"The student and I began this lesson discussing the definition of key math terms:
He was asked to define each term; initially, he only defined quotient correctly and left the remaining terms blank. When I asked him to review the definitions he'd written, he remembered the definitions of the remaining words. He needs further review of the product term; though he recalls it eventually, his recall should be close to automatic; I will review the term in isolation and in context of brief word problems (as they are likely to appear on the ISEE). It is good that he recalled the terms independently, I just want to save him some time on the actual test. Revising answers and revisiting difficult questions is always encouraged when any student finishes a section early, but it is preferable that questions are answered correctly on the first read-through.
He was well-focused during this lesson. As a high point, he created a rectangular array as a visual aid to solve a probability problem. In this problem he was given a part to part ratio describing the quantitative relationship between two differently colored roses in a bouquet. He also given the total number of roses in the bouquet; using this information, he was asked to determine the total number of each colored rose in the bouquet. He drew an array of dots-four rows, six dots in each row, each dot representing a rose. He followed the part to part ratio, quickly divided up the dots as white or red (the two colors) and came up with a total answer. In an earlier lesson, I showed him how to use rectangular arrays to interpret ratios; I am impressed that he took the initiative to translate a word problem into a visual image, and then was able to use the image to deduce both answers.
I will continue to review the method for the method for solving probability problems that involves equating similar proportions (part to part vs part to total).
He was given a list of shape properties and asked which property belonged to a triangle. He chose "two sides are of equal length"ù; while this is true of specific type of triangle, it is not a general truth of triangles. The correct answer was "interior angles add up to 180 degrees"ù; We will continue to review relevant shape properties (Squares, Rectangles, and Triangles)
He correctly decoded and solved a word problem. He first had to select an operation, the keywords that signaled the operation, He correctly converted each of four fractions to decimals; when given the area of a rectangle and its length, he correctly inferred the width of the rectangle. When given a series of equations, each identifying a number property (with letters), he incorrectly identified the equation illustrating the commutative property instead of the distributive property; I will prepare a number properties review series (showing each property with numbers and letters) for the next lesson.
I gave him a set of 6 numbers and asked him to calculate four measures of central tendency. He correctly calculated the mean, mode, and range. The median was the average of two middle numbers. He slightly miscalculated (90.5 instead of 91.5). I will review the median in particular in our next session
We did a brief verbal review in which he answered 4/6 multiple-choice synonym questions. The words he missed were corrected and will be included in future review sessions. To assess his ability to deduce the meaning of a word based on the meaning of its prefix. I asked him to define recollect, given that he has had many words in vocab review with the re- prefix. He defined as "doing it (collecting) a second time"ù; the most common meaning of recollect is to remember, but without any syntactical context, the meaning he synthesized is correct.
I emailed him a math review packet following the lesson and asked his parents to have him bring a printout copy ( I will bring one, too, of course) to our next lesson.