A thirteen years old learner is expected to be able to:
- 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.
- 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.
- Solve real-world and mathematical problems involving the four operations with rational numbers. For example, Jesse mixed together cups of grapefruit juice and cups of lemon-lime soda to make punch. How many cups of punch did Jesse make?
- Recognize and apply the properties of integer exponents to discover equivalent numerical expressions. For example,
- Discover the value of the expression having zero exponents.
- Classify the linear equations in one variable as one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
- Apply distributive property and collecting like terms in solving linear equations with rational number coefficients, including equations whose solutions require expanding expressions.
- Apply the technique of solving linear equation in real life word problems. For example, Mary’s brother is three years younger than twice her age. The sum of their ages is 24. How old is Mary?
- Recognize the meaning of absolute value. Use the definition of absolute value on solving equation having absolute value. Discover the case for which absolute value equation has no solution.
- Use distributive property and collecting like terms in solving linear inequalities of the form , , where a, b, c and d are rational numbers.
- Apply the technique of solving inequality in problem solving. For example, Yara is a waitress at the Jumeirah Beach Hotel. In one night she earned at least 122 Aed while working a six hour shift. If she earned 32 Aed in tips. Find all the possible amount she earned in wages per hour.
- Discover the meaning of “and” and “or” in inequality to solve compound sentences. Graph the inequality for the solution using and to represent the inequality.
- Recognize the definition of absolute value inequality. Apply the definition of absolute value inequality in solving inequality having absolute value.
- Identify the parts of the expression as terms, coefficients and like terms. Identify the expression as monomial, binomial, trinomial and polynomial. Recognize the expression as difference of squares and perfect square trinomials.
- Identify the GCF in the polynomial to factor the polynomial. Use groups (especially 2) to factor the polynomial completely.
- Factor the quadratic expression by comparing the values of a, b and c with the general quadratic form and identify the sum and product.
- Express the real world expressions in alternate forms. For example, the velocity of a particle is given by the expression , then its alternate form is
- Perform addition and subtraction by grouping the like terms
- Apply distributive property in multiplying polynomials. Use distributive property to discover FOIL method of multiplication in binomials.
- Discover the general formula for perfect square binomial and difference of squares to find the product easily.
- Identify zeros of polynomials when suitable factorizations are available. Recognize the different words for zeros as roots and solution.
- Apply zero product property in factored form to find the solution. Discover that the sign will be opposite in factored form and solution. Apply factorization to solve real life mathematical problems. For example, If a rock is thrown upward, its height after t seconds is . Find the time when the rock reach the ground.
- 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.
- Sketch and measure the angles. Classify angles as acute, right, obtuse and straight by measuring the angles.
- 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.
- Discover the meaning of bisectors as divide into half and apply that in finding the measure of the angle or length.
- 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.
- Discover and apply segment addition postulate and angle addition postulate. Apply the postulates in real life situation. For example, to go to her home, Hannah walks 1km to reach the metro station and 2 km from metro station to her home. How many distance she walks to go to home?
- 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; remote exterior angle theorem; centroid theorem.
- Discover abscissa and ordinate from the ordered pair. Identify and plot the point in the coordinate plane. Recognize the coordinate on which the ordered pair lies
- Graph the linear equation by identifying two or more ordered pairs from the linear equation. Recognize the meaning of slope. Use the skills to find the slope. Discover the nature of the slope as positive, negative, no slope etc. Apply the formula of slope to find the slope in real life situation. For example, Hannah is jogging through an inclined place. If the horizontal and vertical length of the inclined place is 48 and 32 respectively. Find the slope of the inclined place.
- Apply the definition of congruence in terms of rigid motions to predict if the given shapes are congruent. Identify the congruent objects from the real life situations. For example, ear rings are congruent.
- Use the definition of congruence to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
- Discover the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.