Interpret a multiplication equation as equal groups (e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each). Represent verbal statements of equal groups as multiplication equations.
Represent the concept of multiplication of whole numbers with the following models equal-sized groups, arrays, area models, and equal 'jumps' on a number line. Understand the properties of 0 and 1 in multiplication.
Represent the concept of division of whole numbers with the following models partitioning, sharing, and an inverse of multiplication. Understand the properties of 0 and 1 in division.
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).
Multiply and divide within 100 using strategies, such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 5 = 8), or properties of operations.
Create scaled picture graphs, scaled bar graphs, and frequency tables to represent a data setincluding data collected through observations, surveys, and experimentswith several categories. Solve one- and two-step how many more and how many less problems regarding the data and make predictions based on the data.
Identify and describe the following cube, sphere, prism, pyramid, cone, and cylinder.
Tell and write time to the nearest minute from analog clocks, using a.m. and p.m., and measure time intervals in minutes. Solve realworld problems involving addition and subtraction of time intervals in minutes.
Find the value of any collection of coins and bills. Write amounts less than a dollar using the symbol and write larger amounts using the $ symbol in the form of dollars and cents (e.g., $4.59). Solve real-world problems to determine whether there is enough money to make a purchase.
Read and write whole numbers up to 10,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 10,000.
Represent a fraction, 1/b, on a number line by defining the interval from 0 to 1 as the whole, and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
Represent a fraction, a/b, on a number line by marking off lengths 1/b from 0. Recognize that the resulting interval has size a/b, and that its endpoint locates the number a/b on the number line.
Understand two fractions as equivalent (equal) if they are the same size, based on the same whole or the same point on a number line.
Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent (e.g., by using a visual fraction model).
Compare two fractions with the same numerator or the same denominator by reasoning about their size based on the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model).
Use place value understanding to round 2- and 3-digit whole numbers to the nearest 10 or 100.