Award-Winning Math Tutors serving Cambridge

The student and I reviewed adding mixed and improper fractions from our previous lesson. We then moved on to multiplying fractions that required several steps in order to find the final answer. ( Ex 4 1/8 x 4 2/8) first, we had to change the fraction to an improper fraction, multiply it, divide, and then changing it back to a mixed fraction. The problems were much tougher but she did a good job executing the problem and working independently.

Worked on multiplying two digit numbers. Learned a shortcut to multiplying a two digit number ending in zero. Worked on division word problems. Reviewed long division and practiced dividing three digit numbers by one digit numbers.

The student had a very hard time remembering skills she's already mastered, but she pushed through it. The perseverance she showed was incredible, and I would say our session was the best one yet.

Today we went through the Common Core for 6th and 7th together, discussing what we have covered, what she already knew, and what she both needed to learn or practice more. Then we jumped in with using a protractor, measuring angles, drawing angles. Then we reviewed a compass, how to find area and circumference of a circle. We worked on ratios, setting them up, simplifying, determining if correct, and filling in a variable. We also worked on area and perimeter of irregular polygons, and more.

Reviewed the topics that are most likely to be featured on the student's upcoming math placement test. Concepts included addition and multiplication with fractions, conversion from improper fractions to mixed numbers and vice versa, fraction reduction, and word problems.

The student did poorly on a math pop quiz involving adding and subtracting mixed numbers, so we spent some time looking at what he did wrong. His mom had him re-do all of the questions that he got wrong on the quiz prior to my arrival. It looks like he was not simplifying his final answer correctly. When he had a mixed number that he needed to reduce to lowest terms, he simplified not only the fraction, but the whole number as well. We identified this problem and corrected it. We did many new problems to correct this method, and try to get the wrong method out of his head. The student impressed me with his knowledge of how to subtract mixed numbers, when the second number was bigger than the first. It involves borrowing from the first mixed number and making it into an improper fraction. He knew how to do this, and was quite good at it. We practiced some of these questions anyway. He will bring me the actual quiz that he did poorly on the next time I see him, so that I can identify where he went wrong with this. His teacher said that he will now work on multiplying and dividing fractions for the rest of the week. I showed him two different ways to divide fractions, and let him choose the method he prefers, which is cross multiplication. He has an excellent grasp of this concept. We practiced some of these, but he could use more practice because he is still attempting to put the denominator on the top of the fraction when using cross multiplication. This is a common error, which can only be corrected with a lot of practice. The final topic that the student will do in school involves multiplication and division of decimals. We will work on these in the future.