A twelve years old learner is expected to be able to:

 

 

1. Evaluate the unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, If you a person host a party for 12 people. The food and drinks for the party cost Aed 66. Evaluate the unit rate as 66/12 cost per person, which is Aed 5.5 cost per person.

 

 

 

 

2. Recognize and represent proportional relationships between quantities.

• Investigate whether two quantities are in a proportional relationship, e.g., by discovering the equivalent ratio, or by checking the equality of equation using cross product.
• Recognize the constant of proportionality (unit rate) in equations, and verbal descriptions of proportional relationships.
• Symbolize proportional relationships using equations. For example, human hair grows about 0.7 centimeter in 2 weeks, to find the number of weeks that take the hair to grow 14 centimeters we can form the equation or .

 

 

 

3. Apply proportional relationships in solving multistep ratio and percent problems. Examples: An artist’s collection of paintings includes 22 portraits. The portraits make up 40% of the collection. To find the number of paintings in his collection we can use the proportionality equation .

• Recognize the difference between factors and multiples. Identify factors and multiples for a given number. For example; the factors of 12 are 1, 2, 3, 4, 6, 12 and multiples of 12 are 12, 24, 36, 48 …
• Determine whether a number is prime or composite by applying divisibility rule. Express the given number as a product of prime numbers
• Determine the least common multiple and greatest common factor by drawing tree diagram, by using prime factorization or by finding the multiples or factors of the numbers.

 

 

 

 

4. Relate and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction using fraction bars.

• Discover situations in which opposite quantities combine to make 0. For example, if I walk forward 5 steps, but then walk backwards 5 steps. Then my position will not change because two 5 steps are in opposite direction.
• Investigate p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Discover that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
• Relate subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
• Apply properties of operations as strategies to add and subtract rational numbers.

 

 

 

 

5. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

• Recognize that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
• Recognize that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real- world contexts.
• Apply properties of operations as strategies to multiply and divide rational numbers.
• Change a rational number to a decimal using long division; recognize that the decimal form of a rational number terminates in 0s or eventually repeats.

 

 

 

 

6. Solve real-world and mathematical problems involving the four operations with rational numbers.

• Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
• Discover that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, means that “increase by 3” is the same as “multiply by 4.”
• Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: each morning a person feed his love birds cup of dry bird food and at night he feed them cup of the bird food. The person bought a bag of bird food that contains 40 cups. To know the number of days the bag last we use the rational operations with numbers.

 

 

 

 

7. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

• Solve word problems leading to equations of the form and , where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, Tom’s spend Aed 33 on the supermarket. He purchased 3 cartons of milk and some loaves of bread. Bread costs Aed 3 each and milk costs Aed 6 each. To know number of loaves of bread he bought we need to solve the equation .
• Solve word problems leading to inequalities of the form or , where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: you have Aed 18.50 to spend on pizza. A cheese pizza costs Aed 14 and each extra topping costs Aed 0.75. to know the number of extra topping you can buy, you need to solve the inequality .

 

 

 

 

 

 

8. Identify and apply the properties of integer exponents to generate equivalent numerical expressions or to simplify the expression. For example, .

 

 

 

 

9. Express the number in scientific notation. Rewrite the scientific notation number into standard form. For example, the population of the UAE is .

 

 

 

 

10. Arrange the numbers that are in the form of standard or scientific in ascending or descending order. For example: is in ascending order.

 

 

 

11. Determine whether the expression is a polynomial by applying laws of exponents. Identify term, coefficient and degree from a polynomial. Classify the polynomial as monomial, trinomial.

 

 

 

12. Discover that polynomial form a system similar to the integers, namely they are closed under the operations of addition, subtraction and multiplication.

 

 

 

 

13. Perform addition, subtraction and multiplication in polynomial.

 

• Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
• Sketch (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
• Construct the perpendicular bisector and angle bisector using the geometric tools e.g.; ruler, compass, protractor etc.

 

 

 

 

14. Identify the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

 

 

 

15. Apply the facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

 

 

 

16. Classify triangles, polygons and quadrilaterals. Solve the real world mathematical problems using the properties of triangles, polygons. Solve real-world and mathematical problems involving area of two- dimensional objects composed of triangles, quadrilaterals, polygons.

 

 

 

 

17. Verify and apply theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line  segment are exactly those equidistant from the segment’s endpoints; angle bisector cut the entire angle half way.

 

 

 

 

18. Demonstrate and apply theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent.

 

 

 

 

19. Apply the definition of congruence in terms of rigid motion to show that two triangle are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

 

 

 

20. Identify the congruent sides and congruent angles in congruent triangles to write the congruency statement

 

 

 

 

21. Understand the different properties of the coordinate plane. Plot the points on the coordinate plane. Identify the points in the coordinate plane.

 

 

 

22. Determine the slope of the line formed from linear equation by counting rise and run from the graph. Classify the straight lines as parallel and perpendicular by finding the slope of the lines.

 

 

 

 

23. Recognize that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

 

 

 

24. Make predictions and determine the probability of an outcome by constructing sample space.

 

 

 

25. Find the frequency for a given probability. For example, probability of rolling a blue ball from a bag of 50 balls is 0.25. Find the number of blue balls in the bag.