## 4th Grade Power Standards (also refer to 3rd, 2nd and 1st grade skills)

4.1.1.1-4.1.1.6

4.1.2.1-4.1.2.7

· accurately add and subtract fractions with like denominators and describe the process for this computation.

4.3.2.1-4.3.2.4

4.3.2.1-4.3.2.4

- demonstrate fluency with multiplication and division facts
- use understanding of place value to multiply by 10, 100, 1000
- multiply multi-digit #s, using efficient & generalizable procedures based on knowledge of place value - incl. standard algorithm
- estimate products & quotients of multi-digit whole numbers to assess reasonableness of solutions
- solve multi-step story problems using add/sub/mult of multi-digit whole numbers
- divide multi-digit whole #s by 1- or 2-digit numbers; strategies include: mental math, partial quotients, commutative, associative, distributive properties, and repeated subtraction

__Background Knowledge:__- experiences with array models, skip counting, and relationships among facts (fact families)
- understanding the
*concepts*of multiplication and division - understand the relationship between multiplication and division
- relate multiplication to repeated addition
- relate division to repeated subtraction
- understanding equal groupings and shared model for multiplication;
- understanding the relationship between multiplication and division;
- strategies to accurately find the product of multiplication of a 2 or 3 digit number by a single digit.
- understanding how to solve real world and mathematical problems that include both "how many in each group" and "how many groups" as a means of solving sharing (division) problems;
- using various strategies to represent division facts such as repeated subtraction, equal sharing and forming equal groups;
- recognizing the relationship between multiplication and division.

__Mastery Expectations:__- Demonstrate fluency with multiplication and division facts.
- multiply one- and two-digit numbers by 10, 100 and 1000;
- use rounding, knowledge of benchmarks and place value to make a reasonable estimate of the product or quotient of a multi-digit problem;
- assess the reasonableness of answers and apply more than one strategy to check their work;
- understand and explain why the solution strategies work based on place value and properties of operations, and use them to solve problems;
- solve multi-step addition, subtraction and multiplication problems with solutions less than 100,000;
- accurately solve multi-digit multiplication problem: a one- or two-digit by a two- or three-digit number.
- solve both partitive and measurement division problems with dividends containing at most three-digits;
- develop fluency with efficient procedures for dividing whole numbers with dividends containing at most three digits;

- apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they
- develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends;
- select and accurately apply appropriate methods to estimate and mentally calculate quotients;
- explain what a remainder means and how to use it when finding a solution to a division problem. These division problems need to be in a context

4.1.2.1-4.1.2.7

- represent equivalent fractions using models: sets, circles, strips, number lines, other manipulatives & use models to determine equivalence
- locate fractions on number line - use models to order & compare whole #s & fractions, incl mixed #s & improper fractions
- use fraction models to add/sub fractions with like denominators; develop rule for add/sub of fractions with like denominators
- read/write decimals with words & symbols; describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths, thousandths
- compare/order decimals & whole #s using place value, number line, grids, Base 10 blocks
- read/write 10ths, 100ths in decimal & fraction notation; know fraction & decimal equivalents for halves & fourths
- round decimal values to nearest tenth

__Background Knowledge:__- know fractions can represent parts of a set, parts of a whole, a point on a number line as well as distance on a number line
- understand the concept of numerator and denominator
- understand that the size of a fractional part is relative to the size of the whole (a half of a small pizza is smaller than a half of a large pizza but both represent one-half)
- compare and order unit fractions
- compare and order fractions with like denominators
- read, write and represent whole numbers up to 100,000
- compare and order whole numbers
- used place value to represent numbers up to 100,000
- round whole numbers to the nearest ten thousand, thousand, ten and one.

__Mastery Expectations:__- use fraction models, including the following, to represent and determine equivalent fractions
- parts of whole--fractions circles, fraction strips
- parts of a set
- number lines
- use models to compare and order whole numbers, fractions, including mixed numbers and improper fractions.

· accurately add and subtract fractions with like denominators and describe the process for this computation.

- Students will be able to:
- read and write decimals using words and symbolic notation
- describe decimals in terms of place value (thousands, hundreds, tens, ones, tenths, hundredths and thousandths)
- compare and order decimals
- place decimals on a number line
- represent tenths and hundredths in both fraction and decimal form
- know fraction and decimal equivalents for halves and fourths
- round decimals to the nearest tenth.

4.3.2.1-4.3.2.4

- measure angles in geometric figures & real-world objects with protractor or angle ruler
- compare angles according to size; classify angles as acute, right, obtuse
- area of 2-D figure can be found by counting the total # of same size square units; justify why length & width are multiplied to find area of rectangle
- find areas of geometric figures & real-world objects that can be divided up into rectangular shapes - use square units to label area measurements

__Background Knowledge:__- Students have previously worked in building polygons based on the number of vertices's (corners or angles- depending on the language used by teachers) and sides it has. Based on these experiences, they have prior knowledge of the importance of angles in a shape.
- Measure to the nearest half unit using inches, feet, yards, centimeters and meters.
- Understand perimeter is a measure of distance.
- Find the distance around a figure in inches, feet, yards, centimeters, and meters to the nearest half unit.
- Find the length of an unknown side given the length of the other sides and the perimeter.
- Find the perimeter of polygons having at most six sides.
- Identify two-dimensional shapes.
- Understand multiplication can be represented as an array.

__Mastery Expectations:__- identify and classify angles as acute (less than 90 degrees)
- identify and classify angles as right (exactly 90 degrees) or
- identify and classify angles as obtuse (greater than 90 degrees)
- identify and classify real life examples of angles
- use a protractor or angle ruler to accurately measure a given angle (within 3-5 degrees)
- compare and order angles based on their size- specifically angle measure
- understand area as covering
- find area by counting the number of same-size units that cover a shape without gaps or overlays.
- justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into 1 x 1 unit squares and seeing them as grouped into rows and columns.
- label area measurements using square units (cm, inches, feet, etc.) .

4.3.2.1-4.3.2.4

- use tables, bar graphs, timelines, Venn diagrams to display data sets; data may include fractions /decimals; understand spreadsheet tables/graphs can be used to display data

__Background Knowledge:__- 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.

__Mastery Expectations:__- Create, read, and analyze tables
- Create, read, and analyze bar graphs
- Create, read, and analyze time lines
- Create, read, and analyze Venn diagrams
- Create, read, and analyze spreadsheets
- Understand decimal and fraction data
- Understand relationships and differences between tables, graphs, time lines, and Venn diagrams
- Recognize applications of spreadsheet tables and graphs