Algebraic reasoning - 4th grade

I solve a variety of simple pan balance (scales) problems using just logical reasoning. These "puzzles" prepare students to solve equations in later grades, and it's just fun!

I solve a variety of simple pan balance (scales) problems using just logical reasoning. These "puzzles" prepare students to solve equations in later grades, and it's just fun!

Once students have learned about division, it is time to learn a bit about the order of operations. You can draw a "bubble" or a "cloud" around the operation to be done first! That will make it kind of fun. :) This lesson uses the four basic operations plus parenthesis (no exponents or roots yet). In the 2nd part of the lesson, we write simple expressions that use several operations:

Once students have learned about division, it is time to learn a bit about the order of operations. You can draw a "bubble" or a "cloud" around the operation to be done first! That will make it kind of fun. :) This lesson uses the four basic operations plus parenthesis (no exponents or roots yet). In the 2nd part of the lesson, we write simple expressions that use several operations:

Students can start learning proportional reasoning in 4th grade (or earlier) with the help of ratio tables. I don't call them that in this video though, but that's what we are doing: first filling in these tables that show values for two quantities that vary proportionally, and then later using these tables to help us solve word problems. I don't use this type of language in the actual lesson though, so as to not confuse the students. The idea is very simple and accessible to anyone! Check out also my inexpensive math workbooks (actually worktexts) available for instant download, at

Students can start learning proportional reasoning in 4th grade (or earlier) with the help of ratio tables. I don't call them that in this video though, but that's what we are doing: first filling in these tables that show values for two quantities that vary proportionally, and then later using these tables to help us solve word problems. I don't use this type of language in the actual lesson though, so as to not confuse the students. The idea is very simple and accessible to anyone! Check out also my inexpensive math workbooks (actually worktexts) available for instant download, at

We write simple expressions (number sentences) from the verbal description, using several operations and parenthesis. In other words, we need to take into account the order of operations here! For example, subtract 12 and 6, and multiply the result by 4.... one needs parenthesis to make sure the subtraction happens BEFORE multiplication. If you write 12 - 6 x 4, the multiplication would be done first according to the order of operations. Therefore, the right answer is either 4 x (12 - 6) or (12 - 6) x 4. Lastly, we get to solve some puzzles where the operation signs are missing. Mathy my mascot mammoth is of course excited about that! The first part of the lesson explains the order of operations (using the four operations plus parenthesis), and is found here:

We write simple expressions (number sentences) from the verbal description, using several operations and parenthesis. In other words, we need to take into account the order of operations here! For example, subtract 12 and 6, and multiply the result by 4.... one needs parenthesis to make sure the subtraction happens BEFORE multiplication. If you write 12 - 6 x 4, the multiplication would be done first according to the order of operations. Therefore, the right answer is either 4 x (12 - 6) or (12 - 6) x 4. Lastly, we get to solve some puzzles where the operation signs are missing. Mathy my mascot mammoth is of course excited about that! The first part of the lesson explains the order of operations (using the four operations plus parenthesis), and is found here: