Building blocks of Common Core math: A grade-by-grade look
PRESCHOOL
Concepts: Numbers as amounts, counting to 10, comparing, sorting
Strategies: Count everything, stack, sort, measure.
Tips: Expect mistakes. Recount with them. Celebrate discovery.
KINDERGARTEN
Concepts: Counting to 100, add/subtract up to 10 using objects and drawings, and up to 5 by recall; seeing adding as putting things together (composing) and subtracting as taking them apart (decomposing); identify and describe shapes
Strategies: Put toys in order by size, count down days on the calendar, play with measuring cups (helps fractions make sense later); play board games, dominoes and easy card games; use laundry to add, subtract socks; count out forks for dinner.
Tips: Any quantity, distance or size is an opportunity to ask math questions. Use car rides to look for car colors, shapes, numbers.
FIRST GRADE
Concepts: Count to 120; add/subtract up to 100 using objects, strategies or drawings; solve simple equations; understand place values; tell time to half hour and hour; measure lengths with objects like paper clips or cereal pieces.
Strategies: Try counting starting at different numbers, not always 1; talk through figuring out how big a closet is, what shapes can fit inside.
Tips: Mix up equations, like 8 + ? =11, to foster thinking through the logic of a problem.
SECOND GRADE
Concepts: Add/subtract to 1,000 using objects, strategies or drawings; understand place values to 1,000; know odd and even; time units up to a year; measure lengths in centimeters and inches.
Strategies: Count by 2s, 5s, 10s and 100s as a chant for repetition; use greater-than, less-than symbols when comparing.
Tips: Talk through two-step word problems with drawings and graphs; describe shapes by numbers of sides, size of angles and volume.
THIRD GRADE
Concepts: Introduction to fractions, multiply/divide to 100 using equal groups called arrays, understand dividing can have remainders (an unequal group), by end of year, know multiplication facts from 1 x 1 through 9 x 9 from memory.
Strategies: Put numbers and fractions on number line, divide shapes to show fractions, working with area and perimeter.
Tips: Talk about fractions like 1/4 as 1 whole divided into 4 equal parts. Use rounding to nearest 10 or 100 to check reasonableness of answers.
FOURTH GRADE
Concepts: Understand place values to 1 million, different but equal fractions (like 1/2 and 2/4 ), decimal notation for fractions, convert measurements; know how to multiply and divide whole numbers using strategies; easily add and subtract traditional column problems.
Strategies: Identify shapes by lines and angles; word problems using comparisons (Alaska is how many times as big as California?); analyze patterns in strings of numbers.
Tips: Talk about how problems might be solved in other ways – being able to summarize and clarify will help in writing tasks, as well as math. Work with money as decimal figures in problems.
FIFTH GRADE
Concepts: Multiply, subtract, divide, estimate fractions with unlike denominators with understanding; understand volume and cubic measurement; easily multiply using traditional column notation.
Strategies: Graph points on the coordinate axis to solve real-world problems, use brackets to organize equations like 3 x (8+2) = 30.
Tips: Practice rounding numbers as a way of estimating. Work on conceptualizing three-dimensional spaces as shapes with volume.
SIXTH GRADE
Concepts: Connect ratio and rate to whole number multiplication and division; write, interpret and use simple equations; easily divide using traditional column notation.
Strategies: Use ratios to solve problems and make sense of statistics; use tables and charts to explain problems, get data.
Tips: Work with statistics in the news or sports scores to make comparisons, draw inferences; figure out miles per gallon, miles per hour, cost per pound, dollars per hour and percents (like tips, tax, discounts)
Sources: California Department of Education and Stanislaus County Office of Education
At every grade
1. MAKE SENSE OF PROBLEMS: As in life, success in math takes focus and perseverance.
2. REASON ABSTRACTLY AND QUANTITATIVELY: Math problems require students not only to consider how to find the answer with the numbers given, but to see if their answer makes sense in the context of the problem.
3. CONSTRUCT ARGUMENTS: Math problems can be solved with evidence (like measurements) or logic. Exploring, testing and trying things out in a group takes the ability to explain an idea and hear alternatives.
4. MODEL WITH MATHEMATICS: Attack a real-world problem with drawings, diagrams and equations. That step-by-step concrete process helps in finding solutions. Finding the area of a rectangle on a page or a square of grassy lawn is the same math problem.
5. USE TOOLS APPROPRIATELY: Using a ruler, a compass, a drawing (like a tape diagram), a graphing calculator or computer program also takes knowing what they can and cannot do.
6. ATTEND TO PRECISION: Students need to be precise to get the right answer, being attentive with the numbers given and the operations they use, and using precise language to describe the process. Precision is simply being intentional about what you say and do in math.
7. LOOK FOR AND USE STRUCTURE: Finding logical order. Seeing patterns in math – the structure of numbers, equations or geometric objects – helps with big-picture thinking and identifying efficient strategies.
8. LOOK FOR REPEATED REASONING: Seeing past the details and finding common patterns simplifies the work and expands understanding. Students find shortcuts because they understand the math reasoning behind them.
This story was originally published March 16, 2016 at 3:56 PM with the headline "Building blocks of Common Core math: A grade-by-grade look."