The purpose of this Choral Count is to invite students to practice counting by and notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students recognize and generate equivalent fractions. In the Activity Synthesis, students have the opportunity to notice that both and are equal to 1 whole.
“Cuenten de en , empezando en ” // “Count by , starting at .”
Record as students count. Record 2 fractions in each row, and then start a new row. There will be 4 rows.
Stop counting and recording at .
Activity
“¿Qué patrones ven?” // “What patterns do you see?”
1–2 minutes: quiet think time
Record responses.
None
Student Response
Loading...
Advancing Student Thinking
Activity Synthesis
Display the count by from a previous lesson. There should be 4 rows and 4 fractions in each row, with the count ending at .
“¿En qué se parecen estos dos conteos? ¿En qué son diferentes?” // “How are these two counts the same? How are they different?” (The denominator stays the same in both counts—4 for the last count, and 2 for today’s count. The numerators change in the same way because they both count by 1. They start a new line at and , which are both whole numbers.)
Consider asking:
“¿Quién puede describir el patrón con otras palabras?” // “Who can restate the pattern in different words?”
“¿Alguien quiere compartir otra observación sobre por qué ocurre ese patrón aquí?” // “Does anyone want to add an observation as to why that pattern is happening here?”
“¿Están de acuerdo o en desacuerdo? ¿Por qué?” // “Do you agree or disagree? Why?”
Activity 1
Standards Alignment
Building On
Addressing
3.NF.A.3.a
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
The purpose of this activity is for students to consider equivalent fractions, using diagrams. One-half has been chosen to introduce equivalent fractions because there are many ways to see and represent fractions that are equivalent to . Many students may be familiar with the concept of halves and justify equivalence by saying 2 is half of 4. This reasoning is helpful with 1 half and 2 fourths but may not be generalizable to other cases of equivalence. For this reason, the Activity Synthesis focuses on justifications about whether or not the shaded parts are the same size. The idea that and are the same size is used to define equivalent fractions as fractions that are the same size.
Students need to use language carefully as they explain why the shaded parts of a shape show (MP6). For example, they may say that 2 of 4 equal parts in Shape D are shaded, but if they combine those parts, the total shaded amount is the same as in the shape in which 1 of 2 equal parts is shaded.
This activity uses MLR7 Compare and Connect. Advances: representing, conversing.
Engagement: Provide Access by Recruiting Interest. Synthesis: Invite students to share connections between finding one-half in fractions with more than two equal parts in this activity and when they might, in their own lives, see one half when there are more than two equal parts. Supports accessibility for: Visual-Spatial Processing
Launch
Groups of 2
“¿Qué saben sobre ?” // “What do you know about ?” (There are 2 equal parts. The parts have to be the same size. One of the parts would be shaded.)
1 minute: quiet think time
Share and record responses.
Activity
“Ahora, con su compañero, seleccionen todas las figuras en las que la sección sombreada representa de la figura. Luego, expliquen por qué puede haber más de una figura en la que esto sucede” // “Now work with your partner to select all the shapes in which the shaded portion represents of the shape, and explain how there is more than one shape where this is the case.
5–7 minutes: partner work time
Monitor for students who explain that the shading in A and in D represents of each shape.
Activity Synthesis
Invite students to share their responses.
MLR7 Compare and Connect
Display C and D.
“¿En qué se parecen las figuras C y D?” // "How are Shapes C and D the same?" (Both are squares. Both are partitioned into rectangles. The shaded portion is of the shape.)
“¿En qué son diferentes?” // "How are they different?" (Shape D is partitioned into fourths. There's only 1 part shaded in Shape C, but 2 parts are shaded in Shape D. The parts are in Shape D are smaller than the parts in Shape C.)
“¿Cómo es posible que la sección sombreada de cada figura muestre si las figuras se partieron en números diferentes de partes iguales?” // “How can the shaded portion in each shape show when the shapes have been partitioned into different numbers of equal parts?” (The shaded parts are the same size even though they look different. The same amount of each shape is shaded.)
“Aunque C está partida en medios y D está partida en cuartos, podemos decir que de cada figura está sombreado porque la misma cantidad está sombreada en ambas figuras, lo que significa que las dos fracciones tienen el mismo tamaño” // “Even though C is partitioned into halves and D is partitioned into fourths, we can say that of each shape is shaded because the same amount is shaded in both shapes, which means the two fractions are the same size.”
“Dos números que tienen el mismo tamaño son equivalentes, así que las fracciones y son fracciones equivalentes” // “Two numbers that are the same size are equivalent, so the fractions and are equivalent fractions.”
Activity 2
Standards Alignment
Building On
Addressing
3.NF.A.3.a
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
The purpose of this activity is for students to use fraction strips to identify equivalent fractions and to explain why they are equivalent. Highlight explanations that make clear that the parts representing the fractions are the same size and refer to the same-size whole.
Launch
Groups of 2
Ask students to refer to the fraction strips they made in an earlier lesson.
Activity
“Encuentren tantas fracciones como puedan que sean equivalentes a las fracciones de la lista. Para lograrlo, usen sus tiras de fracciones” // “Use your fraction strips to find as many fractions as you can that are equivalent to the listed fractions.”
5–7 minutes: independent work time
If students have extra time, encourage them to use their fraction strips to find other pairs of fractions that are equivalent.
“Ahora compartan con su compañero las fracciones equivalentes que encontraron. Asegúrense de compartir cómo razonaron” // “Now share the equivalent fractions you found with your partner. Be sure to share your reasoning.”
3–5 minutes: partner discussion
Monitor for students who explain equivalence by saying that the fractions are the same size.
Usa las tiras de fracciones que usaste en una lección anterior para encontrar tantas fracciones como puedas que sean equivalentes a:
Prepárate para mostrar cómo sabes que las fracciones son equivalentes.
Student Response
Loading...
Advancing Student Thinking
If students don’t generate an equivalent fraction for one of the given fractions, consider asking:
“¿Cómo representaste la fracción con las tiras de fracciones?” // “How did you represent the fraction with the fraction strips?”
“¿Cómo puedes usar las tiras de fracciones para hacer una fracción equivalente?” // “How could you use the fraction strips to make an equivalent fraction?”
Activity Synthesis
Invite students to share pairs of equivalent fractions and why they are equivalent. Highlight that the fractions are equivalent because the part of the strips that represent the fractions are the same size.
Display a fraction-strips diagram for all to see.
As students share, mark up the fraction-strips diagram to illustrate the equal size of the parts (for example, by drawing lines or by circling the parts). Then record pairs of equivalent fractions, using the equal sign, such as: .
Lesson Synthesis
“Si les dan dos fracciones, ¿cómo pueden decidir si son equivalentes?” // “If you were given two fractions, how could you determine whether they are equivalent?” (I would look at diagrams of them to see if the fractions are the same size. I would use fraction strips to see if the fractions are the same size.)
Standards Alignment
Building On
Addressing
3.NF.A.3.b
Recognize and generate simple equivalent fractions, e.g., , . Explain why the fractions are equivalent, e.g., by using a visual fraction model.
