GRADES 4, 5, and 6 MATH BIG IDEAS

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1 Table 1: Strand A: NUMBER SENSE Introduce ratio and proportions. Introduce the exploration of factors of a number Introduce the relationship between numerators and denominators Introductory Introduce comparing, ordering and renaming fractions Recall Extend Extend place value to including comparing and ordering Extend decimals to hundredths including their comparison and ordering Extend comparing and ordering fractions Extend decimal place value to thousandths Extend place value to the millions Introduce positive and negative integers Introduce large numbers in a variety of forms (ex: standard, extended, 10 2 ) beyond the millions Introduce common factors Introduce prime and composite numbers Extend ratio to include comparing part to part and whole to whole, equivalent ratio and percent Extend the factors of decimals to make connections between the two Extend place value to billions 07/04/2005 1

2 Table 2: Strand B: OPERATION SENSE ctory Introduce addition and subtraction of decimals to hundredths including their estimation Introduce addition of simple fractions with common denominators Introduce multiplication of 2 and 3 digit numbers by a single digit number including their estimation Introduce division of 2 and 3 digit numbers by a single digit number including their estimation Introduce multiplication of 2 digit numerals by 10 and 100 mentally Introduce mathematical stories Introduce 4 digit number multiplied by 1 digit number Introduce 2 digit by 2 digit multiplication Introduce multiplying and dividing a whole by a decimal Introduce adding and subtracting different combinations of whole numbers and decim (including estimation of the answer) Introduce solving and creating problems u 4 operations involving decimals and combinations of both Introduce estimation of products and quoti using both whole numbers and decimals Introduce estimating and multiplying two decimals Introduce estimating and dividing two dec Recall multiplication facts in a 3-second response Recall division facts in a 3-second Recall adding and subtracting single fracti (9 x 9) Extend mental math strategies for addition and subtraction computations to 3 digit numbers. Extend addition and subtraction to decimal tenths and hundredths and whole numbers including five digits Extend multiplication to array, number line, (comparison, combinations) representations Extend division to arrays, number lines, (combinations, comparisons), treatment of remainders in various contexts Extend subtraction facts to 10s, 100s, 1000s. Extend mental multiplication to 2-digit numbers by 10 or 100 response (9 x 9). Extend story problems to new concepts Extend division to 2 digit 2 digit. Extend mental multiplication to include whole numbers by 0.1, 0.01, Extend addition and subtraction to decimal tenths, hundredths, and thousandths Extending multiplication to 2 digit x 2 digit Mastery of multiplication facts up to 9 x 9 Mastery of division facts Extend mental dividing to include 0.1, Extend solving problems using whole num and decimals Extend adding and subtracting fractions us models to include unlike denominators Extend estimating and calculating sums, differences, products, and quotients of who numbers and decimals using the most appr method Extend solving and creating problems 07/04/2005 2

3 Table 3: Strand C: PATTERNS and RELATIONS Introduce graphing measurement relationships Introduce the formula for the area of a rectangle Introductory Introduce the use of patterns to solve computational problems Introduce the effects of changes to results in a or b in a + b, a b, a x b, or a b Introduce the patterns in multiply by increasing powers of ten Recall Recall tabular and/or graphical form of multiplication facts Extend Extend open sentences to include multiplication and division Extend understanding of number representations to the millions using patterns Extend rearranging factors to make multiplication simpler Extend the exploration of the effect of change on a factor affects a product or quotient Extend the understanding of the multiplicative nature between numerators and denominators for equivalent fractions Introduce strategies to solve, explore, explain, and recognize patterns in many ways (concretely, pictorially, and symbolically) Introduce how the change in one element of the pattern effects a change in the output, ratio, and area of parallelograms, and triangles Introduce formula for the volume of a rectangular prism Introduce concept of equivalence in terms of ratios Introduce strategies to solve simple linear equations using open frames and then using variables Extend problem solving using patterns. Extend division by 0.1, 0.01, and using patterns Extend area to include how the change in one element of the pattern effects a change in the area of rectangles Extend ratios to include how the change in one element of the pattern effects the other to maintain equivalency 07/04/2005 3

4 Table 4: Strand D: MEASUREMENT Introduce graphing measurement relationships Introduce the development of a formula for perimeter and area of squares and rectangles Introduce estimating and measuring angles (in º) Introductory Introduce volume using standard units (centimeter cubes) Introduce the relationships between the area and perimeter of different shapes Introduce angle measure in terms of the amount of a turn Recall Recall volume and capacity Recall SI units Extend o Extend angle measure to include the use of non-standard units o Extend standard unit measure to include ºC o Extend length measurement to include problem solving in mm, cm, dm, m, and km o Extend area calculations to irregular shapes o Extend volume and capacity to solve problems o Extend angle measure (in º) to include right, acute, and obtuse angles Introduce area formula development for the parallelogram as well as this relationship to the area of a triangle Introduce drawing angles of a given size Introduce the metric tonne Introduce the relationship between volume and surface area of prisms Introduce the 24 hour clock Recall how to use formulas for various measurements (ex: length, area, capacity, volume,) Recall angle measure o Extend SI units to compare objects 07/04/2005 4

5 Table 5: Strand E: GEOMETRY Introduce cross-sections of cubes and prisms Introduce tessellations Introduce diagonal properties of squares and rectangles Introduce rotations of one-quarter, one-half, and three-quarter turns using a variety of turn centres Introduce perpendicular lines/segments; bisectors of angles and segments; perpendicular-bisectors of segments Introduce isometric drawings Introductory Introduce the drawing of various nets for rectangular prisms and cubes Introduce the angle, side, and reflective symmetry properties of all the quadrilaterals Introduce the classification of triangles by sides Introduce the vertices, edges, and face properties of prisms, pyramids, cones, and cylinders Recall Recall facts regarding acute and obtuse angles Extend Extend transformations to include making generalizations about the reflective symmetry property of quadrilaterals Extend acute and obtuse angle knowledge to include properties Recall area and perimeter of squares and rectangles Extend triangles to include acute and obtuse and right triangles Extend drawing nets to include all prisms and pyramids Extend transformations of quadrilaterals to include making generalizations about the properties of translations and reflections as well as applying the properties Extend drawing and interpreting isometric drawings Extend turns to include a variety of turn centres. Introduce similar images Introduce dilatation images of 2-D figures Introduce sums of angles in triangles and quadrilaterals Introduce orthographic drawings Introduce planes of symmetry of 3-D shapes o Extend from 2D to 3D drawings o Extend cross-sections to include cones, cylinders, and pyramids o Extend and explore the properties of quadrilaterals o Extend diagonal properties to include trapezoids, kites, parallelograms, rhombi o Extend transformations to include making generalizations about the rotational symmetry property of quadrilaterals and regular polygons 07/04/2005 5

6 Table 6: Strand F: DATA MANAGEMENT Introductory Introduce bar graphs, pictographs, ordered pairs, line graph, stem-and-leaf plots Introduce mean, maxima, minima, range and frequency Introduce data collection and organization methods Introduce double bar graphs, coordinate graphs (using the first quadrant) Introduce the effect of the mean on data Introduce relevant issues for data collection and appropriate sampling Introduce circle graphs and scatter plots Introduce the differences between the mean, median, and mode Recall Recall mean, median, and mode Extend Extend bar graphs, pictographs and stem-and-leaf plots to include construction and interpolation Extend mean definition to include using it to describe data Extend data collection to real world settings Extend work with mean, median, and mode to include effect of change in data on mean Extend graphs to include double bar graphs and coordinate graphs (first quadrant) Extend stem-and-leaf plots for data description Extend graphs to double bar graphs, circle graphs, scatter plots, stem-andleaf plots, and coordinates in four quadrants Extend the exploration of the differences between mean, median, and mode Extend coordinate graphs to include four quadrants 07/04/2005 6

7 Table 7: Strand G: PROBABILITY Introduce fractions and decimals to describe outcomes Introduce theoretical probabilities Introductory Introduce probability events including ones that rarely occur, ones with a 50% likelihood of occurring, and ones that almost always occur Introduce probability events from everyday life Recall Extend Extend probability experiments with an emphasis on predicting and recording results as fractions Extend predicting outcomes Extend work with probability experiments with an emphasis on predicting and recording results as decimals Introduce determining theoretical probabilities and events associated with a particular theoretical probability. Introduce the reliability of sampling results Introduce analyzing claims involving probability Extend theoretical probabilities to include identifying events associated with a theoretical probability Extend simulation experiments 07/04/2005 7