A cumulative project where students design a structure meeting specific volume requirements and explain their mathematical reasoning.

Decomposing complex, non-overlapping solid figures into rectangular prisms to find total additive volume.

Solving real-world volume problems involving standard units like cubic inches, centimeters, and feet.

Applying volume formulas to solve for unknown dimensions (Length, Width, or Height).

Transitioning from B x h to the specific dimensions of length, width, and height (L x W x H).

Relating the number of layers to the height (h) and discovering the formula V = B x h.

Connecting the area of the base (B) to the first layer of a rectangular prism.

Developing spatial structuring by viewing rectangular prisms as a collection of identical horizontal or vertical layers.

Moving from physical cubes to representing and counting volume in 3D isometric drawings.

Exploring the requirement of packing without gaps or overlaps to accurately measure volume in cubic units.

Introduction to the unit cube as the standard measure of volume, focusing on the definition of a cubic unit (1x1x1).

Students transition from area to volume, understanding volume as the amount of space an object occupies by comparing 'packing' versus 'covering'.

Students participate in a final performance task where they apply their knowledge of fraction multiplication and division to solve a series of interconnected mission challenges.

Students consolidate their understanding of fraction multiplication and division through mixed practice, conceptual card sorts, and error analysis tasks.

Students select the correct operation and model to solve a variety of real-world division problems involving fractions and whole numbers.

Students interpret a whole number divided by a unit fraction as finding how many unit fractions are in the whole number, using visual tape diagrams to represent the division.

Students interpret a unit fraction divided by a non-zero whole number as partitioning the unit fraction into equal parts, using visual area models to represent the division.

Students solve real-world multiplication problems involving fractions and mixed numbers by selecting appropriate visual models and applying the standard algorithm.

Students generalize the process of multiplying fractions by exploring how the product of numerators and denominators relates to the total area of the model.

Students find the area of a rectangle with fractional side lengths by tiling it with unit squares, moving toward the understanding that (a/b) x (c/d) is finding a part of a part.

Students interpret multiplication as scaling by comparing the size of a product to the size of one factor on the basis of the size of the other factor.

Reviewing all four operations with fractions through complex word problems and determining which operation fits the context.

Dividing whole numbers by unit fractions using visual models to show how many 'parts' fit into the whole.

Dividing unit fractions by non-zero whole numbers using visual models to show partitioning of parts.

Applying fraction multiplication to solve real-world problems involving area and multi-step contexts.

Comparing the size of a product to the size of one factor on the basis of the size of the other factor (multiplication as scaling).

Students find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, leading to the formula area = length x width.

Multiplying a fraction by a fraction using area models to represent taking 'a part of a part'.

Finding a fraction of a whole number using tape diagrams and the relationship between multiplication and scaling.

Introduces fractions as division (e.g., 3/4 = 3 ÷ 4) using sharing contexts and tape diagrams.

Students practice solving word problems and using benchmark fractions (0, 1/2, 1) to estimate sums and differences (5.NF.A.2).

Focuses on subtraction with unlike denominators, emphasizing the number line as a tool to find the 'difference' or 'distance' between two values.

Introduces adding fractions with unlike denominators using area models and the concept of a 'common partition' (IM method).

Focuses on using number lines to find equivalent fractions, a foundational skill for adding and subtracting with unlike denominators (ALN HLC 1).

Students interpret the product (a/b) x q as 'a' parts of a partition of 'q' into 'b' equal parts, using set models and tape diagrams to find fractions of whole numbers.

Students explore the relationship between division and fractions by sharing whole items among groups, leading to the understanding that a/b = a divided by b.