Maths Scope and Sequence. Gr. 5 - Data Handling. Mathematics Scope and Sequence Document Last Updated August SM

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1 Maths Scope and Sequence Mathematics Scope and Sequence Document Last Updated ugust SM Gr. 5 - Data Handling Overall expectation - Phase 4 Learners will collect, organize and display data for the purposes of valid interpretation and communication. They will be able to use the mode, median, mean and range to summarize a set of data. They will create and manipulate an electronic database for their own purposes, including setting up spreadsheets and using simple formulas to create graphs. Learners will understand that probability can be expressed on a scale (0 1 or 0% 100%) and that the probability of an event can be predicted theoretically. Statistics Probabilit y Conceptual understandings FROM IBS&S Phase 4 Data can be presented effectively for valid interpretation and communication. Range, mode, median and mean can be used to analyse statistical data. Probability can be represented on a scale between 0 1 or 0% 100%. The probability of an event can be predicted theoretically. FROM IBS&S Phase 4 - understand that different types of graphs have special purposes - understand that the mode, median, mean and range can summarize a set of data - collect, display and interpret data in circle graphs (pie charts) and line graphs - identify, describe and explain the range, mode, median and mean in a set of data - set up a spreadsheet using simple formulas to manipulate data and to create graphs - design a survey and systematically collect, record, organize and display the data in a bar graph, circle graph, line graph - identify, describe and explain the range, mode, median and mean in a set of data - create and manipulate an electronic database for their own purposes - understand that probability can be expressed in scale (0 1) or per cent (0% 100%) - understand the difference between experimental and theoretical probability. Specific xpectations = ssessed at this grade level = xplored at this grade level Design a survey and systematically collect, organize and record the data in displays: pictograph, bar graph, circle graph (pie chart), line graph, line plots Find, describe and explain outliers, clusters, mean, median, mode and range of data Calculate the mean for a set of data and use it to describe the shape of the data set across its range of values, using charts, tables and graphs Compare similarities and differences between two related sets of data, using a variety of strategies (tally charts, double bar graphs) by determining measures of central tendency (mean, median, mode, range, clusters, outliers) Use a numerical probability scale 0 to 1, or 0% to 100% Determine and represent all the possible outcomes in a simple probability experiment Represent, using a common fraction, the

2 - express probabilities using scale (0 1) or per cent (0% 100%). probability that an event will occur in simple games and probability experiments - determine the theoretical probability of an event and explain why it might differ from experimental probability.

3 Gr. 5 - Measurement Overall expectations - Phase 4 Learners will understand that a range of procedures exists to measure different attributes of objects and events, for example, the use of formulas for finding area, perimeter and volume. They will be able to decide on the level of accuracy required for measuring and using decimal and fraction notation when precise measurements are necessary. To demonstrate their understanding of angles as a measure of rotation, the learners will be able to measure and construct angles. Conceptual understandings ccuracy of measurements depends on the situation and the precision of the tool. Conversion of units and measurements allows us to make sense of the world we live in. range of procedures exists to measure different attributes of objects and events. - understand procedures for finding area, perimeter and volume - understand the relationships between area and perimeter, between area and volume, and between volume and capacity - understand unit conversions within measurement systems (metric or customary). - develop and describe formulas for finding perimeter, area and volume - use decimal and fraction notation in measurement, for example, 3.2 cm,1.47 kg, 11/2 miles - read and interpret scales on a range of measuring instruments - measure and construct angles in degrees using a protractor - carry out simple unit conversions within a system of measurement (metric or customary). - select and use appropriate units of measurement and tools to solve problems in real-life situations - determine and justify the level of accuracy required to solve reallife problems involving measurement - use decimal and fractional notation in measurement, for example, 3.2 cm, 1.47 kg, 11/2 miles - use timetables and schedules (12- hour and 24-hour clocks) in reallife situations - determine times worldwide. Specific xpectations = ssessed at this grade level = xplored at this grade level Identify and use appropriate metric units and tools to estimate, measure and solve problems involving weight, length, volume, time and temperature m, cm, mm, kg, g, l, ml, cl, C o Develop procedures for finding the volume of rectangular prism Describe and determine the perimeter and area of a polygon (square, rectangle and right triangle) and apply to practical situations Use formulas to determine the perimeter and areas of triangles, parallelograms Measure and/or determine the surface area and volume of objects that are shaped like rectangular prisms Find actual distance using a map scale Use decimal notation in measurement: 3.2 cm / 1.47 kg up to the 1000 th place Carry out unit conversions within the metric system of measurement Reasonably estimate, accurately measure and construct angles (using a protractor) up to 360 o Understand supplementary (add to 180 o ) and complimentary (add to 90 o ) Understand and apply the sum of angles in triangles, rectangles stimate, measure and represent time intervals to the nearest second Solve problems involving the relationship between a 12-hour clock and a 24-hour clock stimate and determine elapsed time, with and without using a timeline, given the durations of events expressed in minutes, hours, days, weeks, months or years Determine times world-wide

4 Gr. 5 - Shape and Space Overall expectations Phase 4 Learners will understand the properties of regular and irregular polyhedra. They will understand the properties of 2D shapes and understand that 2D representations of 3D objects can be used to visualize and solve problems in the real world, for example, through the use of drawing and modelling. Learners will develop their understanding of the use of scale (ratio) to enlarge and reduce shapes. They will apply the language and notation of bearing to describe direction and position. Conceptual understandings Manipulation of shape and space takes place for a particular purpose. Consolidating what we know of geometric concepts allows us to make sense of and interact with our world. Geometric tools and methods can be used to solve problems relating to shape and space. - understand the common language used to describe shapes - understand the properties of regular and irregular polyhedra - understand the properties of circles - understand how scale (ratios) is used to enlarge and reduce shapes - understand systems for describing position and direction - understand that 2D representations of 3D objects can be used to visualize and solve problems - understand that geometric ideas and relationships can be used to solve problems in other areas of mathematics and in real life. - analyse, describe, classify and visualize 2D (including circles, triangles and quadrilaterals) and 3D shapes, using geometric vocabulary - describe lines and angles using geometric vocabulary - identify and use scale (ratios) to enlarge and reduce shapes - identify and use the language and notation of bearing to describe direction and position - create and model how a 2D net converts into a 3D shape and vice versa - explore the use of geometric ideas and relationships to solve problems in other areas of mathematics. - use geometric vocabulary when describing shape and space in mathematical situations and beyond - use scale (ratios) to enlarge and reduce shapes - apply the language and notation of bearing to describe direction and position - use 2D representations of 3D objects to visualize and solve problems, for example using drawings or models. Specific xpectations = ssessed at this grade level = xplored at this grade level Use geometric vocabulary of 2-D and 3-D shapes: parallel, perpendicular, edge, corner, vertex, edge, face, degree, diagonal, interior and exterior angles, congruence Identify and explore congruent, non-congruent and similar figures, congruent sides & angles Discuss groups and subgroups of polygons using their characteristics (including interior angles, perpendicular or parallel sides, and congruence of sides): scalene, isosceles, equilateral, rightangles, rhombus, trapezium, parallelogram, kite, square, rectangle, pentagons, hexagons and other polygons Understand and use the vocabulary of types of angles: right, obtuse, acute, straight, reflex, supplementary and complimentary, interior and exterior Identifies possible range of degrees in obtuse and acute angles Use a pair of compasses accurately Understand and use the vocabulary of points, lines, rays and segments: parallel, perpendicular, intersecting Turn a 2-D net into a 3-D shape and vice versa and identify different nets for a closed cube Build 3-dimensional models using connecting cubes, given isometric sketches or different views of the structure Sketch, using a variety of tools, isometric perspectives and different views of 3-dimensional figures Read co-ordinates in four quadrants and plot in first quadrant Use the vocabulary of rotation to describe how a shape has rotated about on of its vertices: ¼ turn/90 o, ½ turn/180 o, ¾ turn, full turn/360 o Recognize the images of figures resulting from: slide, flip or rotation

5 Gr. 5 - Pattern and Function Overall expectations - Phase 4 Learners will understand that patterns can be represented, analysed and generalized using algebraic expressions, equations or functions. They will use words, tables, graphs and, where possible, symbolic rules to analyse and represent patterns. They will develop an understanding of exponential notation as a way to express repeated products, and of the inverse relationship that exists between exponents and roots. The students will continue to use their understanding of pattern and function to represent and make sense of real-life situations and to solve problems involving the four operations. Conceptual understandings Patterns can often be generalized using algebraic expressions, equations or functions. xponential notation is a powerful way to express repeated products of the same number. - understand that patterns can be generalized by a rule - understand exponents as repeated multiplication - understand the inverse relationship between exponents and roots - understand that patterns can be represented, analysed and generalized using tables, graphs, words, and, when possible, symbolic rules. - represent the rule of a pattern by using a function - analyse pattern and function using words, tables and graphs, and, when possible, symbolic rules. - select appropriate methods to analyse patterns and identify rules - use functions to solve problems. Specific xpectations = ssessed at this grade level = xplored at this grade level Understand and use the relationship between multiplication and addition. nalyze and determine the rules for extending symbolic, arithmetic and geometric patterns Determine a term, given its term number, by extending growing and shrinking patterns (For the pattern: 5000, 4750, 4500, 4250, 4000, 3750,, find the 15 th term. xplain your reasoning) Replace variables with given values and evaluate/ simplify Determine and algebraically express the function of a two-column table, given the input and output data Graph and analyze/ explain a constant rate of change over time Graph and analyze/ explain a varied rate of change over time Calculate using exponents

6 Gr. 5 - Number Overall expectations - Phase 4 Learners will understand that the base 10 place value system extends infinitely in two directions and will be able to model, compare, read, write and order numbers to millions or beyond, as well as model integers. They will develop an understanding of ratios. They will understand that fractions, decimals and percentages are ways of representing whole-part relationships and will work towards modelling, comparing, reading, writing, ordering and converting fractions, decimals and percentages. They will use mental and written strategies to solve problems involving whole numbers, fractions and decimals in real-life situations, using a range of strategies to evaluate reasonableness of answers. Conceptual understandings The base 10 place value system extends infinitely in two directions. Fractions, decimal fractions and percentages are ways of representing whole-part relationships. For fractional and decimal computation, the ideas developed for whole-number computation can apply. Ratios are a comparison of two numbers or quantities. - model numbers to millions or beyond using the base 10 place value system - model ratios - model integers in appropriate contexts - model exponents and square roots - model improper fractions and mixed numbers - simplify fractions using manipulatives - model decimal fractions to thousandths or beyond - model percentages - understand the relationship between fractions, decimals and percentages - model addition, subtraction, multiplication and division of fractions - model addition, subtraction, multiplication and division of decimals. - read, write, compare and order whole numbers up to millions or beyond - read and write ratios - read and write integers in appropriate contexts - read and write exponents and square roots - convert improper fractions to mixed numbers and vice versa - simplify fractions in mental and written form - read, write, compare and order decimal fractions to thousandths or beyond - read, write, compare and order percentages - convert between fractions, decimals and percentages. Specific xpectations = ssessed at this grade level = xplored at this grade level Read, write, compare, order whole numbers & decimal numbers to 9-digit whole numbers & thousandths xpress standard, expanded and written forms of whole numbers to 9-digits Demonstrate an understanding of place value in whole numbers and decimals to thousandths Round whole numbers to the appropriate place using the approximation sign from decimal to whole numbers. Select and use a variety of strategies (rounding, regrouping ) to estimate the results of computation and to judge the reasonableness of the answer Identify patterns in and differences between Roman and Hindu-rabic counting systems utomatically recall & use basic number facts, multiplying & dividing by power of 10, identifying pattern dd and subtract whole numbers and add and subtract decimal numbers to thousandths pply multiplication facts to 12 x 12 and related division facts Create and solve multiplication: 3 digit by 2 digit using an efficient algorithm Create and solve multiplication problems: 4-digit by 2- and 3-digit numbers Multiply decimal numbers by 10, 100 & 1000 and divide decimal numbers by 10, 100 & 1000 mentally Create and solve division problems up to 3 digit by 2 digit with/without remainders using short and long division using appropriate notation for remainders (eg fractional remainders) pply the order of operations (excluding exponents) Find all factors and factor pairs of whole numbers to 144 Identify the greatest common factor and least common multiple of a set of numbers

7 - use whole numbers up to millions or beyond in real-life situations - use ratios in real-life situations - use integers in real-life situations - convert improper fractions to mixed numbers and vice versa in real-life situations - simplify fractions in computation answers - use fractions, decimals and percentages interchangeably in real - life situations - select and use an appropriate sequence of operations to solve word problems - select an efficient method for solving a problem: mental estimation, mental computation, written algorithms, by using a calculator - use strategies to evaluate the reasonableness of answers - use mental and written strategies for adding, subtracting, multiplying and dividing fractions and decimals in real-life situations - estimate and make approximations in real-life situations involving fractions, decimals and percentages. Square numbers through 12 x 12 Identify and describe prime and composite numbers and explain the relationship between them Carry out factorization of 2-digit numbers to find prime factors. Find common multiples and factors of a set of numbers Given a dividend with decimals to the hundredths and a single-digit divisor, find the quotient Use mathematical vocabulary of fractions: proper, improper, mixed numbers, simplest form, numerator, denominator dd and subtract fractions and mixed numbers with like and unlike denominators Simplify fractions Find equivalent fractions Compare & order fractions, mixed numbers, decimals & percents, using number line when appropriate Convert fractions to decimals and to percentages and vice versa Identify and determine common equivalent fractions, mixed numbers, decimals and percents Describe multiplicative relationships between quantities by using simple fractions (if you have 4 plums and I have 6 plums, I can say that I have 1 ½ or 1.5 times as many plums as you have) Find fractions of a whole number eg. What is 2/3 of 6? dd and subtract decimals up to the thousandths place Round decimals to the nearest whole number, tenth or hundredth Find the percent of a whole or quantity, including finding a discount Find the ratio of two or three given quantities Find one quantity given the other quantity and their ratio Understand the concept of integers (negative numbers) Represent, solve and create up to 3-step word problems using all the four operations with whole numbers Select and defend the most appropriate and efficient method of solving a problem: (work backwards, draw a picture, make a table, make an organized list, act out the problem or use objects, guess and check, use or look for a pattern, use logical reasoning,

8 make it simpler, brainstorm) Use a calculator to carry out or check computation in problem solving situations

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