Math Games

5.SS.1

Design and construct different rectangles given either perimeter or area or both (whole numbers), and draw conclusions. • Construct or draw two or more rectangles for a given perimeter in a problem-solving context. • Construct or draw two or more rectangles for a given area in a problem-solving context. • Illustrate that for any perimeter, the square or shape closest to a square will result in the • greatest area. • Illustrate that for any perimeter, the rectangle with the smallest possible width will result in the least area. • Provide a real-life context for when it is important to consider the relationship between area and perimeter

5.SS.2

Demonstrate an understanding of measuring length (mm) by • selecting and justifying referents for the unit mm • modelling and describing the relationship between mm and cm units, and between mm and m units • Provide a referent for one millimetre and explain the choice. • Provide a referent for one centimetre and explain the choice. • Provide a referent for one metre and explain the choice. • Show that 10 millimetres is equivalent to 1 centimetre using concrete materials (e.g., ruler). • Show that 1000 millimetres is equivalent to 1 metre using concrete materials (e.g., metre stick). • Provide examples of when millimetres are used as the unit of measure.

5.SS.3

Demonstrate an understanding of volume by • selecting and justifying referents for cm³ or m³ units • estimating volume by using referents for cm³ or m³ • measuring and recording volume (cm³ or m³) • constructing rectangular prisms for a given volume • Identify the cube as the most efficient unit for measuring volume and explain why. • Provide a referent for a cubic centimetre and explain the choice. • Provide a referent for a cubic metre and explain the choice. • Determine which standard cubic unit is represented by a given referent. • Estimate the volume of a 3-D object using personal referents. • Determine the volume of a 3-D object using manipulatives and explain the strategy. • Construct a rectangular prism for a given volume. • Explain that many rectangular prisms are possible for a given volume by constructing more than one rectangular prism for the same volume.

5.SS.4

Demonstrate an understanding of capacity by • describing the relationship between mL and L • selecting and justifying referents for mL or L units • estimating capacity by using referents for mL or L • measuring and recording capacity (mL or L) • Demonstrate that 1000 millilitres is equivalent to 1 litre by filling a 1-litre container using a combination of smaller containers. • Provide a referent for a litre and explain the choice. • Provide a referent for a millilitre and explain the choice. • Determine which capacity unit (mL or L) is represented by a given referent. • Estimate the capacity of a container using personal referents. • Determine the capacity of a container using materials that take the shape of the inside of the container (e.g., a liquid, rice, sand, beads), and explain the strategy.

5.SS.5

Describe and provide examples of edges and faces of 3-D objects, and sides of 2-D shapes, that are • parallel • intersecting • perpendicular • vertical • horizontal • Identify parallel, intersecting, perpendicular, vertical, and horizontal edges and faces on 3-D objects. • Identify parallel, intersecting, perpendicular, vertical, and horizontal sides on 2-D shapes. • Provide examples from the environment that show parallel, intersecting, perpendicular, vertical, and horizontal line segments. • Find examples of edges, faces, and sides that are parallel, intersecting, perpendicular, vertical, and horizontal in print and electronic media, such as newspapers, magazines, and the Internet. • Draw 2-D shapes or 3-D objects that have edges, faces, and sides that are parallel, intersecting, perpendicular, vertical, or horizontal. • Describe the faces and edges of a 3-D object using terms such as parallel, intersecting, perpendicular, vertical, or horizontal. • Describe the sides of a 2-D shape using terms such as parallel, intersecting, perpendicular, vertical, or horizontal.

5.SS.6

Identify and sort quadrilaterals, including • rectangles • squares • trapezoids • parallelograms • rhombuses according to their attributes. • Identify and describe the characteristics of a pre-sorted set of quadrilaterals. • Sort a set of quadrilaterals and explain the sorting rule. • Sort a set of quadrilaterals according to the lengths of the sides. • Sort a set of quadrilaterals according to whether or not opposite sides are parallel.

5.SS.7

Perform a single transformation (translation, rotation, or reflection) of a 2-D shape, and draw and describe the image. • Translate a 2-D shape horizontally, vertically, or diagonally, and describe the position and orientation of the image. • Rotate a 2-D shape about a point, and describe the position and orientation of the image. • Reflect a 2-D shape in a line of reflection, and describe the position and orientation of the image. • Perform a transformation of a 2-D shape by following instructions. • Draw a 2-D shape, translate the shape, and record the translation by describing the direction and magnitude of the movement (e.g., the circle moved 3 cm to the left). • Draw a 2-D shape, rotate the shape, and describe the direction of the turn (clockwise or counter-clockwise), the fraction of the turn, and point of rotation. • Draw a 2-D shape, reflect the shape, and identify the line of reflection and the distance of the image from the line of reflection. • Predict the result of a single transformation of a 2-D shape and verify the prediction.

5.SS.8

Identify a single transformation (translation, rotation, or reflection) of 2-D shapes. • Provide an example of a translation, a rotation, and a reflection. • Identify a single transformation as a translation, rotation, or reflection. • Describe a rotation by the direction of the turn (clockwise or counter-clockwise).

5.PR.1

Determine the pattern rule to make predictions about subsequent elements. • Extend a pattern with or without concrete materials, and explain how each element differs from the proceeding one. • Describe, orally or in writing, a pattern using mathematical language, such as one more, one less, five more. • Write a mathematical expression to represent a pattern, such as r + 1, r – 1, r + 5. • Describe the relationship in a table or chart using a mathematical expression. • Determine and explain why a number is or is not the next element in a pattern. • Predict subsequent elements in a pattern. • Solve a problem by using a pattern rule to determine subsequent elements. • Represent a pattern visually to verify predictions.

5.PR.2

Solve problems involving single-variable (expressed as symbols or letters), one-step equations with whole-number coefficients, and whole-number solutions. • Express a problem in context as an equation where the unknown is represented by a letter variable. • Solve a single-variable equation with the unknown in any of the terms (e.g., n + 2 = 5, 4 + a = 7, 6 = r – 2, 10 = 2c). • Create a problem in context for an equation.

5.N.1

Represent and describe whole numbers to 1 000 000. • Write a numeral using proper spacing without commas (e.g., 934 567 and not 934,567). • Describe the pattern of adjacent place positions moving from right to left. • Describe the meaning of each digit in a numeral. • Provide examples of large numbers used in print or electronic media. • Express a given numeral in expanded notation (e.g., 45 321 = [4 × 10 000] + [5 × 1000] + [3 × 100] + [2 × 10] + [1 × 1] or 40 000 + 5000 + 300 + 20 + 1). • Write the numeral represented in expanded notation.

5.N.10

Compare and order decimals (tenths, hundredths, thousandths) by using • benchmarks • place value • equivalent decimals • Order a set of decimals by placing them on a number line (vertical or horizontal) that contains benchmarks, 0.0, 0.5, 1.0. • Order a set of decimals including only tenths using place value. • Order a set of decimals including only hundredths using place value. • Order a set of decimals including only thousandths using place value. • Explain what is the same and what is different about 0.2, 0.20, and 0.200. • Order a set of decimals including tenths, hundredths, and thousandths using equivalent decimals.

5.N.11

Demonstrate an understanding of addition and subtraction of decimals (to thousandths), concretely, pictorially, and symbolically, by • using personal strategies • using the standard algorithms • using estimation • solving problems • Estimate a sum or difference using front-end estimation (e.g., for 6.3 + 0.25 + 306.158, think 6 + 306, so the sum is greater than 312) and place the decimal in the appropriate place. • Correct errors of decimal point placements in sums and differences without using paper and pencil. • Explain why keeping track of place value positions is important when adding and subtracting decimals. • Predict sums and differences of decimals using estimation strategies. • Solve a problem that involves addition and subtraction of decimals, to thousandths. • Model and explain the relationship that exists between an algorithm, place value, and number properties. • Determine the sum and difference using the standard algorithms of vertical addition and subtraction. (Numbers are arranged vertically with corresponding place value digits aligned.) • Refine personal strategies, such as mental math, to increase efficiency when appropriate (e.g., 3.36 + 9.65 think, 0.35 + 0.65 = 1.00, therefore, 0.36 + 0.65 = 1.01 and 3 + 9 = 12 for a total of 13.01)

5.N.2

Apply estimation strategies, including • front-end rounding • compensation • compatible numbers in problem-solving contexts. • Provide a context for when estimation is used to - make predictions - check reasonableness of an answer - determine approximate answers • Describe contexts in which overestimating is important. • Determine the approximate solution to a problem not requiring an exact answer. • Estimate a sum or product using compatible numbers. • Estimate the solution to a problem using compensation, and explain the reason for compensation. • Select and use an estimation strategy to solve a problem. • Apply front-end rounding to estimate - sums (e.g., 253 + 615 is more than 200 + 600 = 800) - differences (e.g., 974 – 250 is close to 900 – 200 = 700) - products (e.g., the product of 23 × 24 is greater than 20 × 20 or 400 and less than 25 × 25 or 625) - quotients (e.g., the quotient of 831 ÷ 4 is greater than 800 ÷ 4 or 200)

5.N.3

Apply mental math strategies to determine multiplication and related division facts to 81 (9 x 9). • Describe the mental mathematics strategy used to determine a basic fact, such as - skip-count up by one or two groups from a known fact (e.g., if 5 × 7 = 35, then 6 × 7 is equal to 35 + 7 and 7 × 7 is equal to 35 + 7 + 7) - skip-count down by one or two groups from a known fact (e.g., if 8 × 8 = 64, then 7 × 8 is equal to 64 – 8 and 6 × 8 is equal to 64 – 8 – 8) - halving/doubling (e.g., for 8 × 3 think 4 × 6 = 24) - use patterns when multiplying by 9 (e.g., for 9 × 6, think 10 × 6 = 60, then 60 – 6 = 54; for 7 × 9, think 7 × 10 = 70, and 70 – 7 = 63) - repeated doubling (e.g., if 2 × 6 is equal to 12, then 4 × 6 is equal to 24, and 8 × 6 is equal to 48) - repeated halving (e.g., for 60 ÷ 4, think 60 ÷ 2 = 30 and 30 ÷ 2 = 15) - relating multiplication to division facts (e.g., for 7 x 8, think 56 ÷ 7 = ) - use multiplication facts that are squares (1 x 1, 2 x 2, up to 9 x 9) • Refine personal strategies to increase efficiency (e.g., for 7 x 6, use known square 6 x 6 + 6 instead of repeated addition 6 + 6 + 6 + 6 + 6 + 6 + 6).

5.N.4

Apply mental mathematics strategies for multiplication, such as • annexing then adding zeros • halving and doubling • using the distributive property • Determine the products when one factor is a multiple of 10, 100, or 1000 by annexing zero or adding zeros (e.g., for 3 × 200 think 3 × 2 and then add two zeros). • Apply halving and doubling when determining a product (e.g., 32 × 5 is the same as 16 × 10). • Apply the distributive property to determine a product involving multiplying factors that are close to multiples of 10 [e.g., 98 × 7 = (100 × 7) – (2 × 7)].

5.N.5

Demonstrate an understanding of multiplication (1- and 2-digit multipliers and up to 4-digit multiplicands), concretely, pictorially, and symbolically, by • using personal strategies • using the standard algorithm • estimating products to solve problems. • Illustrate partial products in expanded notation for both factors [e.g., for 36 × 42, determine the partial products for (30 + 6) × (40 + 2)]. • Represent both 2-digit factors in expanded notation to illustrate the distributive property [e.g., to determine the partial products of 36 × 42, (30 + 6) × (40 + 2) = 30 × 40 + 30 × 2 + 6 × 40 + 6 × 2 = 1200 + 60 + 240 + 12 = 1512]. • Model the steps for multiplying 2-digit factors using an array and base-10 blocks, and record the process symbolically. • Describe a solution procedure for determining the product of two 2-digit factors using a pictorial representation, such as an area model. • Model and explain the relationship that exists between an algorithm, place value, and number properties. • Determine products using the standard algorithm of vertical multiplication. (Numbers arranged vertically and multiplied using single digits which are added to form a final product.) • Solve a multiplication problem in context using personal strategies, and record the process. • Refine personal strategies such as mental math strategies to increase efficiency when appropriate [e.g., 16 x 25 think 4 x (4 x 25) = 400].

5.N.6

Demonstrate an understanding of division (1- and 2-digit divisors and up to 4-digit dividends), concretely, pictorially, and symbolically, and interpret remainders by • using personal strategies • using the standard algorithm • estimating quotients to solve problems. • Model the division process as equal sharing using base-10 blocks, and record it symbolically. • Explain that the interpretation of a remainder depends on the context: - ignore the remainder (e.g., making teams of 4 from 22 people) - round up the quotient (e.g., the number of five passenger cars required to transport 13 people) - express remainders as fractions (e.g., five apples shared by two people) - express remainders as decimals (e.g., measurement or money) • Model and explain the relationship that exists between algorithm, place value, and number properties. • Determine quotients using the standard algorithm of long division. (The multiples of the divisor are subtracted from the dividend.) • Solve a division problem in context using personal strategies, and record the process. • Refine personal strategies such as mental math strategies to increase efficiency when appropriate (e.g., 860 ÷ 2 think 86 ÷ 2 = 43 then 860 ÷ 2 is 430).

5.N.7

Demonstrate an understanding of fractions by using concrete and pictorial representations to • create sets of equivalent fractions • compare fractions with like and unlike denominators • Create a set of equivalent fractions and explain why there are many equivalent fractions for any fraction using concrete materials. • Model and explain that equivalent fractions represent the same quantity. • Determine if two fractions are equivalent using concrete materials or pictorial representations. • Formulate and verify a rule for developing a set of equivalent fractions. • Identify equivalent fractions for a fraction. • Compare two fractions with unlike denominators by creating equivalent fractions. • Position a set of fractions with like and unlike denominators on a number line (vertical or horizontal), and explain strategies used to determine the order

5.N.8

Describe and represent decimals (tenths, hundredths, thousandths) concretely, pictorially, and symbolically. • Write the decimal for a concrete or pictorial representation of part of a set, part of a region, or part of a unit of measure. • Represent a decimal using concrete materials or a pictorial representation. • Represent an equivalent tenth, hundredth, or thousandth for a decimal, using a grid. • Express a tenth as an equivalent hundredth and thousandth. • Express a hundredth as an equivalent thousandth. • Describe the value of each digit in a decimal.

5.N.9

Relate decimals to fractions (tenths, hundredths, thousandths). • Write a decimal in fractional form. • Write a fraction with a denominator of 10, 100, or 1000 as a decimal. • Express a pictorial or concrete representation as a fraction or decimal (e.g., 250 shaded squares on a thousandth grid can be expressed as 0.250 or 250 / 1000 ).

5.SP.1

Differentiate between first-hand and second-hand data. • Explain the difference between first-hand and second-hand data. • Formulate a question that can best be answered using first-hand data and explain why. • Formulate a question that can best be answered using second-hand data and explain why. • Find examples of second-hand data in print and electronic media, such as newspapers, magazines, and the Internet.

5.SP.2

Construct and interpret double bar graphs to draw conclusions. • Determine the attributes (title, axes, intervals, and legend) of double bar graphs by comparing a set of double bar graphs. • Represent a set of data by creating a double bar graph, label the title and axes, and create a legend with or without the use of technology. • Draw conclusions from a double bar graph to answer questions. • Provide examples of double bar graphs used in a variety of print and electronic media, such as newspapers, magazines, and the Internet. • Solve a problem by constructing and interpreting a double bar graph.

5.SP.3

Describe the likelihood of a single outcome occurring, using words such as • impossible • possible • certain • Provide examples of events that are impossible, possible, or certain from personal contexts. • Classify the likelihood of a single outcome occurring in a probability experiment as impossible, possible, or certain. • Design and conduct a probability experiment in which the likelihood of a single outcome occurring is impossible, possible, or certain. • Conduct a probability experiment a number of times, record the outcomes, and explain the results.

5.SP.4

Compare the likelihood of two possible outcomes occurring, using words such as • less likely • equally likely • more likely • Identify outcomes from a probability experiment which are less likely, equally likely, or more likely to occur than other outcomes. • Design and conduct a probability experiment in which one outcome is less likely to occur than the other outcome. • Design and conduct a probability experiment in which one outcome is equally as likely to occur as the other outcome. • Design and conduct a probability experiment in which one outcome is more likely to occur than the other outcome.