The purpose of this activity is for students to practice adding tenths and hundredths by sorting a set of expressions, based on whether the value of each expression is less than, equal to, or greater than 1. Students decide whether it is necessary to write equivalent fractions, and if so, whether to use tenths or hundredths.

Through repeated reasoning, students build their ability to compare the size of hundredths to that of tenths and 1 (MP8). They also have an opportunity to look for and make use of structure (MP7). For instance, students may conclude that certain expressions are greater than 1 by noticing that one of the addends is greater than 1.

• Invite 2–3 previously selected groups to share.
• Consider asking:
  • “¿Cómo decidieron dónde debía ir cada expresión? ¿Escribieron siempre una fracción equivalente?” // “How did you decide where each expression should go? Did you always write an equivalent fraction?”
  • “¿Cuándo fue necesario escribir una fracción equivalente? ¿Cuándo no fue necesario?” // “When was it necessary to write an equivalent fraction? When was it not?”
  • “¿Hubo expresiones que pudieron clasificar sin reescribir ninguna fracción ni sumar? ¿Qué características de esas expresiones lo hicieron posible?” // “Were there expressions you were able to sort without rewriting any fractions or adding anything? What was it about those expressions that made that possible?”

In previous activities, students learned to combine tenths and hundredths. In this activity, students complete addition equations. To do so, they rely on a range of understandings and skills: how to write equivalent fractions, how to add fractions, and how to decompose a fraction into a sum. Though many of the equations involve an unknown addend, students are not expected to find them by subtraction.

• “¿Qué ecuaciones fueron difíciles de completar? ¿Qué características de las fracciones dadas hicieron que fuera difícil encontrar los números desconocidos?” // “Which equations were difficult to complete? What was it about the given fractions that made it hard to find the missing numbers?”
• “¿Qué fue más retador: encontrar los décimos desconocidos o los centésimos desconocidos? ¿Por qué?” // “Which did you find more challenging: finding missing tenths or missing hundredths? Why might that be?”

This optional activity allows students to practice adding tenths and hundredths (and to reinforce their ability to compare fractions) through a game. Students use fraction cards to play a game in groups of 2, 3, or 4. To win the game is to draw pairs of cards with the greater (or greatest) sum, as many times as possible.

Consider arranging students in groups of two for the first game or two (so that students would need to compare only 2 sums at a time), and arranging groups of 3 or 4 for subsequent games. Before students begin playing, ask them to keep track of and record pairs of fractions that they find challenging to add.

• Invite groups to share some of the challenging expressions they recorded and how they eventually determined the sums.
• As one group shares, ask others if they have different ideas about how the fractions could be added.