Math+Level+3+Essential+Learnings

= Essential Learnings and Indicators of Success =

== **EL 1** == The whole number system describes place value relationships from ones to 10,000 and forms the foundation for efficient algorithms (steps in mathematical thinking) == **EL 2** == Parts of a whole can be modeled and represented in different way Use drawings, models, and numerals to represent fractions (halves, thirds, fourths, sixths, eighths) based on a whole shape, number set, or number line.
 * 1) Read and write numbers from one to 10,000 and explain place value for four-digit numbers
 * 2) Generalize the change represented when moving from one place value to another place value in a number.
 * 3) Compose and decompose (standard and expanded) multi-digit numbers based on place value.
 * Estimate and justify the reasonableness of solutions to problems involving representations of fractions.
 * Describe why equivalent fractions are two ways of modeling the same quantity using a model or drawing.

== **EL 3** == Formulate, represent, and use algorithms (steps in mathematical thinking) to add and subtract multi-digit whole numbers with flexibility, accuracy, and efficiency. == **EL 4** == Multiplying and dividing are inverse operations modeled in a variety of ways. == **EL 5** == Number patterns are based on operations and relationships.
 * 1) Use number sense to estimate and justify the reasonableness of solutions to problems
 * 2) Use flexible methods of computing, including student-generated strategies and standard algorithms.
 * 3) Estimate using strategies such as front-end estimation or landmark numbers.
 * 1) Demonstrate fluency with multiplication and division facts with single-digit factors.
 * 2) Describe relationships between related facts and between multiplication and division.
 * 3) Represent multiplication and division problems with drawings, models, number sentences, and stories.
 * 4) Model strategies to achieve a personal financial goal using arithmetic operations. (PFL)
 * 1) Extend simple arithmetic and geometric sequences.
 * 2) Count by and analyze patterns in multiples of 2,3,5,9,10,11,25,50, and 100.
 * 3) Use known multiplication facts to solve unknown multiplication problems.

EL 6 Number properties can be used to solve problems.
 * 1) Use the commutative property (order) to solve addition and multiplication problems.
 * 2) Use the associative property (grouping) to solve addition problems.
 * 3) Use the relationship between addition and multiplication to solve problems.

EL 7 Visual displays of data can be used to explore and describe fairness
 * 1) Compose questions to generate data.
 * 2) Collect and organize data from simple experiments or surveys in class.
 * 3) Create picture graphs, bar graphs, dot plots (ordered pair), and frequency tables from a data set.
 * 4) Describe data using the concepts of mode, clusters and gaps.

EL 8 Mathematical models are used to explore and describe fairness
 * 1) Investigate chance devices such as coins, spinners, and number cubes.
 * 2) Apply the concepts of impossible, unlikely and likely.
 * 3) Determine if a chance device is fair or unfair.

EL 9 Geometric figures are described by their attributes and position in the plane.
 * 1) Construct and describe two-dimensional shapes by attributes and properties such as sides, angles, and symmetry.
 * 2) Recognize and demonstrate transformations- reflections, translations, and rotations- of basic shapes or designs.
 * 3) Use geometric properties of points and line segments to describe figures

EL 10 Objects have distinct attributes that can be measured with appropriate tools.


 * 1) Use standard and metric units to measure to the nearest ½ or whole inch or centimeter.
 * 2) Estimate and measure distance and perimeter.