Translate among different representations of a pattern, such as a table, a chart or concrete materials.
• Achievement Indicators:
- 4PR2.1 Create a concrete representation of a given pattern displayed in a table or chart.
- 4PR2.2 Create a table or chart from a given concrete representation of a pattern. -
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4.PR.3
Represent, describe and extend patterns and relationships, using charts and tables, to solve problems.
• Achievement Indicators:
- 4PR3.1 Translate the information in a given problem into a table or chart.
- 4PR3.2 Identify and extend the patterns in a table or chart to solve a given problem. -
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4.4720
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4.7220
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4.7315
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4.7415
-
4.755
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4.7620
-
4.7720
-
4.7820
-
-
4.PR.4
Identify and explain mathematical relationships, using charts and diagrams, to solve problems.
• Achievement Indicators:
- 4PR4.1 Identify a sorting rule for a given Venn diagram.
- 4PR4.2 Describe the relationship shown in a given Venn diagram when the circles intersect, when one circle is contained in the other, and when the circles are separate.
- 4PR4.3 Determine where new elements belong in a given Venn diagram.
- 4PR4.4 Complete a Carroll diagram by entering given data into correct squares to solve a given problem.
- 4PR4.5 Determine where new elements belong in a given Carroll diagram.
- 4PR4.6 Solve a given problem using a Carroll diagram.
- 4PR4.7 Solve a given problem by using a chart or diagram to identify mathematical relationships. -
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4.PR.5
Express a given problem as an equation in which a symbol is used to represent an unknown number.
• Achievement Indicators:
- 4PR5.1 Explain the purpose of the symbol in a given addition, subtraction, multiplication or division equation with one unknown.
- 4PR5.2 Express a given pictorial or concrete representation of an equation in symbolic form.
- 4PR5.3 Identify the unknown in a problem; represent the problem with an equation; and solve the problem concretely, pictorially or symbolically.
- 4PR5.4 Create a problem for a given equation with one unknown. -
4.PR.6
Solve one-step equations involving a symbol to represent an unknown number.
• Achievement Indicators:
- 4PR6.1 Solve a given one-step equation using manipulatives.
- 4PR6.2 Describe, orally, the meaning of a given one-step equation with one unknown.
- 4PR6.3 Solve a given equation when the unknown is on the left or right side of the equation.
- 4PR6.4 Solve a given one-step equation, using guess and test.
- 4PR6.5 Represent and solve a given addition or subtraction problem involving a 'part-part-whole' or comparison context, using a symbol to represent the unknown.
- 4PR6.6 Represent and solve a given multiplication or division problem involving equal grouping or partitioning (equal sharing), using a symbol to represent the unknown.
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4.PR.1
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Statistics & Probability
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4.SP.1
Demonstrate an understanding of many-to-one correspondence.
• Achievement Indicators:
- 4SP1.1 Compare graphs in which the same data has been displayed using one-to-one and many-to-one correspondences, and explain how they are the same and different.
- 4SP1.2 Explain why many-to-one correspondence is sometimes used rather than one-to-one correspondence.
- 4SP1.3 Find examples of graphs in which many-to-one correspondence is used in print and electronic media, such as newspapers, magazines and the Internet, and describe the correspondence used. -
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4.SP.2
Construct and interpret pictographs and bar graphs involving many-to-one correspondence to draw conclusions.
• Achievement Indicators:
- 4SP2.1 Identify an interval and correspondence for displaying a given set of data in a graph, and justify the choice.
- 4SP2.2 Create and label (with categories, title and legend) a pictograph to display a given set of data, using many-to-one correspondence, and justify the choice of correspondence used.
- 4SP2.3 Answer a given question using a given graph in which data is displayed using many-to-one correspondence.
- 4SP2.4 Create and label (with axes and title) a bar graph to display a given set of data, using many-to-one correspondence, and justify the choice of interval used. -
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4.9720
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4.985
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4.995
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4.SP.1
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Number
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4.N.1
Represent and describe whole numbers to 10 000, concretely, pictorially and symbolically.
• Achievement Indicators:
- 4N1.1 Read a given four-digit numeral without using the word ‘and’.
- 4N1.2 Write a given numeral, using proper spacing without commas.
- 4N1.3 Represent a given numeral using a place value chart or other models.
- 4N1.4 Explain the meaning of each digit in a given four-digit numeral, including numerals with all digits the same.
- 4N1.5 Express a given numeral in expanded notation.
- 4N1.6 Write the numeral represented by a given expanded notation.
- 4N1.7 Write a given numeral 0–10 000 in words. -
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4.215
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4.310
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4.410
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4.510
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4.N.10
Relate decimals to fractions and fractions to decimals (to hundredths).
• Achievement Indicators:
- 4N10.1 Express, orally and in written form, a given fraction with a denominator of 10 or 100 as a decimal.
- 4N10.2 Read decimals as fractions.
- 4N10.3 Express, orally and in written form, a given decimal in fraction form.
- 4N10.4 Express a given pictorial or concrete representation as a fraction or decimal.
- 4N10.5 Express, orally and in written form, the decimal equivalent for a given fraction. -
4.N.11
Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths).
• Achievement Indicators:
- 4N11.1 Predict sums and differences of decimals, using estimation strategies.
- 4N11.2 Refine personal strategies to increase their efficiency.
- 4N11.3 Solve problems, including money problems, which involve addition and subtraction of decimals, limited to hundredths.
- 4N11.4 Determine the approximate solution of a given problem not requiring an exact answer.
- 4N11.5 Estimate a sum or difference using compatible numbers.
- 4N11.6 Count back change for a given purchase. -
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4.6115
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4.6215
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4.6315
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4.6410
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4.6520
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4.6615
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4.6715
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4.6820
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4.6920
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4.7010
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4.N.2
Compare and order whole numbers to 10 000.
• Achievement Indicators:
- 4N2.1 Create and order three different four-digit numerals.
- 4N2.2 Identify the missing numbers in an ordered sequence or on a number line (vertical or horizontal).
- 4N2.3 Identify incorrectly placed numbers in an ordered sequence or on a number line (vertical or horizontal).
- 4N2.4 Order a given set of numbers in ascending or descending order, and explain the order by making references to place value. -
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4.N.3
Demonstrate an understanding of addition of whole numbers with answers to 10 000 and their corresponding subtractions (limited to 3and 4-digit numerals) by:
• using personal strategies for adding and subtracting
• estimating sums and differences
• solving problems involving addition and subtraction.
• Achievement Indicators:
- 4N3.1 Describe a situation in which an estimate rather than an exact answer is sufficient.
- 4N3.2 Estimate sums and differences, using different strategies.
- 4N3.3 Refine personal strategies to increase their efficiency.
- 4N3.4 Determine the sum of two numbers using a personal strategy
- 4N3.5 Solve problems that involve addition and subtraction of more than two numbers.
- 4N3.6 Determine the difference of two numbers using a personal strategy. -
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4.620
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4.715
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4.820
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4.920
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4.1020
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4.1120
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4.1220
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4.1320
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4.1420
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4.1515
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4.1620
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4.1720
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4.1820
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4.1920
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4.2020
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4.N.4
Explain and apply the properties of 0 and 1 for multiplication and the property of 1 for division.
• Achievement Indicators:
- 4N4.1 Determine the answer to a given question involving the multiplication of a number by 1, and explain the answer.
- 4N4.2 Determine the answer to a given question involving the multiplication of a number by 0, and explain the answer.
- 4N4.3 Determine the answer to a given question involving the division of a number by 1, and explain the answer. -
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4.2115
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4.2215
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4.2315
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4.2415
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4.N.5
Describe and apply mental mathematics strategies, such as:
• skip counting from a known fact
• using doubling or halving
• using doubling or halving and adding or subtracting one more group
• using patterns in the 9s facts
• using repeated doubling
to determine basic multiplication facts to 9 x 9 and related division facts.
• Achievement Indicators:
- 4N5.1 Provide examples for applying mental mathematics strategies:
• skip counting from a known fact
• doubling
• repeated doubling
• halving
• doubling or halving and adding or subtracting one more group
• use ten facts when multiplying by 9
• relating division to multiplication.
- 4N5.2 Demonstrate understanding and application of strategies for multiplication and related division facts to 9 x 9.
- 4N5.3 Demonstrate recall of multiplication and related division facts to 7 x 7. -
4.N.6
Demonstrate an understanding of multiplication (2or 3-digit by 1-digit) to solve problems by:
• using personal strategies for multiplication with and without concrete materials
• using arrays to represent multiplication
• connecting concrete representations to symbolic representations
• estimating products
• applying the distributive property.
• Achievement Indicators:
- 4N6.1 Use concrete materials, such as base ten blocks or their pictorial representations, to represent multiplication; and record the process symbolically.
- 4N6.2 Solve a given multiplication problem and record the process.
- 4N6.3 Model and solve a given multiplication problem, using an array, and record the process.
- 4N6.4 Model a given multiplication problem, using the distributive property.
- 4N6.5 Estimate a product, using a personal strategy.
- 4N6.6 Refine personal strategies to increase their efficiency.
- 4N6.7 Create and solve a multiplication problem that is limited to 2 or 3-digits by 1-digit. -
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4.2815
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4.2920
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4.3020
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4.3120
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4.3220
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4.3320
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4.3420
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4.N.7
Demonstrate an understanding of division (1-digit divisor and 2-digit dividend) to solve problems by:
• using personal strategies for dividing with and without concrete materials
• estimating quotients
• relating division to multiplication.
• Achievement Indicators:
(It is not intended that remainders be expressed as decimals or fractions.)
- 4N7.1 Solve a given division problem without a remainder, using models, and connect this process to the symbolic representation.
- 4N7.2 Solve a given division problem with a remainder, using models, and connect this process to the symbolic representation.
- 4N7.3 Solve a given division, using a personal strategy, and record the process.
- 4N7.4 Solve a given division problem by relating division to multiplication.
- 4N7.5 Create and solve a division problem involving a 1 or 2-digit dividend, and record the process.
- 4N7.6 Estimate a quotient, using a personal strategy.
- 4N7.7 Refine personal strategies to increase their efficiency -
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4.2565
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4.2620
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4.2720
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4.3515
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4.3620
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4.3720
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4.3820
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4.3920
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4.N.8
Demonstrate an understanding of fractions less than or equal to one by using concrete, pictorial and symbolic representations to:
• name and record fractions for the parts of a whole or a set
• compare and order fractions
• model and explain that for different wholes, two identical fractions may not represent the same quantity
• provide examples of where fractions are used.
• Achievement Indicators:
- 4N8.1 Name and record the shaded and non-shaded parts of a given whole.
- 4N8.2 Represent a given fraction pictorially by shading parts of a given whole.
- 4N8.3 Provide examples of when two identical fractions may not represent the same quantity.
- 4N8.4 Represent a given fraction, using concrete materials.
- 4N8.5 Name and record the shaded and non-shaded parts of a given set.
- 4N8.6 Identify a fraction from its concrete representation.
- 4N8.7 Represent a given fraction pictorially by shading parts of a given set.
- 4N8.8 Provide, from everyday contexts, an example of a fraction that represents part of a set and an example of a fraction that represents part of a whole.
- 4N8.9 Order a given set of fractions that have the same denominator, and explain the ordering.
- 4N8.10 Explain how denominators can be used to compare two given unit fractions with numerator 1.
- 4N8.11 Order a given set of fractions that have the same numerator, and explain the ordering.
- 4N8.12 Identify which of the benchmarks, 0, ½ or 1, is closer to a given fraction.
- 4N8.13 Name fractions between two given benchmarks on a number line (horizontal and vertical).
- 4N8.14 Order a given set of fractions by placing them on a number line (horizontal and vertical) with given benchmarks. -
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4.405
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4.4120
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4.4210
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4.4320
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4.4515
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4.4615
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4.4720
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4.4820
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4.4920
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4.5020
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4.515
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4.5215
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4.535
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4.N.9
Represent and describe decimals (tenths and hundredths), concretely, pictorially and symbolically.
• Achievement Indicators:
- 4N9.1 Write the decimal for a given concrete or pictorial representation of part of a set, part of a region or part of a unit of measure.
- 4N9.2 Represent a given decimal, using concrete materials or a pictorial representation.
- 4N9.3 Provide examples of everyday contexts in which tenths and hundredths are used.
- 4N9.4 Explain the meaning of each digit in a given decimal.
- 4N9.5 Represent a given decimal, using money values (dimes and pennies).
- 4N9.6 Record a given money value, using decimals.
- 4N9.7 Model, using manipulatives or pictures, that a given tenth can be expressed as a hundredth. -
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4.5410
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4.5510
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4.5610
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4.5715
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4.N.1
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Shape and Space
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4.SS.1
Read and record time, using digital and analog clocks, including 24-hour clocks.
• Achievement Indicators:
- 4SS1.1 State the number of hours in a day.
- 4SS1.2 Express time, orally and in writing, form a 12-hour analog clock.
- 4SS1.3 Explain the meaning of a.m. and p.m., and provide an example of an activity that occurs during the a.m., and another that occurs during the p.m.
- 4SS1.4 Express time, orally and in writing, as 'minutes to' or 'minutes after' the hour.
- 4SS1.5 Express time, orally and in writing, from a 12-hour digital clock.
- 4SS1.6 Solve problems related to time, including elapsed time.
- 4SS1.7 Express time, orally and in writing, from a 24-hour analog clock.
- 4SS1.8 Express time, orally and in writing, from a 24-hour digital clock. -
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4.8420
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4.8520
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4.865
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4.8715
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4.SS.2
Read and record calendar dates in a variety of formats.
• Achievement Indicators:
- 4SS2.1 Write dates in a variety of forms.
- 4SS2.2 Relate dates written in the format yyyy/mm/dd to dates on a calendar.
- 4SS2.3 Identify possible interpretations of a given date. -
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4.SS.3
Demonstrate an understanding of area of regular and irregular 2-D shapes by:
• recognizing that area is measured in square units
• selecting and justifying referents for the units cm² or m²
• estimating area, using referents for cm² or m²
• determining and recording area (cm² or m²)
• constructing different rectangles for a given area (cm² or m²) in order to demonstrate that many different rectangles may have the same area.
• Achievement Indicators:
- 4SS3.1 Describe area as the measure of surface recorded in square units.
- 4SS3.2 Identify and explain why the square is the most efficient unit for measuring area.
- 4SS3.3 Determine the area of an irregular 2-D shape, and explain the strategy.
- 4SS3.4 Provide a referent for a square centimetre, and explain the choice.
- 4SS3.5 Estimate the area of a given 2-D shape, using personal referents.
- 4SS3.6 Determine the area of a regular 2-D shape, and explain the strategy.
- 4SS3.7 Provide a referent for a square metre, and explain the choice.
- 4SS3.8 Determine which standard square unit is represented by a given referent.
- 4SS3.9 Construct a rectangle for a given area.
- 4SS3.10 Demonstrate that many rectangles are possible for a given area by drawing at least two different rectangles for the same given area. -
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4.8815
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4.8915
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4.9015
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4.9115
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4.SS.4
Describe and construct right rectangular and right triangular prisms.
• Achievement Indicators:
- 4SS4.1 Identify and name common attributes of right rectangular prisms from given sets of right rectangular prisms.
- 4SS4.2 Identify and name common attributes of right triangular prisms from given sets of right triangular prisms.
- 4SS4.3 Sort a given set of right rectangular and right triangular prisms, using the shape of the base.
- 4SS4.4 Identify examples of rectangular and triangular prisms found in the environment.
- 4SS4.5 Construct and describe a model of a right rectangular and a right triangular prism, using materials such as pattern blocks or modelling clay.
- 4SS4.6 Construct right triangular prisms from their nets.
- 4SS4.7 Construct right rectangular prisms from their nets. -
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4.925
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4.935
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4.945
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4.SS.5
Demonstrate an understanding of congruency, concretely and pictorially.
• Achievement Indicators:
- 4SS5.1 Determine if two given 2-D shapes congruent and explain the strategy used.
- 4SS5.2 Create a shape that is congruent to a given 2-D shape.
- 4SS5.3 Identify congruent 2-D shapes from a given set of shapes shown in different orientations.
- 4SS5.4 Identify corresponding vertices and sides of two given congruent shapes. -
4.SS.6
Demonstrate an understanding of line symmetry by:
• identifying symmetrical 2-D shapes
• creating symmetrical 2-D shapes
• drawing one or more lines of symmetry in a 2-D shape.
• Achievement Indicators:
- 4SS6.1 Identify lines of symmetry of a given set of 2-D shapes, and explain why each shape is symmetrical.
- 4SS6.2 Determine whether or not a given 2-D shape is symmetrical by using an image refl ector or by folding and superimposing.
- 4SS6.3 Complete a symmetrical 2-D shape, given half the shape and its line symmetry.
- 4SS6.4 Sort a given set of 2-D shapes as symmetrical and non-symmetrical.
- 4SS6.5 Provide examples of symmetrical shapes found in the environment, and identify the line(s) of symmetry.
- 4SS6.6 Sort a given set of 2-D shapes as those that have no lines of symmetry, one line of symmetry, or more than one line of symmetry.
- 4SS6.7 Identify the characteristics of given symmetrical and non-symmetrical 2-D shapes and explain the process.
- 4SS6.8 Create a symmetrical shape with and without manipulatives. -
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4.955
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4.SS.1