## 3rd Grade Power Standards (also refer to 2nd and 1st grade skills)

3.1.1.1-3.1.1.5

- Read, write and represent whole numbers up to 100,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives such as bundles of sticks and base 10 blocks.
- Use place value to describe whole numbers between 1000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones.
- Find 10,000 more or 10,000 less than a given five-digit number. Find 1000 more or 1000 less than a given four- or five-digit number. Find 100 more or 100 less than a given four- or five-digit number. 3.1.1.4 Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences.
- Compare and order whole numbers up to 100,000.

__Background Knowledge:__

- Read and write numbers up to 1000.
- Represent whole numbers up to 1000 using words, pictures, and numerals.
- Represent whole numbers up to 1000 using hundreds, tens, and ones. For example, 844 is the same as 800 + 40 + 4, or 8 hundreds, 4 tens and 4 ones, or 6 hundreds and 24 tens and 4 ones, or 844 ones, or 84 tens and 4 ones).
- round three digit numbers up and down to the nearest 10 and 100.
- compare and order numbers to 1000.
- estimate sums and differences up to 100.

__Mastery Expectations:__

- Read and write whole numbers up to 100,000.
- Represent whole numbers up to 100,000 using words, pictures, numerals, expressions with operations, and number lines.
- Using base ten materials, represent numbers from 1000 to 100,000 using ten thousands, thousands, hundreds, tens and ones.
- Represent numbers from 1000 to 100,000 in written form. For example, 4,756 can be represented as 4000 + 700 + 50 + 6 or as 4700 + 56, or as 47 hundreds and 56 ones, or 45 hundreds and 25 tens and 6 ones, or four thousand seven hundred fifty six.
- Identify value and place in large numbers, for example, in the number 4,756, 7 is in the hundreds place and has a value of 700.
- round four and five-digit numbers to the nearest 10,000, 1,000, 100 and 10.
- use rounding to estimate sums and differences.

3.1.2.1-3.1.2.5

- Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms.
- Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Assess the reasonableness of results based on the context. Use various strategies, including the use of a calculator and the relationship between addition and subtraction, to check for accuracy.
- Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division.
- Solve real-world and mathematical problems involving multiplication and division, including both "how many in each group" and "how many groups" division problems.
- Use strategies and algorithms based on knowledge of place value and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties.

__Background Knowledge:__

- Composing and decomposing numbers. For example, adding 84 and 37 could include 80 and 20 and 10, then adding 4 and 7 or 84 + 37 = (80 + 4) + (20 + 10 +7) = 80 + 20 + 10 + 4 +7.
- Knowledge of "making a 10" to include making multiples of 10 to add and subtract more efficiently.
- Understand place value up to the thousands place.
- Place value understanding when adding and subtracting with two-digit numbers.
- Use multiple strategies to solve problems involving addition and subtraction.
- Round numbers to the nearest 10, 100.
- Write numbers in expanded form.
- Estimate sums and differences up to 100.
- Knowledge of basic addition and subtraction facts.
- Use a variety of strategies to solve problems.
- Use base-ten blocks to complete problems by grouping in ones, tens and hundreds.
- Round numbers to the nearest 10, 100 and add the rounded numbers.
- Understand place value up to but not including the thousands place.
- Understand the concept of adding and subtracting.
- Know basic addition and subtraction facts.
- Complete rep.

__Mastery Expectations:__

- Apply place value understanding when adding and subtracting multi-digit numbers. Students develop meaningful strategies to subtract across zero in three- and four-digit numbers.
- Solve real-world and mathematical problems involving multi-digit addition and subtraction using a variety of strategies. These strategies include assessing reasonableness of results, use of technology and the relationship between addition and subtraction, place value understanding when using the standard algorithm.
- Use multiple strategies to compose and decompose numbers flexibly in problem solving situations.
- Demonstrate an understanding of the relationship between addition and subtraction and using one of these operations to check for reasonableness of the answer.
- Compose and decompose numbers. For example, adding 184 and 37 could include 180 and 30, then adding 4 and 7 or 184 + 37 = (180 + 4) + (20 + 10 +7) = 180 + 20 + 10 + 4 +7.
- Expand their knowledge of "making 10" to include making multiples of 10 or 100 or 1,000 to add and subtract more efficiently.
- Demonstrate an understanding of multiplication being how many groups times how many in a group.
- Demonstrate multiplicative thinking by understanding that multiplication involves. counting groups of like size and determining how many there are in all.
- Understand that multiplication and division are related and inverse operations.
- Demonstrate an understanding of multiplication as repeated addition and division as repeated subtraction.
- Complete multiplication and division problems using a variety of strategies including: repeated addition, constructing arrays, breaking apart two- or three-digit times one-digit multiplication problems to solve, using repeated subtraction.
- Use knowledge/skills of one-digit multiplication to complete two- or three-digit by one digit multiplication problems.
- Group objects in rows and columns or use manipulatives to form an array in completing a multiplication problem.
- Separate objects into groups either by drawing or using manipulatives to complete a division problem.
- Solve division problems involving
*How many in each group?*and*How many groups?* - Recognize the concept of multiples of numbers (i.e. 6, 9, 12 are multiples of three and the same as multiplying 3 x 2, 3 x 3, and 3 x 4).

3.1.3.1-3.1.3.3

- Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line.
*For example*: Parts of a shape (3/4 of a pie), parts of a set (3 out of 4 people), and measurements (3/4 of an inch). - Understand that the size of a fractional part is relative to the size of the whole.
*For example*: One-half of a small pizza is smaller than one-half of a large pizza, but both represent one-half. - Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator.

__Background Knowledge:__

- Compare and order whole numbers up to 1000
- Understand greater than and less than
- Informal knowledge of a half

__Mastery Expectations:__

- read fractions written in word form and number form.
- identify fractions as parts of a whole, parts of a set and points/distances on a number line
- understand the meaning of the numerator and denominator.
- translate between concrete and symbolic representations of fractions
- demonstrate the size of a fraction in comparison to the whole using multiple fraction models, fraction circles, fraction bars, grids, number lines, etc. ( how many pieces of each size do you need to make a whole).
- understand that as the number of equal pieces of a whole increases the size of each piece decreases in size
- understand a fraction 1/
*b*as the quantity formed by 1 part when the whole is partitioned into*b*equal parts; understand a fraction*a*/*b*as the quantity formed by a parts of size 1/*b*. - represent a fraction 1/
*b*on a number line diagram 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 diagram by marking off a lengths 1/*b*from 0. Students will recognize that the resulting interval has size*a*/*b*and that its endpoint locates the number*a*/*b*on the number line. - compare and order unit fractions and fractions with like denominators

3.4.1.1

- Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units.

__Background Knowledge:__

- pose questions and gather data about themselves and their surroundings.
- represent data using concrete objects, pictures, and graphs.
- describe parts of the data and the set of data as a whole to determine what the data show.
- understand that titles and labels are needed on data representations so the information can be interpreted correctly.
- use the information on a graph to answer questions.

__Mastery Expectations:__

- formulate questions and collect data.
- organize and classify data from surveys and questionnaires using a tally chart or frequency table.
- understand the concept of scale and key in a data representation.
- display data using
- frequency tables,
- bar graphs,
- picture graphs (keys not exceeding 5),
- number line plots with scale increments not exceeding 5.
- understand that appropriate titles, labels, units, and keys are needed on data representations so the information can be interpreted correctly.
- describe parts of the data and the set of data as a whole to determine what the data show.
- use the information on a graph to answer questions.