A nine years old learner is expected to be able to:
- Describe a multiplication equation as a comparison, e.g., describe as 40 is 5 times as many 8 or 8 times as many 5. Denote verbal statements of multiplicative comparisons as multiplication equations.
- Perform Multiplication or division to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
- Use four operations to solve multistep word problems posed with whole numbers and having whole-number answers, including problems in which remainders must be interpreted. Denote these problems using equations with a letter standing for the unknown quantity. Check the reasonableness of answers using mental computation and estimation strategies including rounding.
- Discover all factor pairs for a whole number in the range 1–100. Identify that a whole number is a multiple of each of its factors. Check whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
- Create a number or shape pattern that follows a given rule. Recognize apparent features of the pattern that were not explicit in the rule itself.For example, given the rule “add 2” starting number 2. The resulting sequence is multiples of 2 even though the rule was adding 2. Explain informally why the numbers will continue to alternate in this way.
- Discover that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, discover that by applying concepts of place value and division.
- Use base-ten numerals, number names, and expanded form to read and write multi digit whole numbers. Arrange two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
- Apply place value understanding to round multi-digit whole numbers to any place.
- Use standard algorithm to perform addition and subtraction of multi-digit whole numbers.
- Apply strategies based on place value and properties of operations to perform multiplication of a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers. Demonstrate and discuss the calculation by using equations, rectangular arrays, and/or area models.
- Calculate whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
- Examine why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Apply this principle to recognize and generate equivalent fractions.
- Arrange two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Identify that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
- Recognize a fraction a/b with a >1 as a sum of fractions 1/b.
- Recognize addition and subtraction of fractions as joining and separating parts referring to the same whole.
- Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: .
- Perform addition and subtraction of mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
- Apply adding and subtracting fraction having like denominator to solve word problems e.g., by using fraction bars and equations to represent the problem.
- Write a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 For example, .
- Express fractions with denominators 10 or 100 using decimal notation. For example, , .
- Arrange two decimals to hundredths by reasoning about their size. Discover that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
- Recognize relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, 2km is 2000m
- Apply the perimeter formulas for rectangles in real world and mathematical problems. For example, find the length of the unknown side of the triangle if the perimeter of it is 55cm and the length of the other two sides are 11 and 17.
- Identify angles as geometric shapes that are formed wherever two rays share a common endpoint, and recognize the concepts of angle measurement:
- An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
- An angle that turns through n one-degree angles is said to have an angle measure of n
- Use protractor to measure angles in whole-number degrees. Sketch angles of specified measure.
- Sketch points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Recognize these in two-dimensional figures.
- Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Identify right triangles as a category, and recognize right triangles.