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Hawaiian Culturally Relevant Lessons & Resources Connecting Mathematics from the Waʻa to the ʻĀina

Kamuela E Yong

Chapter 6 Mālama Wai (Runoff, Rectangles, and Rain Gardens)

An integrated 3rd or 4th-grade lesson connecting the traditional Hawaiian value of mālama wai (caring for water) with foundational math concepts. Students analyze geometric area using multiplication models, calculate liquid volumes, and partition land distributions using fractional representations.
Time Allotment: 60 minutes

Section 6.1 Lesson Overview & Preparation

In this lesson, students explore the concept of mālama wai by studying how stormwater runoff impacts local streams (kahawai) and the ocean (kai). Students learn the operational difference between impervious surfaces (such as roofs, concrete, and asphalt) which prevent rain from soaking into the ground and create polluted runoff, and pervious surfaces (such as grass, soil, and rain gardens) which absorb and filter rainwater. Using a grid-based “Schoolyard Design Challenge,” students apply multiplication to find rectangular area (\(A = L \times W\)), calculate liquid volume runoff in liters, and represent complex land use allocations using fractional metrics.

Note 6.1. Required Materials.

  • Grid Map Handout: A \(6 \times 8\) grid representing a schoolyard (total area of 48 square units).
  • Colored Markers/Pencils: Red (for impervious surfaces like concrete and roofs) and Green (for pervious surfaces like grass and rain gardens).
  • Vocabulary Anchor Chart: Displaying key terms (mālama wai, kahawai, pervious, impervious, runoff).
  • Water & Sponge Demonstration: A sponge (pervious) and a plastic plate (impervious) with a small spray bottle of water to visually model runoff physics.

Section 6.2 Phase 1: Introduction & Science Demonstration

The session launches with an experiential, real-world connection to anchor mathematical design patterns in functional ecosystem management.

Subsection 6.2.1 Cultural Connection: Mālama Wai

Introduce the Hawaiian value of mālama wai (caring for clean water). In traditional ahupuaʻa systems, water flowed from the wet mountain forests (uka) down through streams (kahawai) to irrigate farm fields before reaching the sea (kai). The land acted as a natural filter, keeping the ocean pristine.
Contrast this balance with modern structural changes: today, towns have many hard surfaces. Prompt the group: “When rain falls on concrete or asphalt, where does the water go?”
Example 6.2. Sponge vs. Plate Simulation.
Spray water onto a household sponge. Explain that this represents a pervious surface (like grass or a forest). Ask: “What happens to the water?” (It absorbs/filters in).
Next, spray water onto a plastic plate. Tilt it over a capture tray. Explain that this represents an impervious surface (like a concrete driveway or building roof). Ask: “What happens here?” (Water runs off immediately).
Explain that stormwater runoff picks up oil, trash, and dirt from roads and washes it directly into our streams and beaches. To practice mālama wai, we must design spaces that allow water to soak safely into the earth.

Section 6.3 Phase 2: Guided Practice — Modeling the Yard

Draw a small \(4 \times 6\) grid on the whiteboard (24 total square units). Explain that each square unit represents an adjustable “plot of land.”

Activity 6.1. Step 1: Partition the Yard.

Model building a classroom roof that tracks at 3 units wide by 4 units long. Shade this section Red (impervious).
Designate the remainder of the yard as open grass space. Shade this section Green (pervious).

Activity 6.2. Step 2: Area Calculations.

Calculate the Area of the Roof (Impervious):
\begin{equation*} \text{Area} = 3 \times 4 = 12 \text{ square units} \end{equation*}
Calculate the Area of the Grass (Pervious) based on the total 24-unit yard canvas:
\begin{equation*} 24 - 12 = 12 \text{ square units} \end{equation*}

Activity 6.3. Step 3: Runoff and Fractional Volume Scaling.

Establish the underlying volume rules: “Every red square generates 2 liters (L) of dirty runoff during a heavy rainstorm. Green squares absorb all water, generating 0 L of runoff.”
Calculate total runoff entering the stream from this setup:
\begin{equation*} 12 \text{ red squares} \times 2\text{ L each} = 24\text{ L of runoff} \end{equation*}
Express the concrete footprint as a fraction of the full yard asset:
\begin{equation*} \frac{12}{24} \end{equation*}
Identify the structural equivalent fraction to show that exactly half of our entire yard is concrete:
\begin{equation*} \frac{12}{24} = \frac{1}{2} \end{equation*}

Section 6.4 Phase 3: Independent Practice — Schoolyard Design Challenge

Provide students with a \(6 \times 8\) grid handout (total area of 48 square units) and instruct them to execute structural solutions matching specific targets.
Table 6.3. Mālama Wai Design Challenge Criteria
Activity Requirements Grade 3 Challenge Grade 4 Challenge
Grid Dimensions \(6 \times 8\) (48 square units total) \(6 \times 8\) (48 square units total)
Required Buildings School Building: \(3 \times 4\) rectangle; Concrete Parking Lot: \(2 \times 6\) rectangle School Building: \(3 \times 4\) rectangle; Concrete Parking Lot: \(2 \times 6\) rectangle
Flexible Design Space Design the remaining area using green grass or rain gardens (pervious) and concrete pathways (impervious). Design the remaining area. You must include at least 1 rain garden (minimum area of 6 square units).
Runoff Constraints Keep total stormwater runoff under 40 L. (Rule: 1 impervious square = 2 L; pervious = 0 L) Keep total stormwater runoff under 32 L. (Rule: 1 impervious square = 2 L; pervious = 0 L)
Fraction Goal Find what fraction of your total schoolyard (48 units) is green space. Simplify using denominators of 2, 3, 4, 6, 8. Decompose your land fractions. Write an equation showing:

Subsection 6.4.1 Student Action Steps

  1. Color & Layout: Students map out their schoolyard blueprints. They must draw and label their school building and parking lot, then optimize how they map the remaining square units to master runoff targets.
  2. Calculate Area: Students list the exact mathematical area of each mapped component using geometric multiplication formulas.
  3. Runoff and Fraction Math: Students calculate the net runoff volume (L) generated across their structural design and complete their designated fractional equations.

Section 6.5 Phase 4: Closure & Strategic Support

Subsection 6.5.2 Differentiation & Tiered Support

Intervention / Support:
  • Reduce the baseline canvas to a smaller \(4 \times 5\) grid (20 square units total) to isolate multiplication and make basic counting-by-twos calculations more approachable.
  • Incorporate tactile pre-cut colored paper tiles (red and green) so students can physically balance and adjust their grid distributions before drawing permanent lines.
Language Learners (EL):
  • Anchor vocabulary charts with clean visual icons alongside technical terms, such as matching “pervious” with a sponge or grass icon, and “impervious” with a brick or asphalt icon.
  • Provide scaffolding sentence frames for the reflection phase: “My schoolyard has ___ square units of green space. This helps protect the stream because...”
Extension (Grade 4+):
  • Engineering Cost Analysis: Introduce realistic structural budgetary boundaries: “Installing grass costs $10 per square unit. Installing a specialized rain garden costs $15 per square unit, but decreases nearby runoff. Paving concrete costs $5 per square unit. You have a maximum project budget of $400.”

Section 6.6 Worksheet

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