The purpose of this activity is to introduce students to division situations that don’t have whole number quotients. Students write division situations to represent an expression. Once students generate a list of situations, students ask a question and solve one of the problems that does not involve dividing the remainders into pieces. Students create a poster of their work and do a Gallery Walk, with a focus on how each group represented the leftovers in the situation. At the end of the Activity Synthesis the term remainder is introduced to describe “leftovers” when dividing.

• “¿En qué se parecen y en qué se diferencian las formas en que representamos lo que sobraba?” // “What is the same and what is different about the way students represent the leftovers?”
• 30 seconds quiet think time
• 1 minute: partner discussion
• “Este problema tenía un residuo. Cuando dividimos y nos sobra algo, lo llamamos residuo, porque representa lo que queda después de dividir en grupos iguales” // “This problem had a remainder. When we divide and end up with leftovers we call them remainders, because they represent what is remaining after we divide into equal groups.”

The purpose of this activity is for students to use what they know about factors and multiples to determine if division expressions will have remainders. Students analyze expressions without finding the value and then choose to find the value of one expression that will result in a remainder and one without a remainder.

“En la síntesis de la lección, vamos a representar cocientes en los que sobra algo cuando le quitamos a un número todos los grupos iguales que podemos” // “In the Lesson Synthesis, let’s represent quotients that have leftovers when we take away as many equal groups as we can from a number.”