identify volume as an attribute of a solid figure.
explain that a cube with 1 unit side length is “one cubic unit” of volume.
explain a process for finding the volume of a solid figure by filling it with unit cubes without gaps and overlaps.
- measure the volume of a hollow three-dimensional figure (i.e., rectangular prism and cube) by filling it with unit cubes without gaps and counting the number of unit cubes.
use unit cubes to create two different rectangular prisms with one given volume.
- relate finding the product of three numbers (length, width, and height) to finding volume.
use the formula for area (3rd grade skill) to develop an understanding of volume.
relate the associative property of multiplication to finding volume.
calculate volume of rectangular prisms and cubes, with whole number edge lengths, using the formula for volume (V = lwh or
V = Bh) in real world and mathematical problems.
- label appropriate units of measure for volume.
decompose a composite solid into non-overlapping rectangular prisms to find the volume of the solid by finding the sum of the volumes of each of the decomposed prisms.
determine a missing dimension of a rectangular prism given two dimensions and the volume.
generate possible dimensions of a rectangular prism when given the volume.
solve real world problems involving volume.
- compare and describe the geometric attributes of two-dimensional figures. I.e., triangle, quadrilateral, rectangle, square, rhombus, trapezoid, pentagon, hexagon, octagon, circle, half-circle, quarter circle
categorize two-dimensional figures according to their individual and shared geometric (defining) attributes.
HINT: Geometric (defining) attributes include properties of sides (i.e., parallel, perpendicular, congruent), properties of angles (i.e., type, measurement, congruent), and properties of symmetry (i.e., point and line).
explain the reasoning for the determined categories.
select two-dimensional figures belonging to a given subcategory.
- organize two-dimensional figures into a Venn diagram (graphic organizer) based on determined attributes.
classify two-dimensional figures based on defining attributes.
- draw a coordinate plane with two intersecting perpendicular lines. identify the intersection as the origin and the point where 0 lies on each of the lines. label the horizontal axis as the x-axis, and the vertical axis as the y-axis. identify an ordered pair such as (3,2) as an x-coordinate followed by a y-coordinate. explain the relationship between an ordered pair and its location on the coordinate plane. HINT: Students are only expected to utilize the first quadrant which includes only positive numbers.
- determine when a mathematical problem has a set of ordered pairs. use appropriate tools strategically to identify, locate and plot ordered pairs of whole numbers on a graph in the first quadrant of the coordinate plane. locate an unknown point on a coordinate plane when given horizontal and vertical movements from another point. describe the horizontal and vertical movements necessary to get from one point to another on a coordinate plane. HINT: Students need to be able to use directional language (i.e., left or right) or a compass rose and cardinal directions. I.e., north, south, east, or west relate the coordinate values of any graphed point to the context of the problem. name or graph the point that would complete a specified, two-dimensional geometric shape in the first quadrant.
- generate two numerical patterns with the same starting number for two given rules.
explain the relationship between the two numerical patterns by comparing how each pattern grows or by comparing the relationship between each of the corresponding terms from each pattern.
form ordered pairs out of corresponding terms from each pattern.
graph the ordered pairs on a coordinate plane.
identify relationships between two patterns and use these relationships to make predictions or generalizations.
- explain the inverse relationship between multiplication and division.
describe and demonstrate the process of division using a variety of models and strategies (e.g., expanded notation/place value, partial quotients, repeated subtraction, equal sharing, place-value, properties).
illustrate and explain calculations by using equations, rectangular arrays, and/or area models.
model and apply a variety of strategies to find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.
solve for a quotient by continuing the steps of a given division strategy.
interpret remainders in the context of a story.
use an understanding of the relationship between multiplication and division to check the quotient.
Students will be provided hands on practice from the concrete to the conceptual practice of fractions. This will be provided through center activities, whole group practice, and collaborative learning.
Centers will consist of skill based practice in a teacher led station, seat-work practice, collaboration station, paired practice/game style, and technology.