Available courses

Counting & Cardinality

  • Know number names and the count sequence.
    • Count to 100 by ones and by tens.
    • Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
    • Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
  • Count to tell the number of objects.
    • Understand the relationship between numbers and quantities; connect counting to cardinality.
      • When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
      • Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
      • Understand that each successive number name refers to a quantity that is one larger.
    • Count to answer "how many?" questions about as many as 20 things in a scattered configuration.
  • compare numbers.
    • Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group.
    • Compare two numbers between 1 and 10 presented as written numerals.

    Number & Operations in Base Ten

    • work with numbers 11-19 to gain foundations for place value.
      • Compose and decompose numbers from 11 to 19 into ten ones and some further ones (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
    Operations & Algebraic Thinking:

    • Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
      • Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. (coming soon!)
      • Decompose numbers less than or equal to 10 into pairs in more than one way (e.g., 5 = 2 + 3 and 5 = 4 + 1).
      • For any number from 1 to 9, find the number that makes 10 when added to the given number.
      • Fluently add and subtract within 5.

    Number & Operations in Base Ten

    • Extend the counting sequence.
      • Count to 120, starting at any number less than 120.
    • Understand place value.
      • Understand that the two digits of a  two-digit number represent amounts of tens and ones.
        • 10 can be thought of as a bundle of ten ones - called a "ten."
        • The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
        • The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
      • Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
    • Use place value understanding and properties of operations to add and subtract.
      • Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
      • Given a two-digit number, mentally fine 10 more or 10 less than the number, without having to count.
      • Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences).

    Operations & Algebraic Thinking

    • Represent and solve problems involving addition and subtraction. (coming soon!)
      • Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.
      • Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20.
    • Understand and apply properties of operations and the relationship between addition and subtraction.
      • Apply properties of operations as strategies to add and subtract. Examples: To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.
    • Add and subtract within 20.
      • Relate counting to addition and subtraction. (e.g., by counting on 2 to add 2).
      • Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9).
    • Work with addition and subtraction equations.
      • 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.
      • Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? - 3, 6 + 6 = ?

    Number & Operations in Base Ten

    • Understand place value.
      • Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. 
        • 100 can be thought of as a bundle of ten tens - called a "hundred".
        • The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
      • Count within 1000; skip-count by 5s, 10s, and 100s.
      • Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
      • Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
    • Use place value understanding and properties of operations to add and subtract.
      • Fluently add and subtract within 100 using strategies based on place value and properties of operations.
      • Add up to four two-digit numbers using strategies based on place value and properties of operations.
      • Add and subtract within 1000. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
      • Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

    Operations & Algebraic Thinking

    • Represent and solve problems involving addition and subtraction. (coming soon!)
      • Use addition and subtraction within 100 to solve one- and two-step word problems involving situation of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.
    • Add and subtract within 20
      • Fluently add and subtract within 20 using mental stragegies. By end of Grade 2, know from memory all sums of two one-digit numbers.
    • Work with equal groups of objects to gain foundations for multiplication.
      • Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addend
      • Use addition to fine the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

    Number & Operations in Base Ten

    • Use place value understanding and properties of operations to perform multi-digit arithmetic.
      • Use place value understanding to round whole numbers to the nearest 10 or 100.
      • Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
      • Multiply one-digit whole numbers by multiplies of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
    Operations & Algebraic Thinking

    • Represent and solve problems involving multiplication and division. (coming soon!)
      • Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
      • Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
      • Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (coming soon!)
      • Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ? ÷ 3, 6 × 6 = ?
    • Understand properties of multiplication and the relationship between multiplication and division.
      • Apply properties of operations as strategies to multiply and divide. Examples: if  6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication). 3 × 5 × 2 can be found by  3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication). Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56 (Distributive property).
      • Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
    • Multiply and divide within 100.
      • Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
    • Solve problems involving the four operations, and identify and explain patterns in arithmetic.
      • Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
      • Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.