An eleven years old learner is expected to be able to:

 

 

1. Understand and evaluate quotients of fractions, and apply the strategies of division of fractions by fractions to solve word problems by writing the equations to represent the problem. For example, . (In general, (a/b) ÷ (c/d) = ad/bc.) An electrician needs 5 rolls of electrical wire to wire each room in a house. How many rooms can he wire with 1/2 of a roll of wire?

 

 

2. Use standard algorithm to fluently divide multi-digit numbers.

 

 

 

3. Use standard algorithm to fluently add, subtract, multiply, and divide multi-digit decimals.

 

 

 

4. Discover the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Apply the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

 

 

 

 

5. Recognize that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

 

 

 

6. Recognize a rational number as a point on the number line. Extend number line diagrams to represent points on the line and in the plane with negative number coordinates.

 

 

 

7. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; discover that the opposite of the opposite of a number is the number itself, e.g., .

 

 

 

8. Understand arranging integers and absolute value of rational numbers.

• Understand statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, means 3 is located on the right of on the number line.
• Write, understand, and describe statements of order for rational numbers in real-world contexts. For example, write below sea level means  is deeper than .
• Recognize the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, drug test result is negative means you do have drug in your system.
• Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 Dirhams represents a debt greater than 30 Dirhams.

 

 

 

 

9. Express and evaluate numerical expressions involving whole-number exponents.

 

 

 

10. Write, read, and calculate expressions in which letters stand for numbers.

• Write expressions that record operations with numbers and with letters standing for numbers. For example, sum of x and 4 means .
• Recognize parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression as a product of 3 and .
• Find the value of the expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, evaluate the expression for .

 

 

 

11. Generate equivalent expression by applying the properties of operations. For example, use distributive property to write the equivalent expression for ; apply properties of operations to to produce the equivalent expression .

 

 

 

12. Recognize when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions and  are equivalent because they name the same number regardless of which number x stands for.

 

 

 

 

13. Recognize solving an equation as a process of answering a question: which values from a specified set, if any, make the equation true? Use substitution to check whether a given number in a specified set makes an equation true.

 

 

 

14. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

 

 

 

15. Apply the technique of solving equation to real-world mathematical problems. Write and solve equations of the form and  in which p, q and x are all nonnegative rational numbers.

 

 

 

16. Evaluate the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.