• # Math Extended Curriculum (EC): Grades 3-5

The new math Illinois Learning Standards, based on the Common Core State Standards (CCSS), are more rigorous for all students. Units of study were developed in algebra, geometry and statistics to expose students to these mathematical strands and prepare them for pre-algebra. See timeline below:

## Students in third grade have not yet been identified for Extended Curriculm (EC) services. However, in the spring they are exposed to hands-on equations, which help them visualize concepts of algebra. This is important as some students have not fully developed their abstract thinking sense. In the last trimester of the school year, students:

• create algebraic expressions to represent patterns
• learn the importance of balancing an equation
• graph ordered pairs on a coordinate plane

Teachers emphasize:

• finding and correcting errors in solutions
• using manipulatives and pictures to represent expressions and equations
• solving problems using multiple methods
• writing extended responses to explain thinking

### Firsttrimester: Algebraic Problem-Solving

• Reading, writing and evaluating algebraic expressions
• Creating equivalent expressions
• Understanding the concept of opposites and inverse relationships
• Writing and solving equations to solve word problems
• Finding more than one way to solve a problem

### Second trimester: Programming Logic

• Learning computer programming
• Applying programming logic on various apps and computer programs as part of the ITSE (International Society for Technology in Education) standards
• Integrating student knowledge of coding with classroom learning objectives (i.e. the use of a robot/coding apps to animate a fable or teach multiplication facts)
• Using problem-solving to find and resolve coding errors in a student’s personal work and the work of other

### Third trimester: Statistics

• Displaying numerical data in number lines, dot plots, histograms, and box plots
• Summarizing numerical data sets, identifying: center (mean, median), interquartile range, and absolute deviation
• Describing overall data patterns and deviations
• Relating the choice of measures of center and variability to the shape of the data
• Analyzing how data trends help us make assumptions about the future

### First trimester: Algebraic Problem-Solving

• Solving algebraic equations without manipulatives or pictorials, using traditional notation
• Combining like terms
• Using the associative, commutative, and distributive properties to solve equations
• Focusing on problem-solving and finding multiple ways to find the answer
• Solving word problems

### Second trimester: Geometry Unity

• Heavily based on 8th grade Connected Math Unit Looking for Pythagoras
• Finding the areas of triangles and quadrilaterals
• Calculating the lengths of sides of polygons in a coordinate plane
• Evaluating square roots
• Representing 3-dimensional shapes using nets
• Finding surface area
• Determining the volume of 3-dimensional shapes

### Third trimester: Statistics

• Understanding the difference between statistics and probability
• Finding the measures of central tendency (mean, median, mode, range, etc.)
• Using Standard Deviation to interpret data
• Understanding the impact of outliers on data
• Applying Mean Absolute Deviation to solve real world problems (how far each data point is from the mean)