Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
These challenges require higher-order thinking and an understanding of using Venn diagrams to find the GCF and LCM. This is how I have always taught these concepts to all students, and a written explanation with step-by-step directions is included.
Students are not given numbers and asked to find the GCF and LCM, but rather are given clues and asked to find the numbers. They will use the same concept, but will use it in reverse and use reasoning to place the remaining factors.
There are 12 mystery cards with 2 numbers. Mysteries I, J, K, and L require more reasoning. To promote higher-order thinking, you could also ask students to find which mysteries have more than one solution and why that is true. Answers are included, and the answers have a Venn diagram so students can understand the solution.
These could be used in centers. They could also be used as a formative assessment, because everyone at the table could easily have a different task. The more challenging tasks allow you to differentiate.
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