Lesson objective: Extend understanding of the rules for all operations to include decimals and to understand that, like whole-numbers, decimal operations are based on the place value system.

Students bring prior knowledge of whole-number operations using the standard algorithm from Grade 4 (4.NBT.4) and Grade 5 (5.NBT.5). This prior knowledge is extended to include decimal operations as students use the standard algorithm to efficiently solve problems. A conceptual challenge students may encounter is believing the placement of the decimal in a product, quotient, sum or difference is based on an arbitrary rule, when it is actually based on place value.

The concept is developed through work with the standard algorithm, which shows the most efficient method of using place value to record operations. This work helps students deepen their understanding of number because place value is essential to the standard algorithm returning the correct answer.

Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they notice how the placement of a digit in the algorithm, in relation to the other numbers within the algorithm, gives it its place value - that the “place” it is in determines its “value”. Students engage in Mathematical Practice 7 (Look for and make use of structure) as they understand how the structure of the standard algorithm shows place value of each of the digits within the algorithm.

Key vocabulary:

Special materials needed:

- Solution sort cards, cut out for partner/group work