2. Numbers, operations, and equality

Connect addition with joining amounts and subtraction with finding the difference or missing part. Trace how these inverse operations undo each other in simple number sentences.

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See multiplication as equal groups and division as splitting into equal parts or groups. Use fact families to connect multiplication and division as inverse operations.

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Find factors, multiples, and prime numbers, then use them to break numbers into useful pieces. Practice recognizing greatest common factors and least common multiples in small arithmetic tasks.

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Use commutative, associative, identity, and zero properties to make arithmetic easier without changing a value. Recognize when regrouping or reordering numbers is safe and when order matters.

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Read powers like 3² and 2⁵ as repeated multiplication. Calculate powers, identify the base and exponent, and notice common mistakes such as confusing 3² with 3 × 2.

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Treat square roots and cube roots as questions about which number makes a power. Match perfect squares and cubes with their roots and estimate roots that fall between whole numbers.

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Follow the standard order for multi-operation arithmetic: grouping symbols, exponents and roots, multiplication or division, then addition or subtraction. Work left to right when operations have the same priority.

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Read the equals sign as “has the same value as,” not as a signal that an answer comes next. Decide whether number sentences are true by comparing the value on both sides.

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Keep an equality true by doing the same arithmetic move to both sides. Use balanced scales and number sentences to see why changing only one side breaks equality.

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Interpret fractions as parts of a whole, points on a number line, and division. Connect numerator and denominator to what is being counted and how the whole is split.

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Create equivalent fractions by multiplying or dividing numerator and denominator by the same nonzero number. Simplify fractions and recognize when two different-looking fractions name the same value.

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Compare fractions by using common denominators, benchmarks, or number lines. Reason about which fraction is larger without relying only on cross-multiplication.

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Add and subtract fractions by making like denominators first. Track what changes and what stays the same so the size of each fractional piece is handled correctly.

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Multiply fractions by multiplying numerators and denominators, then simplify when helpful. Use area or “part of a part” reasoning to see why the rule works.

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Divide fractions by using reciprocals and multiplying. Connect the procedure to the question “how many of this fraction fit into that amount?”

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Read decimals using tenths, hundredths, thousandths, and place value to the right of the decimal point. Place decimals on a number line and compare them by aligning place values.

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Add, subtract, multiply, and divide decimals while keeping track of place value. Use estimation to check whether the decimal point in an answer is reasonable.

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Move between fractions and decimals by division or by making denominators such as 10, 100, or 1000. Recognize terminating and repeating decimals from common fraction forms.

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Place positive and negative numbers on a number line and identify opposites. Use absolute value as distance from zero, regardless of direction.

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Add and subtract signed numbers by thinking about direction, distance, and opposites. Decide when a result moves farther from zero, closer to zero, or crosses zero.

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Multiply and divide positive and negative numbers using sign rules. Reason through why same signs give a positive result and different signs give a negative result.

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Compare whole numbers, fractions, decimals, and negatives by placing them in a common form or on a number line. Choose the form that makes the comparison clearest.

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Round numbers to a chosen place value and use estimation to predict the size of an answer. Check arithmetic results for reasonableness before trusting exact calculations.

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Review this chapter with practice based on your mistakes.