Lesson 10

• Display one statement.
• “Hagan una señal cuando sepan si la afirmación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

• Share and record answers and strategies.
• Repeat with each statement.

• Arrange counters to show 5 rows of 3 counters:

• “¿Cómo podemos hacer que la última afirmación sea verdadera basándonos en este arreglo? Expliquen” // “How could we make the last statement true based on this array? Explain.” (To make this true we need \(3 + 3 + 3 + 3 + 3\). I know that if \(5 + 5 + 5\) means 3 columns of 5, there would be 5 rows of 3.)

The purpose of this activity is for students to write equations that represent the number of objects in the rows or columns of an array. In a previous lesson, students matched arrays to expressions. In this activity, they write their own equations and describe how each equal addend represents the number of counters in each row or each column.

• Groups of 2
• Give students counters.

• “Primero, organicen fichas para hacer un arreglo. Después, escriban una ecuación que tenga sumandos iguales. Hay 2 ecuaciones que corresponden a cada arreglo. Para encontrar el número total de fichas, pueden usar cualquier método que tenga sentido para ustedes” // “First, you will arrange counters to make an array. Then you will write an equation that has equal addends. There are 2 equations that match each array. To find the total number of counters, you can use any method that makes sense to you.”
• 6 minutes: independent work time
• “Trabajen con un compañero en el problema número 3. Cada uno debe hacer su propio arreglo y seguir las instrucciones. Después, muéstrenle su arreglo a su compañero y permitan que responda las mismas preguntas. Comprueben si están de acuerdo en las respuestas” //  “For number 3, work with a partner. You should each make your own array and follow the steps. Then show your partner your array and let them answer the same questions. Check to see if you agree.”
• 6 minutes: partner work time
• Monitor for students to share different equations for an array they create that uses between 6 and 24 counters.

• “¿Cómo corresponden los sumandos de tu ecuación a tu arreglo?” // “How do the addends in your equation match your array?”
• “¿Cómo corresponde el número de sumandos de tu ecuación a tu arreglo?” // “How does the number of addends in your equation match your array?”
• “¿La suma de tu ecuación corresponde al número total de fichas?” // “Does the sum of your equation match the total number of counters?”

• Invite previously identified students to share their arrays and ask others to decide how many rows and columns the student’s array could have.
• “_____ escribió esta ecuación. ¿Cuántas filas y cuántas columnas podría tener el arreglo de _____?” // “_____ wrote this equation. How many rows and columns could _____’s array have?”

• Groups of 2
• Give students access to counters.
• “¿Qué saben sobre el cultivo de las plantas?” // “What do you know about growing plants?” (Plants need soil, water, and sunlight. You can grow plants to eat them. You can grow flowers. Plants can grow inside or outside.)
• 1 minute: quiet think time
• 1–2 minutes: partner discussion
• Share responses.
• “¿Cómo se organizan las plantas en las huertas o en los campos?” // “How are plants arranged in gardens or in fields?” (Sometimes the same plants are together. Flowers might be mixed up to make a design. On a farm, some plants are arranged in rows.)

• “Un agricultor local necesita ayuda para organizar sus cultivos en la huerta. Dependiendo del número de vegetales sembrados, dibujen arreglos que muestren cómo se puede organizar cada cultivo. Usen fichas si les ayuda” // “The local farmer needs help arranging crops in the vegetable garden. Based on the number of veggies planted, draw arrays to show how each crop could be arranged. Use counters if it helps.”
• 10 minutes: independent work time
• Monitor for a variety of ways students arrange the 16 carrot seeds, including 4 rows of 4.

If students represent the crops using one row or multiple rows with 1 in each, consider asking:

• “¿Hay otra forma de organizar los cultivos para que haya por lo menos 2 filas?” // “Is there another way to arrange the crops so there are at least 2 rows?”

• Invite 2–3 previously identified students to share how they arranged 16 carrot seeds. Select the student who arranged in 4 rows of 4 carrots seeds last.
• If no student arranged the carrots seeds in 4 rows, arrange counters to show 4 rows of 4 counters.
• “¿Qué ecuación con sumandos iguales representa el arreglo?” // “What equation would represent the array using equal addends?” (\(4 + 4 + 4 + 4 = 16\))
• “¿Los sumandos representan el número de semillas de zanahoria que hay en cada fila o en cada columna?” // “Do the addends represent the number of carrot seeds in each row or in each column?” (It could represent both.)
• “¿Pueden encontrar otra ecuación que muestre el número que hay en cada fila o en cada columna?” // “Can you find another equation that shows the number in each row or each column?” (No, since there are the same number of rows and columns, there is only one equation.)