An eight years old learner is expected to:

 

 

1. Recognize products of whole numbers, e.g., recognize as the total numbers of objects are classified in 3 groups each has 5 objects. For example, there are three houses. Each house has 5 people living in it. To find the number of people live in the houses is.

 

 

2. Explain the meaning of quotients of whole numbers, e.g., understand as the number of objects in each share when 63 objects are partitioned equally into 9 shares, or as a number of shares when 63 objects are partitioned into equal shares of 9 objects each. For example, Sara needs 3 lemons to make a glass of lemonade. If Sara has 36 lemons, she can  glasses of lemonade.

 

 

3. Perform multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using diagrams, models and equations with a symbol for the unknown number to represent the problem.

 

 

4. Discover the unknown whole number in a multiplication or division equation relating three whole numbers. For example, fill in the blanks with whole numbers , .

 

 

5. Perform multiplication and division using the properties of operations as strategies. Examples: If is known, then is also known.(Commutative property of multiplication.) 2 × 5 × 7 can be found by 2 × 5 = 10, then 10 × 7 = 70, or by 5 × 7 = 35, then 35 × 2 = 70. (Associative property of multiplication). can be easily found as . (Distributive property).

 

 

 

6. Discover division as an unknown-factor problem. For example, means .

 

 

7. Use the properties of operations or strategies such as the relationship between multiplication and division, to multiply and divide the numbers within 100 fluently. Memorize the multiplication table from 1 to 10.

 

 

8. Solve two-step word problems using the four operations by using the strategy – write a number sentence.

 

 

9. Discover arithmetic patterns (including patterns in the addition table or multiplication table), and discuss them using properties of operations. For example, even number times any number is even.

 

 

10. Apply place value understanding to round whole numbers to the nearest 10 or 100.

 

 

11. Perform addition and subtraction within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

 

 

12. Use the strategies based on place value and properties of operations to multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60).

 

 

13. Recognize a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

 

 

14. Recognize a fraction as a number on the number line; denote fractions on a number line diagram.
15. Denote a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and dividing it into b equal parts. Identify that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
16. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Identify that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

 

 

15. Discuss equivalence of fractions in special cases, and compare fractions by reasoning about their size.
16. Recognize two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
17. Identify and form simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Discuss why the fractions are equivalent, e.g., by using a fraction bars.
18. Represent whole numbers as fractions, and identify fractions that are equivalent to whole numbers. Examples: different form of is , is 1 and is 4.

 

 

16. Compare and order two fractions with the same numerator or the same denominator by reasoning about their size. Discover that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a fraction bar.

 

 

17. Recognize that shapes in different categories (e.g., rhombuses, rectangles, and others) may share characteristics (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Identify rhombuses, rectangles, and squares as examples of quadrilaterals, and sketch the examples of quadrilaterals that do not belong to any of these subcategories.