2.1.1: read, represent, compare, and order whole numbers to 100 000, decimal numbers to hundredths, proper and improper fractions, and mixed numbers;
2.2.1: represent, compare, and order whole numbers and decimal numbers from 0.01 to 100 000, using a variety of tools (e.g., number lines with appropriate increments, base ten materials for decimals);
2.2.2: demonstrate an understanding of place value in whole numbers and decimal numbers from 0.01 to 100 000, using a variety of tools and strategies (e.g., use numbers to represent 23 011 as 20 000 + 3000 + 0 + 10 + 1; use base ten materials to represent the relationship between 1, 0.1, and 0.01) (Sample problem: How many thousands cubes would be needed to make a base ten block for 100 000?);
2.2.5: represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, number lines) and using standard fractional notation;
2.2.6: demonstrate and explain the concept of equivalent fractions, using concrete materials (e.g., use fraction strips to show that 3/4 is equal to 9/12);
2.2.7: demonstrate and explain equivalent representations of a decimal number, using concrete materials and drawings (e.g., use base ten materials to show that three tenths [0.3] is equal to thirty hundredths [0.30]);
2.3.1: count forward by hundredths from any decimal number expressed to two decimal places, using concrete materials and number lines (e.g., use base ten materials to represent 2.96 and count forward by hundredths: 2.97, 2.98, 2.99, 3.00, 3.01...; "Two and ninety-six hundredths, two and ninety-seven hundredths, two and ninety-eight hundredths, two and ninety-nine hundredths, three, three and one hundredth...") (Sample problem: What connections can you make between counting by hundredths and measuring lengths in centimetres and metres?).
2.4.1: solve problems involving the addition, subtraction, and multiplication of whole numbers, using a variety of mental strategies (e.g., use the commutative property: 5 x 18 x 2 = 5 x 2 x 18, which gives 10 x 18 = 180);
2.4.2: add and subtract decimal numbers to hundredths, including money amounts, using concrete materials, estimation, and algorithms (e.g., use 10 x 10 grids to add 2.45 and 3.25);
2.4.5: multiply decimal numbers by 10, 100, 1000, and 10 000, and divide decimal numbers by 10 and 100, using mental strategies (e.g., use a calculator to look for patterns and generalize to develop a rule);
2.4.6: use estimation when solving problems involving the addition, subtraction,multiplication, and division of whole numbers, to help judge the reasonableness of a solution (Sample problem: Mori used a calculator to add 7.45 and 2.39. The calculator display showed 31.35. Explain why this result is not reasonable, and suggest where you think Mori made his mistake.).
2.5.1: describe multiplicative relationships between quantities by using simple fractions and decimals (e.g.,"If you have 4 plums and I have 6 plums, I can say that I have 1 1/2 or 1.5 times as many plums as you have.");
3.1.1: estimate, measure, and record perimeter, area, temperature change, and elapsed time, using a variety of strategies;
3.2.1: estimate, measure (i.e., using an analogue clock), and represent time intervals to the nearest second;
3.2.2: estimate and determine elapsed time, with and without using a time line, given the durations of events expressed in minutes, hours, days,weeks, months, or years (Sample problem:You are travelling from Toronto to Montreal by train. If the train departs Toronto at 11:30 a.m. and arrives in Montreal at 4:56 p.m., how long will you be on the train?);
3.2.4: estimate and measure the perimeter and area of regular and irregular polygons, using a variety of tools (e.g., grid paper, geoboard, dynamic geometry software) and strategies.
3.3.1: select and justify the most appropriate standard unit (i.e., millimetre, centimetre, decimetre, metre, kilometre) to measure length, height, width, and distance, and to measure the perimeter of various polygons;
3.3.5: determine, through investigation using a variety of tools (e.g., concrete materials, dynamic geometry software, grid paper) and strategies (e.g., building arrays), the relationships between the length and width of a rectangle and its area and perimeter, and generalize to develop the formulas [i.e., Area = length x width; Perimeter = (2 x length) + (2 x width)];
3.3.6: solve problems requiring the estimation and calculation of perimeters and areas of rectangles (Sample problem:You are helping to fold towels, and you want them to stack nicely. By folding across the length and/or the width, you fold each towel a total of three times.You want the shape of each folded towel to be as close to a square as possible. Does it matter how you fold the towels?);
3.3.8: determine, through investigation using stacked congruent rectangular layers of concrete materials, the relationship between the height, the area of the base, and the volume of a rectangular prism, and generalize to develop the formula (i.e., Volume = area of base x height) (Sample problem: Create a variety of rectangular prisms using connecting cubes. For each rectangular prism, record the area of the base, the height, and the volume on a chart. Identify relationships.);
4.1.3: identify and describe the location of an object, using the cardinal directions, and translate two-dimensional shapes.
4.4.1: locate an object using the cardinal directions (i.e., north, south, east,west) and a coordinate system (e.g.,"If I walk 5 steps north and 3 steps east, I will arrive at the apple tree.");
4.4.2: compare grid systems commonly used on maps (i.e., the use of numbers and letters to identify an area; the use of a coordinate system based on the cardinal directions to describe a specific location);
4.4.3: identify, perform, and describe translations, using a variety of tools (e.g., geoboard, dot paper, computer program);
4.4.4: create and analyse designs by translating and/or reflecting a shape, or shapes, using a variety of tools (e.g., geoboard, grid paper, computer program) (Sample problem: Identify translations and/or reflections that map congruent shapes onto each other in a given design.).
5.1.1: determine, through investigation using a table of values, relationships in growing and shrinking patterns, and investigate repeating patterns involving translations;
5.2.1: create, identify, and extend numeric and geometric patterns, using a variety of tools (e.g., concrete materials, paper and pencil, calculators, spreadsheets);
5.2.2: build a model to represent a number pattern presented in a table of values that shows the term number and the term;
5.2.3: make a table of values for a pattern that is generated by adding or subtracting a number (i.e., a constant) to get the next term, or by multiplying or dividing by a constant to get the next term, given either the sequence (e.g., 12, 17, 22, 27, 32, ...) or the pattern rule in words (e.g., start with 12 and add 5 to each term to get the next term);
5.2.4: make predictions related to growing and shrinking geometric and numeric patterns (Sample problem: Create growing L's using tiles. The first L has 3 tiles, the second L has 5 tiles, the third L has 7 tiles, and so on. Predict the number of tiles you would need to build the 10th L in the pattern.);
5.2.5: extend and create repeating patterns that result from translations, through investigation using a variety of tools (e.g., pattern blocks, dynamic geometry software, dot paper).
6.1.1: collect and organize discrete or continuous primary data and secondary data and display the data using charts and graphs, including broken-line graphs;
6.1.2: read, describe, and interpret primary data and secondary data presented in charts and graphs, including broken-line graphs;
6.1.3: represent as a fraction the probability that a specific outcome will occur in a simple probability experiment, using systematic lists and area models.
6.2.2: collect data by conducting a survey or an experiment (e.g., gather and record air temperature over a two-week period) to do with themselves, their environment, issues in their school or community, or content from another subject, and record observations or measurements;
6.2.3: collect and organize discrete or continuous primary data and secondary data and display the data in charts, tables, and graphs (including broken-line graphs) that have appropriate titles, labels (e.g., appropriate units marked on the axes), and scales that suit the range and distribution of the data (e.g., to represent precipitation amounts ranging from 0 mm to 50 mm over the school year, use a scale of 5 mm for each unit on the vertical axis and show months on the horizontal axis), using a variety of tools (e.g., graph paper, simple spreadsheets, dynamic statistical software);
6.2.5: describe, through investigation, how a set of data is collected (e.g., by survey, measurement, observation) and explain whether the collection method is appropriate.
6.3.1: read, interpret, and draw conclusions from primary data (e.g., survey results, measurements, observations) and from secondary data (e.g., precipitation or temperature data in the newspaper, data from the Internet about heights of buildings and other structures), presented in charts, tables, and graphs (including broken-line graphs);
6.3.2: calculate the mean for a small set of data and use it to describe the shape of the data set across its range of values, using charts, tables, and graphs (e.g.,"The data values fall mainly into two groups on both sides of the mean."; "The set of data is not spread out evenly around the mean.");
6.3.3: compare similarities and differences between two related sets of data, using a variety of strategies (e.g., by representing the data using tally charts, stem-and-leaf plots, double bar graphs, or broken-line graphs; by determining measures of central tendency [i.e., mean, median, and mode]; by describing the shape of a data set across its range of values).
6.4.2: represent, using a common fraction, the probability that an event will occur in simple games and probability experiments (e.g.,"My spinner has four equal sections and one of those sections is coloured red. The probability that I will land on red is 1/4.");
6.4.3: pose and solve simple probability problems, and solve them by conducting probability experiments and selecting appropriate methods of recording the results (e.g., tally chart, line plot, bar graph).
Correlation last revised: 8/18/2015