Wednesday, August 27, 2014

The Math Year Begins with Facts and Models

We'll plot these ordered pairs. 
A solid foundation of math facts serves children well.

To begin the fifth grade year, we'll revisit and solidify facts by using those facts to create, study, and discuss math models.

First, we'll begin with the number card project. Students and I will look at the shape of numbers by creating arrays, decomposing numbers, and looking at number relationships.

Next, students will study the use of single and double number lines in relation to facts.

After that, students will complete fact patterns and plot those patterns on coordinate grids.

While we're reviewing facts and learning about the many models we can use to demonstrate number values and relationships, students will practice these skills at home using similar paper/pencil models, Xtra Math, That Quiz, and Khan Academy.

After the introductory activities above, students will take a fact assessment. Individualized practice schedules and goals will be set after this assessment. Students will also be formally and informally assessed on the standards below during the unit.

Beginning the year with these activities give students a review of fourth grade standards, a fact foundation, and models to use as we continue to study math concepts throughout the year. After this focus we'll move on to a dual focus including place value and standard algorithm review and practice.

These activities meet a number of fifth grade standards including the following:

  • CCSS.Math.Content.5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
  • CCSS.Math.Content.5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
  • CCSS.Math.Content.5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
  • CCSS.Math.Content.5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
  • CCSS.Math.Content.5.G.A.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.