The purpose of this Warm-up is to draw students’ attention to the first few multiples of 45, which will be helpful as students continue to work with benchmark angles and use a protractor to measure angles. Students have the skills to perform the multiplication in each equation, but computing each product may be time-consuming. Students can more efficiently tell if the equations are true or false if they consider properties of operations and look for and make use of structure.
Launch
Display one equation.
“Hagan una señal cuando sepan si la ecuación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the equation is true and can explain how you know.”
1 minute: quiet think time
Activity
Share and record answers and strategies.
Repeat with each statement.
Student Task Statement
En cada caso, decide si la afirmación es verdadera o falsa. Explica tu razonamiento.
Student Response
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Advancing Student Thinking
Activity Synthesis
Some students may notice that it is handy to think in terms of because it would mean dealing with multiples of 90 rather than with multiples of 45. Highlight their explanations.
If no students decomposed expressions such as , , and into sums of and , discuss how this could be done. (See Sample Responses.)
This activity develops an understanding of the degree as a unit of rotation used to measure angles and introduces students to the protractor.
By now students have encountered many angle measurements and have some intuitive awareness of the sizes relative to a full turn (), half of a full turn (), and a quarter of a full turn (). In this activity, students learn that a angle is of a full turn and that an angle that is composed of angles has a measurement of . For example, a angle is made up of seven angles.
MLR2 Collect and Display. Synthesis: Direct attention to words collected and displayed from the previous lesson. Invite students to borrow language from the display as needed, and update it throughout the lesson. Advances: Conversing, Reading
Launch
Groups of 2
2 minutes: independent work time to find the fractions of a full turn
Record students’ responses. Solicit some ideas on the side of a angle. Emphasize that a angle is of a turn and that it’s the size of the angle formed by the sides of the pieces of the circle created if we cut a full circle into 360 equal parts.
“Para medir ángulos en grados, podemos usar un transportador” // “To measure angles in degrees, we can use a protractor.” (Consider displaying different types of protractors.)
Give each student a protractor.
“Comparen esta herramienta con la herramienta que usaron en la lección anterior. ¿En qué se parecen? ¿En qué son diferentes?” // “Compare this tool to the tool you used in the previous lesson. How are they the same? How are they different?” (Both are semicircles. Both show angles, like , , , and . The protractor is transparent or has a hole, while the paper version is solid. The protractor shows many more lines or tick marks and more numbers around the curve.)
Activity Synthesis
“Cuando los transportadores no mostraban números ni escalas, ¿cómo encontraron el tamaño de los dos ángulos?” // “How did you find out the size of the two angles when the protractors show no numbers or scales?” (We know that the turn from one tick mark to the next is . We can use the tick marks to count the number of turns. We can imagine the tick marks split the angle into a number of angles. We can count each angle to find the measurement.)
Activity 2
20 mins
Usemos un transportador
Standards Alignment
Building On
Addressing
4.MD.C.5.b
An angle that turns through one-degree angles is said to have an angle measure of degrees.
In this activity, students learn how to use a protractor. They align a protractor to the vertex and a ray of an angle so that its measurement can be read. The given angles are oriented in different ways, drawing students’ attention to the two sets of scales on a protractor. Students need to consider which set of numbers to pay attention to and think about a possible explanation for when or how to use each scale. Moreover, one of the scales is only marked in increments of 10 degrees, so if students use this scale, they need to reason carefully about the precise angle measure (MP6).
This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing.
Action and Expression: Internalize Executive Functions. Invite students to estimate the size of the angle before finding each precise measurement. Offer the sentence frame: “Este ángulo será mayor que _____ y menor que _____. Estará más cerca de _____” // “This angle will be greater than _____ and less than _____. It will be closer to _____.” Supports accessibility for: Conceptual Processing, Visual-Spatial Processing, Attention. Advances: reading, writing.
Launch
Groups of 2–4
Activity
5 minutes: independent work time
2–3 minutes: group discussion
Monitor for students who find each measurement by:
Looking for the scale, with a ray on , and counting up on that scale.
Subtracting the two numbers (on the same scale) that the rays pass through.
MLR1 Stronger and Clearer Each Time
“Compartan su respuesta al último problema con su compañero. Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta ese momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share your response to the last problem with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
3–5 minutes: partner discussion
Repeat with 2–3 different partners.
“Ajusten su borrador inicial basándose en los comentarios que les hicieron sus compañeros” // “Revise your initial draft, based on the feedback you got from your partners.”
2–3 minutes: independent work time
Activity Synthesis
Select students who used different strategies to share their responses and reasoning.
Display the image of Elena and Kiran’s angle. If no students mentioned that is not possible because the angle clearly appears greater than a right angle (), consider asking how Elena can use what she knows about right angles to think about her measurement.
Lesson Synthesis
“Hoy usamos ángulos de y un transportador para medir el tamaño de un ángulo” // “Today we used angles and a protractor to measure the size of an angle.”
“¿Qué saben sobre un ángulo de ?” // “What do you know about a angle?” (It’s of a full turn of a ray through a circle. It's a small angle compared to the other angles we have seen. It’s of a half turn of a ray through a circle, like on a protractor.)
“¿Cómo pueden los ángulos de decirnos los tamaños de otros ángulos?” // “How can angles tell us the sizes of other angles?” (It’s a smaller angle, so we can use it to be more precise when we measure or compare angles. We can count or find the number of angles in an angle to find its measurement.)
“¿Cómo sabríamos cuántos ángulos de hay en otro ángulo?” // “How would we know how many angles are in another angle?” (We can use a protractor, which is marked with 180 or 360 one-degree angles.)
Display:
“Vimos que un transportador tiene dos conjuntos de números. ¿Cómo saben cuál conjunto de números usar cuando miden un ángulo?” // “We saw that a protractor has two sets of numbers. How do you know which set of numbers to use when measuring an angle?” (Either set could be used, but it is easier to use the set that counts up from 0 rather than counts back from 180.)
“Tómense 1 o 2 minutos para agregar a su muro de palabras las palabras nuevas de la lección de hoy. Compartan sus palabras nuevas con un compañero y agreguen las nuevas ideas que surjan de su conversación” // “Take 1–2 minutes to add any new words from today’s lesson to your word wall. Share your new entries with a neighbor and add any new ideas you learn from your conversation.”
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Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
2–3 minutes: group work time on the second set of questions.
Monitor for students who look for structure to find the number of increments on the protractor (for example, noticing that every group of ten increments are marked, and counting those instead of counting individual tick marks).
Pause for a discussion. Make sure students see that a angle on the protractor results when we draw rays through a pair of neighboring tick marks.
2–3 minutes: individual or group work time on the remaining questions
Student Task Statement
Un rayo que da una vuelta entera alrededor de su punto de inicio ha dado un giro completo o ha girado
¿Qué fracción de un giro completo es cada una de las siguientes medidas de ángulos?
Tu profesor te dará un transportador, una herramienta para medir el número de grados de un ángulo.
¿Cómo se muestra en el transportador?
¿Cuántas medidas de ves?
Pusimos un transportador sin números sobre un ángulo.
El centro del transportador se alinea con el vértice del ángulo.
El borde recto del transportador se alinea con un rayo del ángulo.
¿Cuántos grados mide este ángulo? Explica cómo lo sabes.
Un ángulo contiene treinta ángulos de . ¿Cuántos grados mide este ángulo?
Student Response
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Advancing Student Thinking
Student Task Statement
Estos son 4 ángulos. Se puso un transportador sobre cada ángulo. Mide el tamaño de cada ángulo, en grados.
Elena y Kiran miden un ángulo con un transportador. Elena dice que el ángulo mide . Kiran dice que el ángulo mide . ¿Por qué las medidas son diferentes? ¿Cuál medida es correcta? Explica cómo razonaste.
Student Response
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Advancing Student Thinking
4.MD.C.6
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
