Idea map

Everything a student learns here, and what each idea builds on. This page is a placeholder.

addition

• Changing order or grouping does not change a sum (skill)
• Count on from a number instead of counting everything (skill)
• Solve every kind of adding and subtracting story within 20 (skill)
• Subtracting is finding a missing part (skill)
• Add and subtract within 20 using strategies (skill)
• Act out putting together and taking away with things (skill)
• Add and subtract within 10 (skill)
• Split numbers up to 10 into parts, and find the partner that makes ten (skill)

counting

• Count out up to 20 things in any arrangement (skill)
• Each counting number is one more than the last (skill)
• Match one number word to each thing counted (skill)
• Tell which group or number is more, less, or the same (skill)
• The last number said tells how many there are (skill)
• Say the counting numbers in order, by ones and by tens (skill)

equality

• Find the missing number that makes both sides equal (skill)
• The equal sign means both sides are the same amount (skill)
• Adding nothing leaves a thing as it was (principle)
• A letter can stand for a thing or for how much it weighs (concept)
• A level scale means both sides weigh the same (concept)
• A thing is equal to itself (principle)
• Do the same to both sides and the scale stays balanced (principle)
• If one thing equals another, the second equals the first (principle)
• None of a thing weighs nothing (principle)
• One of a thing is just that thing (principle)
• Putting two things together weighs the same in either order (principle)
• Something can be swapped for anything it equals (principle)
• Two things equal to the same thing are equal to each other (principle)

fractions

• Cut a whole into equal shares: halves, thirds, fourths (skill)
• Compare fractions with the same top or the same bottom number (skill)
• Fractions as points on a number line (skill)
• One part of a whole cut into equal parts, and counting those parts (skill)
• Simple equal fractions, and whole numbers written as fractions (skill)
• Add and subtract fractions with the same denominator, including mixed numbers (skill)
• Compare decimals to hundredths (skill)
• Compare fractions with different denominators (skill)
• Multiply a fraction by a whole number (skill)
• Multiplying top and bottom by the same number keeps a fraction's value (skill)
• Tenths and hundredths as fractions and as decimals (skill)
• Add and subtract fractions with different denominators (skill)
• Multiply a fraction by a fraction (skill)
• Multiplying can make a number bigger or smaller (skill)

geometry

• Build a triangle with three equal sides using compass and straightedge (skill)
• Copy a length with a compass (skill)
• Cutting a shape up and moving the pieces keeps its area (principle)

measurement

• Length is how many units fit end to end (skill)
• Cut a rectangle into rows and columns of equal squares (skill)
• Whole numbers as distances on a number line (skill)
• A measurement says how many, and of what (concept)
• Grams are a unit for how heavy something is (concept)

multiplication

• Equal groups and arrays as repeated adding (skill)
• A rectangle's area is its rows times its columns (skill)
• A times B means A groups of B (skill)
• Dividing as sharing out or as making groups (skill)
• Dividing is finding a missing factor (skill)
• Multiply and divide within 100 quickly and surely (skill)
• Order, grouping and splitting a factor in multiplication (skill)
• Solve multiplying and dividing stories within 100 (skill)
• Multiply larger numbers place by place (skill)
• Times as many: comparing by multiplying (skill)

place-value

• A two-digit number is tens and ones (skill)
• Compare two-digit numbers by their tens and ones (skill)
• Add and subtract within 100 using tens and ones (skill)
• A three-digit number is hundreds, tens and ones (skill)
• Add and subtract within 1000, trading between places (skill)
• Each place is worth ten of the place to its right (skill)
• A teen number is a ten and some ones (skill)

som

• Get the unknown by itself on the scale and read what it weighs (skill)
• Make any amount up to 15 from weights that double: 1, 2, 4, 8 (skill)
• Multiply numbers split into parts with an area diagram (skill)
• Show and read numbers on an abacus (skill)
• Two of the same weight trade for the next weight up (carrying) (skill)
• Weigh something on a steelyard by sliding a known weight along the arm (skill)
• Write down what is on each side of the scale (skill)