Multiplicative Reasoning LT
Research based LT resources
Use these LT resources to identify strength in student thinking and Unpack the learning trajectory using these guiding questions:
1) What are the big ideas? Conceptual principles and the development of the ideas underlying a concept
2) What are the multiple representations, strategies and conceptions that students need experiences with?
3) What are meaningful distinctions, definitions and multiple models?
4) What is the coherent structure? recognizing that there is a pattern in the development of mathematical ideas as a concept becomes more complex?
5) What are "bridging" standards? Knowing what underlying concepts are in between to bridge the gaps between the standards
Learning trajectory for Multiplicative Reasoning
Concrete Modelers with Equal Groups-Children to solve multiplication problems with very small numbers by making equal groups and counting all the objects. They also solve division problems by dealing out one or more objects at a time. (https://www.learningtrajectories.org/math/multiplying-dividing/concrete-modeler-x )
Equal Groups with Parts and Whole-Predicts qualitatively the inverse relation between divisor and quotient in simple, concrete situations. Can re-assemble equal groups or parts to make the collection of the single whole as "n times as many (much)." (https://www.learningtrajectories.org/math/multiplying-dividing/parts-and-wholes-x )
Skip Counter-Uses repeated adding, additive doubling, or skip counting to solve multiplication and for measurement division (finding out how many groups) problems. Uses trial and error for partitive division (finding out how many in each group). Predicts, demonstrates, and justifies outcomes of equipartitioning collections.(https://www.learningtrajectories.org/math/multiplying-dividing/skip-counter-x )
Derived Facts-Uses strategies, patterns, de/composition (12 x 2 = 10 x 2 + 2 + 2) and derived combinations, such as multiplying x 9 as 10 – 1 or 7 x 8 from 7 x 7 + 7. Solves multidigit problems by operating on tens and ones separately. Quantitatively predicts the effects of changes in the number of people sharing one the size of the shares.(https://www.learningtrajectories.org/math/multiplying-dividing/deriver-x )
Array -Quantifier / Problem Solver x/÷- Solves many types of multiplicative problems, with flexible strategies and known combinations. Multidigit may be solved using combinations separately on ones and tens.(https://www.learningtrajectories.org/math/multiplying-dividing/array-quantifier-problem-solver-x )
Multiplicative Comparison -Figures out how many are in each group. May first repeatedly add a divisor until the dividend is reached.(https://www.learningtrajectories.org/math/multiplying-dividing/partitive-divisor )
Check out some curated resources below for LT-based instruction and build up Students' Math Power
to find Math strengths
to find Math strengths
Use formative assessment to find the edges of student understanding
Sequencing learning Activities
Sequencing the learning activities to bridge and advance student understanding
Building teacher agency
Teachers use LT and Resources to advance student understanding