Math: Operations & Algebraic Thinking
Write and interpret numerical expressions.
1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Video: Construct Numerical Expressions Video: Evaluating Expressions With & Without Parentheses How to Speak the Language of Math! 2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Video: Translating Expressions with Parentheses For example, express the calculation “add 8 and 7, then multiply by 2” Answer: 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Learning Farm: terms you want to know, and practice! 2.1 Express a whole number in the range 2–50 as a product of its prime factors. For example, find the prime factors of 24 and express 24 as 2 × 2 × 2 × 3. Video: Prime Numbers Video: Prime Factorization Video: Prime Factorization Exercise |
![]() Analyze patterns and relationships. 3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. Video: Graphing Patterns on a Coordinates Plane Video: Number Patterns: Visualizing Relationships Video: Number Patterns: Interpreting Relationships Video: Interpreting Relationships in Ordered Pairs Practice: Relationships Between 2 Patterns For example, given two rules: Rule #1: “Add 3” and the starting number 0, Rule #2: “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. We start with 0: Rule 1: 0 + 3 = 3 Rule 2: 0 + 6 = 6 That gives us 3 and 6. To use those numbers on a coordinate plane, we need a value for X (the horizontal axis of the plane) and a value for Y (the vertical axis). Rule #1 will give us a value for X. So, X = 3 Rule #2 will give us a value for Y. So, Y = 6 Now we can create an "ordered pair", where we write the X and Y values inside parentheses: (X,Y) = (3,6) (3,6) is located here on the coordinate plane. You will see a pattern if we use "1" instead of "0", and then "2" instead of "0". For 1, X = 1 + 3 = 4 and Y = 1 + 6 = 7 (4,7) For 2, X = 2 + 3 = 5 and Y = 2 + 6 = 8 (5,8) |