esolbms.weebly.com€¦ · web viewmathematics. distance learning instruction workbook. may 11th...

MathematicsDistance Learning Instruction

WorkbookMay 11th – May 22nd

Math 6 and Math 6 EX

Student Name ________________________School ________________________

Math Teacher ________________________Estimado estudiante,

Este libro de trabajo contiene cuatro actividades que revisarán los temas principales que se enseñaron anteriormente en la clase de matemáticas. Usted notará que hemos incluido una clave de respuesta en la última página de este paquete. Dado que estamos proporcionando una clave, queremos que revise sus respuestas para asegurarse de que entiende.

Por favor, asegúrese de que está haciendo su mejor esfuerzo, ya que esta evaluación es su oportunidad de reforzar lo que ya ha aprendido. Esto incluye mostrar todo su trabajo y tratar de completar todos los problemas. Simplemente copiar las respuestas de la hoja de respuestas sin antes probar los problemas usted mismo le quitaría el valor de este trabajo.

Si tiene problemas, asegúrese de comunicarse con su maestro para obtener apoyo adicional. Estar bien y mantenerse a salvo.

~Your Wicomico County Math Teachers

Math 6 & Math 6EX May 11 – May 22, Page. 1

Wicomico County Public Schools Remote LearningMath 6 and Math 6EX Topics: May 11th – May 22nd Activity #1

1. Calentamiento:Source: Open up


Ejemplo 1:

412 ÷ 3 =

How many groups of 3 are in 412 ?

How many groups of 6 (parts) are in 412 ?

412 ÷ 3 = 13

6 = 112

Pruébalo: 234 ÷ 2

412 ÷ 3 =

Dividing fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.

1. Turn the mixed number into an

improper fraction.

412 = 9

2

2. Write the whole number as a

fraction.

3 = 31

3. Rewrite the problem.

92 ÷ 3

1 =

Now multiply the first fraction by the reciprocal of the second fraction.

Pruébalo: 234 ÷ 2


Ejemplo 2:

535 ÷ 2



535 ÷ 2 = 2 8

10 = 245

Pruébalo: 425 ÷ 2

535 ÷ 2



improper fraction.

535 = 28

5

2. Write the whole number as a

fraction.

2 = 21


285 ÷ 2

1 =


Pruébalo: 425 ÷ 2


Ejemplo 3:

323 ÷ 4



323 ÷ 4 = 11

12

Pruébalo: 338 ÷ 4


323 ÷ 4



improper fraction.

323 = 11

3

2. Write the whole number as

a fraction.

4 = 41


113 ÷ 4

1 =


Pruébalo: 338 ÷ 4

2. Práctica

1. Jillian has 214 pizzas left after her party. The next

day, Jillian and her two brothers split the rest of the

pizzas for lunch. How much of the 214 pizzas will each

person get?

2. Charlie worked hard but could complete only 313 of his worksheets in 5 days. How much work

was he doing each day, assuming he worked the same amount each day?

3. You went to the store and realized you got 514

pounds of chicken. This will get split among 4 meals. How much chicken should you ration out for each meal, so they all have the same amount?

4. The track coach told the relay team that the 3 runners need to split the race evenly. If the total

relay race is 812 miles, how far will each runner

need to run?


5. Lorena is planting vegetables in a garden in her backyard in the shape of a rectangle. The total area of

her garden is 1914 ft2.

A.) If the length of the garden is 5 ft, what would be the width?

B.) If each plant needs 2 ft2 of the total space, how many plants can she fit into the whole garden?

6. Michael has 945 cups of flour left to use while

baking. His recipe calls for 2 cups of flour each batch.

A.) Exactly how many batches could he make with all the flour?

B.) How many whole batches can Michael make with the flour he has?

7. David bought 579 pounds of candy at the store and

ate it all in 10 days. How much did he consume each day?

8. Maria’s car used 469 gallons of gasoline in the

week (assume she drove 7 days in the week). If she drove the same amount each day, how much gas did she use each day?

3. Extensión opcional

Below is the recipe needed to make 3 batches of cookies.

623 cups of flour 3

12 cups of sugar 4 cups of chocolate

chips

114 cups of butter 1

12 Tbs of salt


Reescribir la receta que se necesitaría para 2 lotes de galletas.__________ cups of flour __________ cups of sugar

__________ cups of chocolate chips __________ cups of butter

__________ Tbs of salt

Reescribir la receta que se necesitaría para 5 lotes de galletas__________ cups of flour __________ cups of sugar

__________ cups of chocolate chips __________ cups of butter

__________ Tbs of salt


Wicomico County Public Schools Remote LearningMath 6 and Math 6EX Topics: May 11th – May 22nd Activity #21. Calentamiento:

The following diagram shows the base ten models we can use to add, subtract, multiply, or divide whole numbers. These models should be familiar because they were used often in elementary school.

Part A: How can we use the base ten diagram below to model 812 ÷ 4?

Model:

Answer:

Part B: Charlie solved the problem 812 ÷ 4 and found an answer of 23. His work is shown below:Explain the error Charlie made when working out the problem.


2. Nota de revisión:

Dividing Whole Numbers

Common ways we see division written:

Vocabulary:

Quotient: the answer to a division problem/ la respuesta a un problema de división

Dividend: the number that is divided/ el número que se divide

Divisor: the number used to divide your dividend / el número utilizado para dividir su dividendo

Numerator: The top number in a fraction that represents the number of parts. When dividing, the numerator is the dividend./ El número superior de una fracción que representa el número de partes. Al dividir, el numerador es el dividendo.

Denominator: The bottom number in a fraction which represents the number needed to reach 1 whole. When dividing, the denominator is the divisor. / El número inferior en una fracción que representa el número necesario para alcanzar 1 entero. Al dividir, el denominador es el divisor.

Remainder: the number left after a quotient is found/ el número que queda después de un cociente se encuentra

In fifth grade you probably wrote your answers with remainders like this:

174 ÷ 12 = 14 r. 6

In sixth grade, however, we learned that we place the remainder over the divisor:

174 ÷ 12 = 14 612

This is even easier to keep in mind when you set your division problems up in fraction form:


Pasos para dividir números enteros

Example 1: 573

2

Step 1. Estimate 600 ÷ 2 = 300

Your answer should be somewhere around 300.

Step 2. Divide the Hundreds

Divide 5 ÷ 2 = 2Multiply 2 x 2 = 4Subtract 5 – 4 = 1Bring down the 7 in the tens place.Repeat these steps to divide the tens.

Step 3. Divide the Tens

Divide 17 ÷ 2 = 8Multiply 8 x 2 = 16 Subtract 17 – 16 = 1Bring down the 3 in the ones placeRepeat these steps to divide the ones.

Step 4. Divide the Ones

Divide 13 ÷ 2 = 6Multiply 6 x 2 = 12 Subtract 13 – 12 = 1

Answer: Your final answer is 286 remainder 1, which can be written as 28612 .

Comparing our answer to our estimate of 300, this answer is reasonable.


Example 2: 9,763 ÷ 13

Step 1. Estimate 10,000 ÷ 10 = 1,000

Your answer should be somewhere around 1,000.

Step 2. Divide the Thousands

Divide 9 ÷ 13Since you can’t get a full group of 13 from 9, place a 0 in the thousands place as a place holder.


Divide 97 ÷ 13 = 7Multiply 13 x 7 = 91Subtract 97 – 91 = 6Bring down the 6 in the tens place.Repeat these steps to divide the tens.


Divide 66 ÷ 13 = 5Multiply 13 x 5 = 65Subtract 97 – 91 = 6Bring down the 6 in the tens placeRepeat these steps to divide the ones.


Divide 13 ÷ 13 = 1Multiply 13 x 1 = 13Subtract 13 – 13 = 0


Answer: Your final answer is 751.Comparing 751 to our estimate of 1,000, this answer is reasonable.

Example 3: 3,651 ÷ 12

Step 1. Estimate 3,600 ÷ 12 = 300

Your answer should be somewhere around 300*Notice that we did not round 3,651 to 3,700. Instead 3,600 was chosen because it is compatible with 12. Sometimes it is necessary to break away from standard rounding when estimating division problems and use numbers that are compatible. This can make the estimation tricky if you are not as comfortable with your basic facts./Observe que no redondeamos 3.651 a 3.700. En su lugar, se eligieron 3.600 porque es compatible con 12. A veces es necesario romper con el redondeo estándar al estimar los problemas de división y utilizar números que son compatibles. Esto puede hacer que la estimación sea complicada si no se siente tan cómodo con sus hechos básicos

Step 2. Divide the Thousands

Divide 3 ÷ 12Since you can’t get a full group of 12 from 3, place a 0 in the thousands place.


Divide 36 ÷ 12 = 3Multiply 12 x 3 = 36Subtract 26 – 36 = 0Bring down the 5 in the tens placeRepeat these steps.


Divide 5 ÷ 12 Since you can’t get a full group of 12 from 5 place a 0 in


Bring down the 1.Divide 51 ÷ 12 = 4


the tens place. Multiply 12 x 4 = 48Subtract 51- 48 = 3

Answer: Your final answer is 304 remainder 3, which can be written as 304312 .

Don’t forget that 304312 can also be written as 304

14 or as 304.25.

Comparing our answer to our estimate of 300, this answer is reasonable.

3. Practice:Part A. Solve the following problems without using a calculator. You may use the grid paper provided, or the space below, but show all work.


Part B. Pandemic Planning

The Salisbury Middle School math teachers are collecting necessary items to donate during the quarantine. They are collecting canned foods, toilet paper, and water. The math teachers will also be volunteering at local food banks.

1. Mrs. Wilson purchased canned foods during the quarantine in order to donate. She purchased 168 canned foods. If she splits the 168 cans between 3 food banks, how many cans will each food bank receive?/ Sñr. Wilson compró alimentos enlatados durante la cuarentena para donar. Compró 168 alimentos enlatados. Si divide las 168 latas entre 3 bancos de alimentos, ¿cuántas latas recibirá cada banco de alimentos?

2. Mrs. Hare found toilet paper while shopping at Walmart. She was able to purchase 5 cases each with 36 rolls of toilet paper. She knows 9 families that need toilet paper, so she is going to split the rolls of toilet paper evenly


Image Source: https://www.flickr.com/photos/bibbit/43647466505

https://www.flickr.com/photos/bibbit/43647466505

between the families./Sñr.Hare encontró papel higiénico mientras compraen Walmart. Ella fue capaz de comprar 5 cajas cada una con 36 rollos de papel higiénico. Ella conoce a 9 familias que necesitan papel higiénico, así que va a dividir los rollos de papel higiénico uniformemente entre las familias.

a. How many toilet-paper rolls did Mrs. Hare purchase?

b. Estimate the number(Estimar el número) of toilet-paper rolls each family will receive.

c. How many toilet-paper rolls will each family receive?

3. Ms. Wainwright purchased cases of water to donate to local food banks. She purchased 15 cases each with 24 bottles of water. She is donating to 3 food banks./La Sra. Wainwright compró cajas de agua para donar las bancos de alimentos locales. Compró 15 cajas cada una con 24 botellas de agua. Está donando a 3 bancos de alimentos.

a. How many water bottles did she purchase altogether?

b. How many water bottles will each food bank receive?

4. Mrs. Nordhoff was volunteering at a local food bank. She was splitting water bottles into care packages for local families. The food bank told Mrs. Nordhoff they had 2,056 water bottles and they were putting 8 bottles in each care package. They told her they could provide for 32 families. Explain whether they are correct or incorrect and how you know/sñr. Nordhoff era voluntaria en un banco de comida local. Estaba dividiendo botellas de agua en paquetes de cuidado para familias locales. El banco de alimentos


Image Source: https://www.flickr.com/photos/thadz/16466809032

Image Source: https://www.flickr.com/photos/baltimoreheritage/35465874664

https://www.flickr.com/photos/baltimoreheritage/35465874664

https://www.flickr.com/photos/thadz/16466809032

https://www.flickr.com/photos/chriswaits/6780129193/

le dijo a la señora Nordhoff que tenían 2.056 botellas de agua y que estaban poniendo 8 botellas en cada paquete de cuidado. Le dijeron que podían proveer para 32

familias. Explicar si son correctos o incorrectos y cómo sabe.

They are correct/incorrect because….I know they are correct/incorrect because….

4. Optional Extension: After you have completed your work, here is an optional activity.Extensión opcional: Una vez que haya completado su trabajo, aquí hay una actividad opcional.


Solve the following problems without using a calculator. Show all work. Then find the letter that matches your answer and record it at the bottom of the page to answer the riddle. / Resuelva los siguientes problemas sin usar una calculadora. Muestre todo el trabajo. A continuación, busque la letra que coincida con su respuesta y regístrela en la parte inferior de la página para responder al acertijo

Wicomico County Public Schools Remote LearningMath 6 and Math 6EX Topics: May 11th – May 22nd Activity #31. Calentamiento:

Source: (https://wodb.ca/)

Which one doesn’t belong?/ ¿Cuál no pertenece?

2. Nota de revisiónSource: Khan Academy

A conversion is a change in the form of measurement (units), without a change in the size or amount. / es un cambio en la forma de medida (unidades), sin un cambio en el tamaño o la cantidad.

Example 1: We can covert1 gallons into cups, using the conversion factor.

1 convertirMath 6 & Math 6EX May 11 – May 22, Page. 19

https://wodb.ca/

Based on this double number line, you can do 64 ÷ 4 to find the unit rate that there are 16 cups in 1 gallon. To figure out how many cups are in 3 gallons, we multiply 16 cups by 3 to get 48 cups in 3 gallons. Example 2: The ratio table below shows that 1 inch is equivalent to 2.54 centimeters.

If there are two times as many centimeters, there are also two times as many inches.

If there are ten times as many inches, there are also ten times as many centimeters.

Conversion Resource


3. Practice 1) The tape measure below contains both customary and metric units. Which of the following statements are true? Select all that apply./ ¿Cuáles de las siguientes afirmaciones son verdaderas? Seleccione todos los que correspondan (Discovery Techbook)

A. There are 2.54 centimeters per inch.

B. The ratio of centimeters to inches is 1 to 2.54.

C. For every 1 inch, there are 2.54 centimeters.

D. 2.54 in. = 1 cm

E. For every 2.54 inches, there is 1 centimeter.

F. The ratio of inches to centimeters is 1 to 2.54.

2) At birth, Elinor weighed 7 pounds 3 ounces. How many ounces is this? (Discovery Techbook, 1 pound =16 oz)

A) 21 ounces B) 59 ounces C) 73 ounces D) 115 ounces

3) Marshawn’s birthday is in 105 days. Complete the ratio table to determine how many weeks until

Marshawn’s birthday2. (Discovery Techbook)

4) How could you best use the double number line to show the conversion of 480 hours into days? (Discovery Techbook)

5) Some new information has been collected about the tallest building in the world. Use

2 cuántas semanas hasta el cumpleaños de MarshawnMath 6 & Math 6EX May 11 – May 22, Page. 21

Days

Hours

https://wcboe.discoveryeducation.com/learn/techbook/units/ab3684f2-eab8-4912-8989-66650de8b9b7/concepts/239465a9-9e59-4430-8f2e-5b3f0743e36b

what you know about meters and miles to circle which building is the tallest in the world./ Usa lo que sabes sobre metros y millas para rodear qué edificio es el más alto del mundo (Teacher Created)

Burj Khalifa: 12 of a mile Tokyo Skytree: 634 meters

1 mile= 1609.34 meter/ 1 meter=0.000621371 miles

6) Use what you know about meters and inches to figure out who holds the world record for the longest platform-to-platform bicycle jump. Circle the world record holder./ averiguar quién tiene el récord mundial para el salto de bicicleta de

plataforma a plataforma más largo. Círculo del poseedor del récord mundial (Teacher Created)

Vittorio jumped 158 inches Mario jumped 4 meters1 meter =39.3701 inches/ 1 inch= 0.0254 meter


https://en.wikipedia.org/wiki/Burj_Khalifa




4. Optional/Opcional:Source: Open Up

Decide if each measurement is length, area, volume, or weight (or mass)/longitud, área, volumen o peso (o masa) and write on the line.

a) How many centimeters across a handprint _____ length ______

b) How many square inches of paper needed to wrap a box _________________

c) How many Gallons of water in a fish tank _________________

d) How many pounds in a bag of potatoes ____________________

e) How many feet across a swimming pool _____________________

f) How many ounces in a bag of grapes ____________________

g) How many liters in a punch bowl __________________

h) How many square feet of grass in a lawn _________________

Find something in your home that would best be measured with the following units of measure./Encuentre algo en su hogar que mejor se mida con las siguientes unidades de medida

Feet Pounds Centimeters Fluid Ounces Cups Fahrenheit

House Item

Measurement Estimate


This page was left blank intentionally.

Wicomico County Public Schools Remote LearningMath 6 & Math 6EX May 11 – May 22, Page. 24

Math 6 and Math 6EX Topics: May 11th – May 22nd Activity #41. Calentamiento:

EXPRESSION MATCHING GAME Cut the “cards” apart and match the verbal expression with the correct algebraic expression; OR, write the algebraic expression under the matching verbal expression. These cards may also be used to play a memory game with a family member or by yourself. Use the extra cards to make up your own matching expressions! /Cortar las "tarjetas" aparte y hacer coincidir la expresión verbal con la expresión algebraica correcta; O, escriba la expresión algebraica bajo la expresión verbal coincidente. Estas cartas también se pueden utilizar para jugar un juego de memoria con un miembro de la familia o por sí mismo. ¡Usa las cartas adicionales para componer tus propias expresiones coincidentes!

a number increased by 6 x less than 3.8 c/4

7 – y

a number divided by 12

4 times a number minus 2 times the same number

(2/5) x

4(n)

the sum of 7 and a number, divided by 3

c divided by 4 c – 1

4x + 2

20 divided by the sum of 5 and a number

1/4 of x 4x – 2x

(7 + y)/3

the sum of 4 times a number and 2

0.25 of n 6m

c ÷ 2

two-fifths of a number 5 times x 5x

x + 6

c divided by 2 45 divided by d (1/4) x

0.25n

7 decreased by a number the product of m and 6 45/d

6(x + 4)

6 times the sum of x and 4 1 less than c 3.8 – x

20 ÷ (5 + b)

a number multiplied by 4 x/12


2. Nota de revisión:Source: Khan

Writing Algebraic Expressions IMPORTANT VOCABULARY: ·   ALGEBRAIC EXPRESSION:  an expression that contains variables, numbers, and operations./ una expresión que contiene variables, números y operaciones·   KEY PHRASE OR SWITCH PHRASE: keywords that tell you what order to put the number, variable or operation in./ palabras clave que le indican en qué orden colocar el número, variable u operación.

Steps to Follow / Pasos a seguir : 1.  You can translate a WORD PHRASE to an algebraic expression. Puede traducir una FRASE WORD a una expresión

algebraica2.  Operation KEY WORDS can help you choose the correct operation to use./ La operación KEY WORDS puede ayudarle a elegir el funcionamiento correcto para usar3.  If the VARIABLE is given, you must use that variable. If there is no variable given, then you may choose your own variable to use. Si se da el VARIABLE, debe utilizar esa variable. Si no hay ninguna variable dada, entonces usted puede elegir su propia variable para utilizar.

REMEMBER: the order of subtraction and division DO matter (and sometimes addition), so make sure to pay attention to those phrases! el orden de resta y la división importa (y a veces suma), así que asegúrese de prestar atención a

esas frases!

Keyword Phrase:

Adding/ agregando Add/ añadir   Sum /sumaIncreased/ aumentado  

 More/ más Altogether/ en conjunto        

Plus/ más , Total       Combined/combinado

Multiplying/ multiplicando   Multiply/ multiplicar      

Product/producto Times /veces   

Double or Twice (•2)/ doble o dos veces Triple (•3)

Half (•12 or •0.5)/medio

Example:   7n7(6)  7•6 X = variable, NOT Multiply

Reverse the Order/ invertir el orden

Than /que(greater than or less than/ mayor

o menor que) From/de

Added To/ añadido a  

Subtracting/ sustraer Subtract/ sustraer  

Difference/diferenciaPassed/pasar    

Remaining/ restante Exceed/ exceder      

Taken/tomado Fewer/ menos      

Decreased/ disminuir Minus/ menos     Less/menos Used/usado

Eliminated/eliminado Deduct/deducir

Loss/pérdida Taller/ Mas alto Bigger/ más grande

Dividing/ divisor   Divide/dividir    

Quotient/ cociente Division/ división    

Average/ promedio   Half/medio (means to ÷2 and

reverse the order)

REMEMBER: Multiplication: Coefficient always

comes before the variable / Multiplicación: El coeficiente

siempre viene antes de la variable 

Division: 1st mentioned goes in the numerator, and 2nd in

denominator when writing a division fraction /

División: 1st mencionado va en el numerador, y 2nd en denominador al

escribir una fracción de división


Examples

Example #1:

11 more than a

a + 11

Example #2:

Sum of d and 9

d + 9

Example #3:

10 multiplied by u

10u

Example #4:

8 divided by d

8 ÷ d or 8d

Example #5:

The product of 8 and k

8k or 8(k)

Example #6:

b split into 14 equal groups

b ÷ 14

Example #7:

Susie ran a race. She ran 5 miles an hour, and the race took her t hours to complete. How long was

the race?

5t or 5(t)

Example #8:

The Running Aces card team won $548 playing in a poker tournament last year. The winnings were

split evenly among the p players/ dividido uniformemente entre los jugadores p. How much did each

player receive?

548p or 548 ÷ p


Example #9:

Sunny earns $12 per hour delivering cakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late delivery Tuesday. How

much money did Sunny earn this week?

12x - 15

Example #10:

There are c players on the Cougars hockey team. The team scored a total of 36 goals this season.

Matthew scored 2 more goals than the average per player. How many goals did he score?

36c + 2

3. Practice:Source: Khan

1. Write an expression for"the quotient of z and 4."

2. Write an expression for “n decreased by 3”

3. Write an expression to representEight more than the product of 2 and a number x

4. Write an expression to representThe sum of seven and the

quotient of a number x and eight

5. Hailey biked 37 miles this morning and another x miles in the evening .

How many kilometers did Hailey bike today?Write your answer as an expression.

6. Riley manages her soccer team. She needs to order 4 practice jerseys for each player . There are y players.

How many total practice jerseys does she need to order? Write your answer as an expression


7. The price of a visit to the dentist is $50. If the dentist fills any cavities, an additional charge of $100 per cavity gets added to the bill.

If the dentist finds n cavities, what will the cost of the visit be? Write your answer as an expression.

8. A large cheese pizza costs $18. Each topping you add on costs $1.50.

How much would it cost to get a large cheese pizza with c toppings added?/ obtener una pizza de queso grande con coberturas c añadidos?Write your answer as an expression.



4. Optional Extension/ extensión opcional:Source: Teacher Pay Teacher Free Resource

Writing Expressions PuzzleTry this puzzle! Cut out the triangle pieces. Then reorganize them by matching each statement line with the correct expression line! ¡Prueba este rompecabezas! Corta las piezas del triángulo. ¡A continuación, reorganícelos haciendo coincidir cada línea de instrucción con la línea de expresión correcta!


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