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## Math Level 5

Number Sense of Whole Numbers

1. Recall – Read and write the numbers to 100,000 in standard form, expended form or words

2. Recall – Place value with the numbers to 100,000

3. Count number to 10 million in concrete and pictorial way

4. Count, read and write the numbers to 10 million

5. Express and show the numbers to 10 million in standard form, expended form and words

6. Compare and order numbers with multiple numbers up to 10 million

Four operations of Whole Numbers

1. Strategy of performing mental multiplication with tens, hundreds and thousands

2. Strategy of performing mental division with tens, hundreds and thousands

3. Order of operations on whole numbers without parenthesis

4. Order of operations on whole number with parenthesis

5. Solve word problems on four operations with/without parenthesis

Fractions

1. Recall – Division of whole numbers as fractions or mixed numbers

2. Recall – Addition and subtraction of like/unlike fractions

3. Recall – Adding and subtracting mixed numbers and fractions

4. General skills of converting fractions to decimals

5. Multiplying proper fractions and whole numbers

6. Multiplying improper fractions and whole numbers

7. Multiplication involves in two proper fractions in algebraic and pictorial way

8. Multiplication involves in proper fractions and improper fractions

9. Multiplication involves in two improper fractions

10. Strategy of performing multiplication with mixed numbers and whole numbers

11. Solve the problems with fraction of a remainder

12. Solve word problems related to fractions

Area of Triangles

1. Recall – Area of squares and rectangles

2. Identify the base and height of a triangle

3. Understanding the idea of formula of area of triangle

4. Apply the formula to calculate the area of triangles

5. Find the area of given triangles and composite figures with splitting or merging method

Volume

1. Recall – Cubes, cuboids, volume and capacity

2. Understand the idea of volume is related to space

3. Show the volume of the given solid with cubic units

4. Draw the given solids on isometric grids

5. Draw the different views of solids on square grids

6. Measure volume in cubic centimeters and cubic meters

7. Find the volume of cubic and cuboid by counting the unit cubes or applying the formula

8. Connection with volume of liquid in cubic centimeters, cubic meters, milliliters and liters

9. Word problems involving volume and liquid

Ratio

1. Understand the idea and the definition of ratios of two quantities

2. Ratios of three quantities without merging ratios

3. Understand and make an equivalent ratio from the given ratio of two and three quantities

4. Simplify the ratios to the simplest form

5. Find a quantity given another quantity and the ratio

6. Find a quantity given the total amount and the ratio

7. Word problems involving ratios of two and three quantities

Decimals

1. Recall – Placing value with tenths, hundredths and thousandths

2. Recall – Four operations involve in decimals

3. Recall – Conversion between fractions and decimals

4. Strategy of performing mental multiplication with tens, hundreds, thousands and decimals

5. Strategy of performing mental division with tens, hundreds, thousands and decimals

6. Measurement conversion involve in decimals

7. Solve word problems involve in operations in decimals

Rate

1. Understand rates, total amount and number of units

2. Finding rates with given total amount and number of units

3. Finding total amount with given rates and number of units

4. Finding units with given rates and total amount

5. Solve the word problems involve in rate and compare the better buy

Percentage

1. Understand the meaning and idea of percentage

2. Conversions between fractions, decimals and percentages

3. Figure out percentage of a quantity

4. Calculate percentage based on quantity, and vice versa

5. Solve word problems related to percentage

6. Understand Goods and Services Tax (GST), discount and annual interest

7. Calculate the GST amount and total payment with given tax rate

8. Find the percentage of discount and price after discounted goods

9. Calculate the annual interest and compare the interest from bank to bank

10. Real-world and daily life examples for GST, discount and annual interest

11. Solve word problems related with GST, discount and annual interest

Average

1. Finding the average in a set of data in concrete and pictorial way

2. Find the average with given total and number of data

3. Find the total with given average and number of data

4. Find the number of data with given average and total

5. Using the given clues to figure out the average, total and number of data

6. Solve word problems involve in average

Angles

1. Recall – Measuring angles in degrees with protractor

2. Properties of the angles on a straight line

3. Figure out the missing angle on the straight line

4. Understanding the vertically opposite angles

5. Finding the unknown angles with the property of vertically opposite angles

6. Understanding the idea and properties of angle at a point

7. Finding the unknown angle with the mixed techniques and skills

Properties of Triangles

1. Understand and identify the different types of triangles

2. Naming the different types of triangles based on angles or lengths

3. Drawing triangles with given measurements

4. Sum of the interior angles of triangle

5. Find the unknown angles within triangles

1. Understand the properties of parallelogram, rhombus and trapezoid

2. Drawing the quadrilaterals with given measurements on square grids

3. Find out the unknown angles from the given figures or composite figures

## Math Level 6

Positive Numbers and Negative Numbers

• Represent numbers on a positive and negative number line

• Write statements of inequality comparing two or more whole numbers by using “greater than”, “less than” symbol

• Represent fractions, mixed numbers and decimals on a horizontal number line

• Write statements of inequality for two or more fractions or decimals by using “greater than”, “less than” symbol

• Interpret and explain statements of order for positive and negative numbers in real-world situations

• Identify composite and prime numbers

• Write a composite number as a product of its prime factors

• Find the greatest common factor and least common multiple of two whole numbers

• Find a square or square root of a whole number

• Find a cube or cubic root of a whole number

• Write the absolute value of a number

• Use absolute value to interpret real-world situations

Algebra

• Use variables to represent unknown numbers and write addition, subtraction, multiplication and division expressions

• Algebraic expressions can be evaluated for given values of the variable

• Simplifying like term expressions by adding and subtracting

• Use order of operations to simplify algebraic expressions

• Collect like terms to simplify algebraic expressions

• Write a four-operation algebraic expression for a real-world problem and evaluate it

• Solve the word problems by setting the notation and solving equations

Fractions and Decimals

• Recall – Adding and subtracting involve in decimals, improper fractions and mixed numbers

• Recall – Conversion between improper fractions and mixed numbers

• Recall – Multiplying fractions

• Dividing a fraction (proper fraction or improper fraction) by a whole number

• Dividing a whole number by a fraction (proper fraction or improper fraction)

• Dividing a proper fraction or improper fraction by another proper fraction or improper fraction

• Division involves in fractions (improper fraction or proper fraction) and mixed number

• Multiply decimals by decimals with one decimal place

• Multiply decimals with one or more decimal places

• Divide a whole number by a decimal with one or more decimal places

• Divide a decimal by another decimal with one or more decimal places

• Solve the real-world problems using four operations related to fractions and mixed numbers

• Solve the real-word problems using four operations related to decimals

•

Ratio

• Recall – Idea of ratio in two and three quantities

• Recall – Making equivalent ratios and simplifying ratios to its simplest form

• The connection between ratios and fractions

• Changing ratios problems related in one unchanged quantity

• Changing ratios problems related in unchanged total

• Changing ratios problems related in unchanged difference

• Solving word problems related to ratios in two or three quantities

Percentage

• Recall – Meaning of percent

• Recall – GST, discount and annual interest

• Recall – Expressing fractions or mixed numbers as percentage

• Recall – Expressing decimals as percentage

• Find the quantity by the percent

• Find the whole given a part and the percentage

• Find the percentage that increase or decrease

• Solve word problems mixed with decimals, fractions and percentage

Angles in Geometrical Figures

• Recall – Find unknown angles on a straight line or at a point

• Recall – The properties of vertically opposite angles, angles on a straight line and angles at a point

• Recall – Angles in triangles and quadrilaterals

• Use angle properties to find unknown angles in geometric figures like square, rectangle, parallelogram, rhombus, trapezoid and different types of triangles

Circles

• Recall – Semicircle and quarter circle

• Identify and recognize center, radius and diameter of a circle

• Identify and calculate circumference of a circle

• Figure out the perimeter of a semicircle, quarter circle or composite figure involve in circle

• Understand and calculate the area of a circle

• Figure out the area of a semicircle, quarter circle or a composite figure

• Solve the real-world problem utilize the formula for area and perimeter of a circle, semicircle or quarter circle

Speed

• Recall – Finding rates, total amounts and number of units

• Understand the idea of speed

• Finding the speed with given distance and time

• Finding the distance with given speed and time

• Finding the time with given speed and distance

• Solve the problems involving speed with two parts in a journey

• Understand and calculate the idea of average speed

• Solve the problems involving speed with two moving objects

Volume

• Recall – Idea and formula of volume of cubes, cuboids and liquids

• Look for one dimension of a cuboid given its volume and other dimensions, or the edge of a cube given its volume

• Look for the area of one face given the volume and edge

• Solve the word problems related to volume

Pie Chart

• Read and interpret pie charts and use data from pie chart to solve word problems

• Presenting data in pie charts

Solid Figures and Nets

• Recognize the net of a solid figure like cubes, cuboids, prisms or pyramids

• Find the surface area of a solid figure like cubes, cuboids, prisms or pyramids

• Find the volume of any prism

• Form cross sections of prisms

• Solve word problems about volume and surface area with the given solid

• Solve word problems about solids with missing dimensions

## Math Level 7

Term 1

Lesson 1-2

• Organize data in a scatter plot

• Use a fitted line to make predictions

• Use a 4-step problem-solving approach

• Use tables, graphs, and equations to model relationship

Lesson 3-4

• Use percents, fractions, and decimals to summarize the results of a survey

• Identify and correct biased survey questions

• Use proportional reasoning to estimate the percent of a number

• Identify representative samples

Lesson 5 Review

Lesson 6

• Estimate percents and use percent to solve real-world problems

• Estimate percents of change

Lesson 7-8

• Graph equations

• Use equations and graphs to model situations

• Use equation to make a prediction

• Identify the y-intercept of a line

• Write an equation of a line in slope-intercept form

Lesson 9 Review

Lesson 10

• Interpret statements with and, or, and not

• Organize information in a Venn diagram

Lesson 11-12

• Find the volume of prisms, cylinders, and spheres

• Find the surface area of a cylinder

• Find and interpret the ratio of a cylinder’s surface area to its volume

Lesson 13

• Recognize the characteristics of rational numbers

• Use notation for repeating decimals

• Solve equations containing rational numbers

Lesson 14 Review

Lesson 15-16

• Use the counting principle to count numbers of choices

• Find the number of permutations of a group of objects

• Find numbers of combinations

• Use the counting principle to determine the probability of an event

Lesson 17-18

• Find a perpendicular bisector of a chord

• Find experimental probabilities

• Use a tree diagram to model and find theoretical probabilities

Lesson 19-20 Review & Non-routine Questions

Lesson 21 Review & Test

Term 2

Lesson 22-23

• Identify irrational numbers

• Simplify square roots, cube roots, and fourth roots

Lesson 24-25

• Multiply and divide powers using properties of exponents

• Simplify powers with zero and negative exponents

• Represent small numbers in scientific notation and in decimal notation

Lesson 26 Review

• Create nets for pyramids and prisms

• Bisect an angle using a compass

• Compare triangles using two sides and the included angle

Lesson 27-28

• Identify and find the measures of pairs of angles formed by intersecting lines

• Explore relationships between perimeters and area of two similar figures

Lesson 29

• Use tables and graphs to model changes in data

• Use tables, graphs, and equations to represent functions

Lesson 30 Review

Lesson 31

• Write an equation to model compound interest

• Model price changes and growth of a savings account

Lesson 32-33

• Use algorithms to transform geometric shapes

• Reflect geometric shapes

• Predict the shape of a parabola

Lesson 34-35

Lesson 36 Review

Lesson 37-38

• Multiply and divide powers using properties of exponents

• Simplify powers with zero and negative exponents

• Represent small numbers in scientific notation and in decimal notation

Lesson 39-40

• Find the distance between points on a coordinate grid

• Find the midpoint of a segment on a coordinate grid

• Use tangent ratio to find unknown side lengths in right triangles

• Use sine and cosine ratios to find unknown side lengths in right triangles

Lesson 41 Review & Non-routine Questions

Lesson 42 Review & Test

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