Lesson objective: Understand that mixed numbers are numbers that can be rewritten as equivalent fractions and the commutative and associative properties apply.
Students bring prior knowledge of decomposing fractions from 3.NF.A.1 and of writing whole numbers as fractions from 3.NF.A.3. This prior knowledge is extended to decomposing mixed numbers to extend students' understanding of addition and subtraction. A conceptual challenge students may encounter is understanding the notation of mixed numbers, and understanding them as both a single number and as the sum of a whole number and a fractional part.
The concept is developed through work with a number line, which allows students to see that a mixed number is represented by a single point on a number line and as the sum of two parts.
This work helps students deepen their understanding of number because mixed numbers and their equivalent fractions are numbers. Students can apply their prior knowledge about numbers and see that what they know about numbers and locations on the number line continues to apply to mixed numbers.
Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they write equivalent forms of mixed numbers. Students will practice using fraction forms of mixed numbers to add and subtract mixed numbers. Students will also practice using properties of operations to add the whole number parts and fractional parts of the mixed numbers separately and then put them together again as a mixed number.
Key vocabulary:
- fraction
- mixed number