The purpose of this Warm-up is for students to notice that figures composed of multiple arrays can be decomposed into smaller arrays, and that this is a strategy to determine the total number of dots. This will be helpful in later lessons when students decompose figures into rectangles to find the total area.

When students find ways to decompose the given arrangements of dots to find the number of dots, they practice looking for and making use of structure (MP7).

• “¿En qué se parecen las formas en las que encontraron el número de puntos de cada imagen?” // “What’s the same in how you found the number of dots in each image?” (I looked for groups of 4. I decomposed each arrangement of dots into smaller arrays.)
• Consider asking:
  • “¿Alguien puede expresar con otras palabras la forma en la que ______ vio los puntos?” // “Who can restate the way ___ saw the dots in different words?”
  • “¿Alguien vio los puntos de la misma forma, pero lo explicaría de manera diferente?” // “Did anyone see the dots the same way but would explain it differently?”
  • “¿Alguien quiere agregar algo a la forma en la que ______ vio los puntos?” // “Does anyone want to add an observation to the way ____ saw the dots?”

The purpose of this activity is for students to make sense of the multiplication table, using what they know about factors and finding the area of a rectangle. They also are encouraged to notice and explain patterns they see as they make sense of the structure of the table.

The purpose of this activity is for students to find the values of products in the multiplication table. Students are encouraged to find familiar products before working on those that are less familiar. They do not need to fill in all of the products in the table. The Activity Synthesis focuses on patterns students find in the table, how they can show the patterns with equations, and how they explain their patterns, using what they know about multiplication and the properties of operations.