In this warm-up, students proceed to think of department in terms of equal-sized groups, using fraction strips as an additional tool because that reasoning.

You are watching: How many rhombuses in a hexagon

Notice how students change from concrete concerns (the first three) come symbolic people (the critical three). Framing department expressions together “how plenty of of this portion in the number?” might not yet be intuitive come students. They will certainly further explore that connection in this lesson. Because that now, assistance them utilizing whole-number instances (e.g., ask: “how perform you translate (6 div 2)?”).

The divisors used right here involve both unit fractions and also non-unit fractions. The last inquiry shows a fractional divisor that is no on the fraction strips. This urges students to carry the reasoning provided with fraction strips come a new problem, or come use an additional strategy (e.g., by an initial writing an equivalent fraction).

As student work, notice those who space able to change their reasoning effectively, also if the strategy may no be effective (e.g., adding a row of (frac 110)s come the fraction strips). Ask them come share later.


Launch


Give college student 2–3 minutes of quiet work-related trewildtv.come. 

Student Facing


Write a portion or totality number as an answer for each question. If you get stuck, use the portion strips. Be all set to share her reasoning.

How numerous (frac 12)s space in 2?How countless (frac 15)s space in 3?How plenty of (frac 18)s room in (1frac 14)?(1 div frac 26 = ?)(2 div frac 29 = ?)(4 div frac 210 = ?)


Description: fraction strips depicting 2 in 8 different ways, through rows. Very first row, 2 1s. 2nd row, 4 of the fraction one end two. 3rd row, 6 that the portion one over three. 4th row, 8 of the portion one end four. Fifth row, 10 that the portion one over five. Sixth row, 12 of the portion one over six. Seventh row, 16 that the fraction one end eight. Eight row, 18 that the fraction one end nine. 



Teachers v a valid occupational email resolve can click below to it is registered or sign in for totally free access to college student Response.


Since the portion strips perform not show tenths, students might think that it is rewildtv.compossible to prize the critical question. Ask lock if they deserve to think the another fraction that is tantamount to (frac210).


For each of the very first five questions, pick a college student to share their solution and questioning the course to indicate whether castle agree or disagree.

Focus the conversation on two things: just how students taken expressions such together (1 div frac26), and on just how they reasoned about (4 div frac 210). Select a couple of students come share their reasoning.

For the last question, highlight techniques that are effective and efficient, such as utilizing a unit fraction that is identical to (frac 210), finding out how countless groups of (frac15) are in 1 and also then multiplying it by 4, etc.


5.2: an ext Reasoning v Pattern blocks (25 minutes)


CCSS Standards

Addressing

Routines and Materials

Instructional Routines

Required Materials


Activity


This task serves two purposes: to explicitly bridge “how countless of this in that?” questions and department expressions, and also to explore department situations in which the quotients space not entirety numbers. (Students explored srewildtv.comilar questions previously, but the quotients were entirety numbers.)

Once again students relocate from reasoning concretely and visually to reasoning symbolically. They begin by thinking around “how countless rhombuses room in a trapezoid?” and then to express that question as multiplication((? oldcdot frac23 = 1) or (frac 23 oldcdot ,? = 1)) and department ((1 div frac23)). College student think around how to address a remainder in together problems.

As students talk about in groups, hear for their explanations because that the inquiry “How countless rhombuses space in a trapezoid?” pick a pair of students to share later—one person to sophisticated on Diego"s argument, and another to assistance Jada"s argument.


Arrange college student in teams of 3–4. Provide access to sample blocks and geometry toolkits. Provide students 10 minutes of quiet occupational trewildtv.come because that the first three questions and a couple of minutes to talk about their responses and collaborate on the critical question.

Classrooms v no accessibility to pattern block or those using the digital materials deserve to use the provided applet. Physical pattern blocks room still preferred, however.


Representation: build Language and Symbols. Display or provide charts v symbols and meanings. Emphasize the difference in between this task where student must discover what fraction of a trapezoid every of the forms represents, contrasted to the hexagon in the ahead lesson. Produce a display screen that includes photo of each shape labeled through the name and also the portion it to represent of a trapezoid. Save this display visible as students move on come the next problems.Supports access for: theoretical processing; Memory
Use the pattern block in the applet come answer the questions. (If you need aid aligning the pieces, you have the right to turn ~ above the grid.)


If the trapezoid to represent 1 whole, what do each the these other shapes represent? Be ready to define or display your reasoning.

1 triangle

1 rhombus

1 hexagon

Use pattern block to stand for each multiplication equation. Use the trapezoid to represent 1 whole.

(3 oldcdot frac 13=1)

(3 oldcdot frac 23=2)

Diego and also Jada to be asked “How plenty of rhombuses room in a trapezoid?”

Diego says, “(1frac 13). If I put 1 rhombus on a trapezoid, the leftover shape is a triangle, i beg your pardon is (frac 13) that the trapezoid.”Jada says, “I think it’s (1frac12). Because we desire to find out ‘how countless rhombuses,’ we should compare the leftover triangle to a rhombus. A triangle is (frac12) of a rhombus.”

Do friend agree v either that them? define or display your reasoning.

Select all the equations that have the right to be used to price the question: “How countless rhombuses are in a trapezoid?”

(frac 23 div ? = 1)

(? oldcdot frac 23 = 1)

(1 div frac 23 = ?)

(1 oldcdot frac 23 = ?)

(? div frac 23 = 1)


Teachers with a valid work email deal with can click here to it is registered or sign in for complrewildtv.comentary access to student Response.


Arrange college student in groups of 3–4. Provide accessibility to sample blocks and also geometry toolkits. Provide students 10 minute of quiet work trewildtv.come for the an initial three questions and a couple of minutes to comment on their responses and collaborate ~ above the critical question.

Classrooms through no accessibility to pattern block or those making use of the digital materials can use the listed applet. Physical pattern blocks space still preferred, however.


Representation: construct Language and also Symbols.Display or carry out charts v symbols and also meanings. Emphasize the difference between this activity where college student must uncover what fraction of a trapezoid every of the shapes represents, compared to the hexagon in the ahead lesson. Develop a screen that includes an rewildtv.comage of each shape labeled v the name and the portion it to represent of a trapezoid. Store this display screen visible as students move on come the following problems.Supports access for: conceptual processing; Memory
Your teacher will give you pattern blocks. Usage them come answer the questions.

If the trapezoid to represent 1 whole, what carry out each the the other shapes represent? Be prepared to present or explain your reasoning.



Use pattern blocks to represent each multiplication equation. Use the trapezoid to represent 1 whole.

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(3 oldcdot frac 13=1)(3 oldcdot frac 23=2)

Diego and also Jada were asked “How many rhombuses space in a trapezoid?”

Diego says, “(1frac 13). If I placed 1 rhombus on a trapezoid, the leftover shape is a triangle, i beg your pardon is (frac 13) the the trapezoid.”Jada says, “I think it’s (1frac12). Since we desire to find out ‘how many rhombuses,’ we need to compare the leftover triangle to a rhombus. A triangle is (frac12) that a rhombus.”

Do girlfriend agree through either the them? explain or present your reasoning.

Select all the equations that have the right to be supplied to price the question: “How many rhombuses are in a trapezoid?”