To mark the 10th anniversary of the Common Core's publication, here are my capsule-length reviews of selected K-8 standards:
(All reviews stolen from movie listings posted daily in The New York Times.)
By the end of Grade 3, know from memory all products of two one-digit numbers.
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false?
6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2
Top notch existential confusion
Understand that attributes belonging to a category of two-dimensional figures also belongs to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
Develop a probability model (which may not be uniform) by observing frequencies in the data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
Predictable but hard to hate
Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.
Disaster by the numbers
Analyze and solve pairs of simultaneous equations.
Zoom, crash, repeat
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.
Almost willful lack of fun
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
Answers questions no one needed to ask
Use place value understanding to round multi-digit whole numbers to any place.
Blunt and sadistic
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies using $ and ¢ symbols appropriately. For example, if you have 2 dimes and 3 pennies, how many cents do you have?
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units--whole numbers, halves, or quarters.
Best when no one's talking
Solve multi-step real life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example, if a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches for each edge; this estimate can be used as a check on the exact computation.
Turgid schedule filler
Fluently multiply multi-digit whole numbers using the standard algorithm.
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
Model shapes in the world by building shapes from components (i.e. sticks and clay balls) and drawing shapes.
Broad, freewheeling fun
|h/t Pauline Kael|