Whole numbers and decimals should be taught in same units as set up in Grade 6 textbooks. The sequence is set with this in mind. PART I: Whole Numbers and Decimals Numeration with numbers through hundred millions place Place value and value through hundred million Reading numbers through hundred million Standard numbers Expanded numbers with values Expanded numbers with exponents for place value Ordering numbers Comparing numbers Rounding numbers Numeration (through millionths) Reading Short and long word form Place value and value of digits Negative exponents for place values Compare and order Round from whole to thousandths place Use number line and place value chart
Addition Up to 6 digits with regrouping Money amounts Estimate sums with and without money Function boxes Problem solving Properties 100 basic facts completed in 4 minutes
Addition of decimals Through thousandths place Relate to money Word Problems Uneven place value
Subtraction Up to 6 digits with and without regrouping Subtract over zeroes Money amounts Determine change Estimate differences with and without money Problem solving Function boxes Subtraction rules 100 basic facts completed in 4 minutes
Subtraction of decimals Through thousandths place Relate to money Word problems Uneven place values
Multiplication Review I digit multiplication Up to 3 by 4 digits Money by a 1 or 2 digits 1 and 2 digits by 10, 100, 1000 and powers of 10 Move decimal point right for short multiplication of positive place values Estimate products Properties Word Problems Uneven place values 100 basic facts completed in 4 minutes
Multiplication of decimals Decimal patterns to multiply 10, 100, 1000 Negative exponents for powers of 10 Move decimal points to the left for short multiplication of negative exponents Decimal by whole numbers Decimal by decimal Zeroes in factors Problem solving
Division: 1 and 2 digit divisors Divisors with multiples of 10, 100, 1000 Divisors with Powers of 10 Move decimal point to the left short division with place values Dividends to at least 4 digits Estimation with compatible numbers Word Problems 90 basic facts completed in 4 minutes
Division of decimals Decimal patterns to divide by 10, 100, 1000 Use negative exponents for place values Move decimal point to the right for negative powers of 10 Introduce decimal divided by whole number Divide decimals by whole number Divide decimals by decimals Terminating and repeating decimals Round quotients Problem solving
PART II: Fractions Numeration (Use models for all lessons) Divisibility rules Prime and composite numbers Find Greatest Common Factor (GCF) with lists, prime factorization and memory Find Least Common Multiple (LCM) with lists, prime factorization and memory Review Identity numerator and denominator Define whole number, fraction, mixed and improper fraction Write in standard and word form Equivalent fractions (renaming) Using multiplication Simplest form using division Fraction patterns Fraction for a whole number Rename and simplify improper to mixed number Compare proper, improper and mixed numbers Order proper, improper and mixed numbers
Fraction and Decimal Concepts Relate fractions and mixed number and decimals Compare and order mixed fractions and decimals Computation Add and subtract with like denominators Using Least Common Denominator (LCD) add and subtract unlike denominators Simplify sums and differences Add like and unlike Add like and unlike mixed numbers Multiply whole numbers by fraction Multiply fraction by fraction Introduce the reciprocal property Divide whole numbers and fractions Simplify products and quotients Order of operations Compute fractions and decimals in the same problem Word problems Estimate sums, differences, products and quotients
Part III: Measurement
Customary Units of Measure Measure length, capacity and weight Practice changing between customary units of length, capacity and weight Use a table of equivalences and choose appropriate units of measure Add and subtract measures, including time with regrouping units Problem solving
Metric Units of Measure Measure length, capacity and weight Change from one metric unit to another by multiplying and dividing by powers of 10 Complete function table involving metric measurements Problem solving Relate Customary and Metric Units With a table of approximate equivalences, convert between customary and metric
Part IV: Collect and Analyze Data Collect and Analyze Data Surveys and sampling Describe data using mean, median, mode and range Review picto, line and bar graphs Line plots with clusters, gaps, and outliers Read and make Double Line Graphs Display frequency in a frequency table and histogram Display on a Line Plot Make and interpret Stem-and-Leaf plots Display data on a Box-and-Whisker Terms: upper quartile, lower quartile, medium, upper extreme and lower extreme Misleading data displays Ordered pairs (X and Y coordinate) Write and read ordered pairs on a 4 quadrant grid naming the coordinates X and Y.
Part V: Geometry Plane Figures Review: points, lines, line segments, rays, parallel lines, perpendicular lines, intersecting lines Congruent and similar figures Symmetry Construct line and angle bisectors Angles: right, acute, obtuse, straight Measure angles with a protractor Triangles: Name by sides and angles Quadrilaterals: Square, rectangles, parallelograms, rhombus, trapezoid Area and perimeter for triangles and quadrilaterals Name polygons up to 12 sides Circles Parts: radius, diameter, tangents, chord Define and identify the numbers for pi Circumference Area Problem solving Solid Figures Terms: faces, vertices and edges Identify: polyhedron, prisms, cubes, pyramids, cylinder, cone, net Rectangular and Triangular prisms Square and triangular pyramid Surface areas Volumes Problem solving
Part VI: Percentages Ratios and Percentages Write ratios in 3 ways Understand equivalent ratios Find unit rates Write and Solve proportions
Understand and Using Percents Relate fractions, decimals, and percents Compare and order fractions, decimals and percents Estimation with percent Find a Percent of a Number Find a Percent Find a Number when a Percent is known Simple Interest Use proportions to solve percent related problems Problem solving
Part VII: Probability
Investigating Probability Possible Outcomes Theoretical Probability Experimental Probability Compound Events Problem solving
Part VIII: Integers Concepts and Computation Define integers as opposites Use number line to identify positive and negative integers Compare and order integers Addition Subtraction Multiplication Division Problem solving
Part IX: Roman Numerals
Numerals up to 5000 Reading Writing standard numerals into Roman numbers Writing Roman numerals into standard numbers