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

Kamuela E Yong

Chapter 3 Lots of Mangos (Commutative and Associative Properties)

This 1st-grade lesson is centered around a story that explores community sharing while introducing properties of operations as addition and subtraction strategies. Students practice making a ten, identifying commutative and associative facts, and managing community sharing without wasting food.

Section 3.1 Lesson Overview & Preparation

Note 3.1. Core Standard: CCSS.MATH.CONTENT.1.OA.A.3.

Apply properties of operations as strategies to add and subtract. Examples: If \(8 + 3 = 11\) is known, then \(3 + 8 = 11\) is also known (Commutative property of addition). To add \(2 + 6 + 4\text{,}\) the second two numbers can be added to make a ten, so \(2 + 6 + 4 = 2 + 10 = 12\) (Associative property of addition).
Note: Students do not need to use formal algebraic terms like "commutative" or "associative" yet!

Note 3.2. Suggested Book.

This lesson integrates with the children’s book by Tammy Paikai.

Section 3.2 Phase 1: Story Time & The Problem of Plenty

Begin the lesson by gathering students at the storytime area to read aloud by Tammy Paikai.

Subsection 3.2.1 Guided Discussion Prompts

After reading, lead a classroom discussion on food preservation, sharing, and community:
  • “What happens if your family has a giant mango tree and there are too many mangos to eat?” (They will go bad, get spoiled, attract bugs, or go to waste.)
  • “How do the characters solve the problem of having too much food?” (By packing them up and sharing them generously with neighbors.)

Section 3.3 Phase 2: Math in Action — Picking Mangos

Transition the students into a narrative math simulation where they spend a summer week at their grandparents’ house helping pick fresh mangos.

Activity 3.1. Day 1 Harvest: Making a Ten.

On the first day, you look up at Grandpa’s mango tree. It is loaded with fruit!
  • Grandpa picks \(8\) mangos.
  • Tutu (Grandma) picks \(2\) mangos.
  • Next, you pick \(5\) mangos.
How many mangos did everyone pick from Grandpa’s tree altogether? Express this as an equation.
Math Strategy: Write out the numbers in order:
\begin{equation*} 8 + 2 + 5 = ? \end{equation*}
Look for "friends of 10" first. We see that \(8 + 2 = 10\text{.}\) Then add the remaining \(5\text{:}\)
\begin{equation*} 10 + 5 = 15 \text{ mangos} \end{equation*}

Activity 3.2. Day 2 Harvest: Commutative Property.

The next day, everyone goes back out to pick more mangos, but the order changes:
  • Grandpa picks first and gets \(8\) mangos.
  • Next, you pick \(5\) mangos.
  • Finally, Tutu picks last and gets \(2\) mangos.
How many mangos did everyone pick today? Express this as an equation.
\begin{equation*} 8 + 5 + 2 = ? \end{equation*}
Reflect and Discuss: Why did we get the exact same total (\(15\)) on both days? Guide students to see that changing the order of the numbers we add does not change our answer.

Subsection 3.3.1 First-Grade Harvest Challenge

When your parents arrive to pick you up at the end of the week, they join the harvest too! Now five people are picking mangos together. Find the grand total:
\begin{equation*} 8 + 2 + 5 + 3 + 7 = ? \end{equation*}
Encourage students to circle all pairs that make a ten first (\(8+2=10\) and \(3+7=10\)).
\begin{equation*} 10 + 10 + 5 = 25 \text{ mangos} \end{equation*}

Section 3.4 Phase 3: Sharing the Harvest (Subtraction Strings)

Bring out a neighborhood layout map. Explain that we must share our fresh harvest down the street before the fruit spoils.

Activity 3.3. Walking Down the Street (Route A).

Grandpa picks \(15\) mangos to give away today. You put them in your wagon and walk down the street:
  1. You go to Aunty Aloha’s house, and she takes \(3\) mangos.
  2. Then you go to Uncle Koa’s house, and he takes \(2\) mangos.
  3. Finally, you stop at Aunty Leimomi’s house. She is hosting a big party, so she takes \(6\) mangos.
How many mangos do you have left in your wagon? Is this enough for our family to eat without wasting? Represent this with an equation.
\begin{equation*} 15 - 3 - 2 - 6 = 4 \text{ mangos left} \end{equation*}

Activity 3.4. Walking the Other Way (Route B).

What if you decided to go the opposite way down the street instead? This time, you visit Aunty Leimomi first (she takes \(6\)), then Uncle Koa (he takes \(2\)), and finally Aunty Aloha (she takes \(3\)).
Write out the new equation:
\begin{equation*} 15 - 6 - 2 - 3 = 4 \text{ mangos left} \end{equation*}
Reflect and Discuss: Point out that the final amount left over remains exactly the same! Highlight that changing the order of what we give away does not affect the outcome, as long as we start with the same total number of mangos (\(15\)).

Section 3.5 Worksheet

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