5th Grade Algebraic Thinking Resources
This applet, while designed primarily to accompany contextual multiplication and division tasks, will work to illustrate any situation in which students are multiplying or dividing whole numbers. The main thinking behind it is that students can struggle with conceptualizing the three components of the majority of these problems: total number of objects, number of groups, and objects in each group. By providing a visual to accompany their thinking, we can help them to see the math they are doing, whether correct or incorrect based on the context. A specific way of using this would be to pair it with the Mathematical Language Routine Co-Craft Questions. Provide the beginning of the stem (like "Four friends have a recipe that makes 15 cookies"), and use this to help students consider different questions they could pose based on it.
An Egyptian fraction is the expansion of a non-unit fraction into a sum on unique unit fractions. For instance, 2/3 = 1/2 + 1/6 is an Egyptian fraction expansion, while 2/3 = 1/3 + 1/3 (not unique) and 2/3 = 1/3 + 2/9 + 1/10 + 1/90 (not all unit fractions) are not. Use this resource to explore these ideas, while getting some visual supports and an answer if needed. The provided answer is generated with what is called the Greedy Algorithm, which is not always the "best" expansion. See https://en.wikipedia.org/wiki/Egyptian_fraction for further explanation.
A random function (or "rule") is generated based on the sliders. Send the numbers through the machine to figure out what the rule is. Click on the boxes to see the rule in equation or word form. Alternatively, show the rule then predict the outputs before sending the number through.