학습 센터 (PKG12)
과외 · 방과후
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Math Level 5
Number Sense of Whole Numbers

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

Recall – Place value with the numbers to 100,000

Count number to 10 million in concrete and pictorial way

Count, read and write the numbers to 10 million

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

Compare and order numbers with multiple numbers up to 10 million
Four operations of Whole Numbers

Strategy of performing mental multiplication with tens, hundreds and thousands

Strategy of performing mental division with tens, hundreds and thousands

Order of operations on whole numbers without parenthesis

Order of operations on whole number with parenthesis

Solve word problems on four operations with/without parenthesis
Fractions

Recall – Division of whole numbers as fractions or mixed numbers

Recall – Addition and subtraction of like/unlike fractions

Recall – Adding and subtracting mixed numbers and fractions

General skills of converting fractions to decimals

Multiplying proper fractions and whole numbers

Multiplying improper fractions and whole numbers

Multiplication involves in two proper fractions in algebraic and pictorial way

Multiplication involves in proper fractions and improper fractions

Multiplication involves in two improper fractions

Strategy of performing multiplication with mixed numbers and whole numbers

Solve the problems with fraction of a remainder

Solve word problems related to fractions
Area of Triangles

Recall – Area of squares and rectangles

Identify the base and height of a triangle

Understanding the idea of formula of area of triangle

Apply the formula to calculate the area of triangles

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

Recall – Cubes, cuboids, volume and capacity

Understand the idea of volume is related to space

Show the volume of the given solid with cubic units

Draw the given solids on isometric grids

Draw the different views of solids on square grids

Measure volume in cubic centimeters and cubic meters

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

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

Word problems involving volume and liquid
Ratio

Understand the idea and the definition of ratios of two quantities

Ratios of three quantities without merging ratios

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

Simplify the ratios to the simplest form

Find a quantity given another quantity and the ratio

Find a quantity given the total amount and the ratio

Word problems involving ratios of two and three quantities
Decimals

Recall – Placing value with tenths, hundredths and thousandths

Recall – Four operations involve in decimals

Recall – Conversion between fractions and decimals

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

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

Measurement conversion involve in decimals

Solve word problems involve in operations in decimals
Rate

Understand rates, total amount and number of units

Finding rates with given total amount and number of units

Finding total amount with given rates and number of units

Finding units with given rates and total amount

Solve the word problems involve in rate and compare the better buy
Percentage

Understand the meaning and idea of percentage

Conversions between fractions, decimals and percentages

Figure out percentage of a quantity

Calculate percentage based on quantity, and vice versa

Solve word problems related to percentage

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

Calculate the GST amount and total payment with given tax rate

Find the percentage of discount and price after discounted goods

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

Realworld and daily life examples for GST, discount and annual interest

Solve word problems related with GST, discount and annual interest
Average

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

Find the average with given total and number of data

Find the total with given average and number of data

Find the number of data with given average and total

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

Solve word problems involve in average
Angles

Recall – Measuring angles in degrees with protractor

Properties of the angles on a straight line

Figure out the missing angle on the straight line

Understanding the vertically opposite angles

Finding the unknown angles with the property of vertically opposite angles

Understanding the idea and properties of angle at a point

Finding the unknown angle with the mixed techniques and skills
Properties of Triangles

Understand and identify the different types of triangles

Naming the different types of triangles based on angles or lengths

Drawing triangles with given measurements

Sum of the interior angles of triangle

Find the unknown angles within triangles
Quadrilateral

Understand the properties of parallelogram, rhombus and trapezoid

Drawing the quadrilaterals with given measurements on square grids

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 realworld 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 realworld 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 fouroperation algebraic expression for a realworld 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 realworld problems using four operations related to fractions and mixed numbers

Solve the realword 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 realworld 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 12

Organize data in a scatter plot

Use a fitted line to make predictions

Use a 4step problemsolving approach

Use tables, graphs, and equations to model relationship
Lesson 34

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 realworld problems

Estimate percents of change
Lesson 78

Graph equations

Use equations and graphs to model situations

Use equation to make a prediction

Identify the yintercept of a line

Write an equation of a line in slopeintercept form
Lesson 9 Review
Lesson 10

Interpret statements with and, or, and not

Organize information in a Venn diagram
Lesson 1112

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 1516

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 1718

Find a perpendicular bisector of a chord

Find experimental probabilities

Use a tree diagram to model and find theoretical probabilities
Lesson 1920 Review & Nonroutine Questions
Lesson 21 Review & Test
Term 2
Lesson 2223

Identify irrational numbers

Simplify square roots, cube roots, and fourth roots

Simplify radical expressions
Lesson 2425

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 2728

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 3233

Use algorithms to transform geometric shapes

Reflect geometric shapes

Predict the shape of a parabola
Lesson 3435

Recognize quadratic equations

Simplify quadratic expressions
Lesson 36 Review
Lesson 3738

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 3940

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 & Nonroutine Questions
Lesson 42 Review & Test