Coordinate Systems
Students build on their understanding of number lines to construct a coordinate system composed of intersecting horizontal and vertical number lines. Students plot points and identify ordered pairs for points. They describe the location of a point in the coordinate plane as a horizontal distance from the y-axis and a vertical distance from the x-axis. Students conclude the topic by using a map on a coordinate plane to identify locations and describe distances and directions between those locations.
Patterns in the Coordinate Plane
Students extend their understanding of the coordinate plane by identifying properties of horizontal and vertical lines in the coordinate plane. Students then work with two number patterns simultaneously, generating terms when given rules and starting numbers, using the patterns to create ordered pairs, and plotting the points that represent the ordered pairs. Students transition to using tables and graphs to examine relationships between corresponding terms in two number patterns. They identify, describe, and compare addition, subtraction, multiplication, and division number relationships in the coordinate plane. Topic B ends with an optional lesson in which students identify and describe mixed-operation number patterns.
Solve Mathematical Problems in the Coordinate Plane
Students begin topic C by examining lines in the coordinate plane. They develop the understanding that lines have an infinite number of points. They realize that one point has many lines through it, but any two points can have only one line that passes through them both. Then students work with geometric figures in the coordinate plane. They classify angles, identify parallel and perpendicular line segments, and use those observations to classify quadrilaterals graphed in the coordinate plane. Students identify lines of symmetry and look for patterns in the coordinates of symmetric points. At the end of the topic, students solve problems by drawing rectangles in the coordinate plane and determining their vertices, perimeters, and areas.
Solve Real-World Problems with the Coordinate Plane
In topic D, students recognize that the coordinate plane is a useful tool for representing data, modeling relationships, and solving real-world problems. They come to understand that graphs can tell stories. Students interpret the meaning of points and line segments in a line graph that represents real-world data. In both an optional lesson and a real-world problem-solving task, students revisit relationships between two number patterns. Students solve problems by using a graph to identify and describe the number patterns in the x- and y-coordinates.
Common Core State Standards covered in Module 5
5.OA.B.3Generate 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.
5.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.B.4.aInterpret the product (𝑎/𝑏) × 𝑞 as a parts of a partition of 𝑞 into 𝑏 equal parts; equivalently, as the result of a sequence of operations 𝑎 × 𝑞 ÷ 𝑏.
For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (𝑎/𝑏) × (𝑐/𝑑) = 𝑎𝑐/𝑏𝑑.)
5.NF.B.4.bFind the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
5.G.A.1Use 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).
5.G.A.2Represent 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.
5.G.B.3Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
5.G.B.4Classify two-dimensional figures in a hierarchy based on properties.
Students can:
1. Solve problems without giving up.
2. Think about numbers in many ways
3. explain their thinking and try to understand others.
4. Show their work in many ways.
5. Use math tools and explain why they used them.
6. Work carefully and check their work.
7. Use what they know to solve new problems.
8. Solve problems by looking for rules and patterns.