8.2 SESAT and TASK Mathematics: Kindergarten Number Sense and High School Mathematics

One Mathematics Subtest at the Two Ends of the Battery

From Primary 1 through Advanced 2, Stanford 10 splits mathematics into Mathematics Problem Solving and Mathematics Procedures. At the two ends of the series there is a single combined Mathematics subtest:

Pearson describes the same four concept areas at every level, "number sense and operations; patterns, relationships, and algebra; geometry and measurement; and data, statistics, and probability," and says the subtests "provide consistency in names of content clusters across levels." What changes is the depth.

SESAT Mathematics (Kindergarten)

At the SESAT levels the teacher reads the questions aloud, and children answer by marking pictures or numbers in the booklet. The mathematics is what kindergarten classrooms teach:

Story problems are spoken, not read. A typical kindergarten problem: "Sam had 3 apples. He got 2 more. How many apples does Sam have now?" The child must hold the story in mind, so practicing short spoken story problems at home is the best preparation.

TASK Mathematics (Grades 9-12)

The Arkansas Department of Education's Stanford 10 guide describes TASK Mathematics this way: it "assesses essential elements of a true high school curriculum. Although every item can be solved by reasoning and an understanding of general mathematics, topics from algebra, geometry, trigonometry, statistics, and discrete mathematics are included." It adds that, as at all levels, the emphasis is on skills and concepts in real contexts.

Testing tools at TASK: calculators are an option (a local decision), rulers are used, and a mathematics reference sheet provides the formulas needed.

Algebra

• Linear equations and slope: the slope of the line through $(2, 5)$ and $(6, 13)$ is $\frac{13 - 5}{6 - 2} = 2$.
• Systems: if $x + y = 10$ and $x - y = 4$, adding the equations gives $2x = 14$, so $x = 7$ and $y = 3$.
• Rates and proportions: a car that travels 150 miles on 5 gallons gets 30 miles per gallon.

Geometry

• Pythagorean theorem: a right triangle with legs 6 and 8 has hypotenuse $\sqrt{6^2 + 8^2} = 10$.
• Similar figures: corresponding sides are proportional, so a 3-4-5 triangle scaled by 2 becomes 6-8-10.
• Area and volume: use the reference sheet, but know when each formula applies.

Trigonometry (right triangles)

For an acute angle $A$ in a right triangle:

$$\sin A = \frac{\text{opposite}}{\text{hypotenuse}}, \quad \cos A = \frac{\text{adjacent}}{\text{hypotenuse}}, \quad \tan A = \frac{\text{opposite}}{\text{adjacent}}$$

Example: with a $30^\circ$ angle and hypotenuse 10, the side opposite the angle is $10 \times \sin 30^\circ = 10 \times 0.5 = 5$.

Statistics

Compare mean and median when data are skewed, read box plots and scatterplots, and recognize when a sample is biased. One very large salary raises a mean far more than it raises the median.

Discrete Mathematics

• Counting principle: 3 shirts and 4 pairs of pants make $3 \times 4 = 12$ outfits.
• Combinations: choosing 2 students from 5 when order does not matter gives $\frac{5 \times 4}{2} = 10$ pairs.
• Probability: the chance of rolling a sum of 7 with two dice is $\frac{6}{36} = \frac{1}{6}$.

Common TASK Mistakes

• Answering the wrong question: solving for $x$ when the item asks for $2x + 1$.
• Unit slips: mixing inches and feet in an area problem, or forgetting that area is in square units.
• Calculator over-reliance: a calculator does not choose the right operation, so estimate first and check that the result is reasonable.
• Misreading graphs: check the axis labels and scale before reading values from a scatterplot or line graph.

Preparation Tips for Each End of the Battery