Learning Series Book
SumBlox Building Blocks teach a wide range of mathematics through guided, hands-on discovery in our SumBlox Learning Activities. Currently available are series that teach addition and subtraction, multiplication, and fractions. Each series empowers the educator to gradually move students to a deeper understanding of the properties of math through step-by-step investigations, engaging discussions and fun challenges.
Teacher: Today we are going to continue to explore adding fractions with different denominators. Let’s start with adding 1/2 and 2/3.
Write 1/2 + 2/3 = ___ and have each student set up their own model.
Teacher: Think about what needs to change so that we can combine these two fraction addends?
Allow think-time and then have each student share.
Student: We need to change one or all of the fractions to an equivalent form so that we are using the same sized whole for both of them.
Teacher: Which fraction do we want to change first?
Student: We should start with the one using the smaller whole, or the fraction with the smaller denominator in the equation, because it is possible that we do not have to change the larger whole at all.
Teacher: How would you change 1/2 but keep its value?
Student: I would start by doubling everything to get an equivalent form.
Teacher: Go ahead and test your prediction.
Allow time for students to discuss and experiment with the blocks to build their equivalent stack.
Teacher: Does your new stack have a value of 1/2?
Student: Yes, 2/4 has the same value as 1/2.
Teacher: Are the size of the two addends’ wholes equivalent?
Student: No, 1/2’s whole is now slightly larger than 2/3’s whole.
Teacher: Let’s move to the 2/3 addend and change it to an equivalent fraction, maybe then we can change the ½ more to find a whole that can be used for both addends. Remember, in some equations you will have to change all of your addends so that they are using the same sized wholes. We also want to change as little as possible so let’s try doubling everything in 2/3.
Allow time to manipulate blocks.
Teacher: What is your new equivalent fraction?
Student: The new equivalent fraction is 4/6.
Teacher: Are the two wholes now equivalent?
Student: No, they are not equivalent.
Teacher: Is it possible to combine the addends at this point?
Student: No, we still do not have equally sized parts, or equally valued parts, because the wholes are not equivalent.
Teacher: We will need to revisit our stack and change it by a greater amount. Before we can change it, remember that we must go back to its original form, so reset your fraction.
Teacher: We have already tried doubling everything, but it was not enough and now we are using a 6-block as the whole. What do you think we should try next and why?
Student: I can see that it would take three 2-blocks to make an equivalent whole. So, we need to triple everything.
Teacher: Test your idea with the blocks.
Allow time to experiment with tripling and then have each student explain what he or she observes.
Teacher: Are the two wholes equivalent?
Teacher: What is the value of each whole? Explain.
Student: They both have a value of 6 because 2 x 3 is 6 and 3 x 2 is also 6.
Teacher: Let’s place a 6-block in front of our whole stacks so we can see this relationship.
Have a student rewrite the new equivalent equation under the original: 3/6 + 4/6 = ___.
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