Exploring Algorithms in Morning Math Session: Grades PreK-5

The morning Math P-5 session began with participants getting warmed up, spending three minutes doing mental math problems. They discussed how to solve addition, subtraction, multiplication, and division problems not using standard algorithms, and to compensate and deconstruct numbers and use the “hidden” associative and distributive properties. The activity set the focus for the morning which was to examine and practice algorithms for the story of functions. These algorithms will provide a fall-­back strategy for students that will always work.

Participants saw examples of how to use the distributive property for multiplication and how algorithms are cyclic in nature: add ones, add tens. Multiply ones, multiply tens.

Participants looked at an array of examples for multiplication and saw an alternate algorithm for multiplying by multiples of ten. The session also covered decomposition and the role of the magnifying glass in subtraction. One participant said, “I wish my teachers explained what was going on behind the scenes as clearly as these algorithms do!”

Later, the session took a quick trip through division algorithms. Participants went over a place value chart, finding the missing side of the array, dividing by multiples of 10, and the final division algorithm covered in grade 5. Each algorithm builds upon the next step.

The second half of morning session focused on looking at Grade 5 Module 2 – multiplication and division of whole numbers and decimal and fraction operations. Participants read the progressions document for Numbers & Operations in Base 10. A question was raised about how to use the progressions in districts in the current form because they are challenging to read, so districts need to somehow make them more palatable for teachers. Participants reviewed the Module 2 overview and compared lessons 2 and 17. The lessons are very similar in approach, but one deals with multiplication while the other covers division. Both lessons place an emphasis on rounding, place value patterns, and fluency with multiplication facts, and both lessons use examples that clearly show what happens when increasing/decreasing by powers of 10 through multiplication and division.

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