Skill. 15 Write and Read Decimals. Using Skill 15 COMMON ERRORS. 69 Holt Matemáticas. MATERIALS place-value chart, base-ten blocks, decimal

(1)

MATERIALS place-value chart, base-ten blocks, decimal models

Begin by displaying base-ten blocks and the following place-value chart, covering the places to the right of the decimal point.

Remind students that our number system is based on 10. The value of each place is 10 times as great as the value of the place to its right. Demonstrate with the blocks. Have students state how many blocks it takes to equal the number in the next place to the left. Then discuss moving to the right on the chart. Explain that the value of each place is one-tenth of the value of the place to its left. Remove the paper from the chart and note that the place-value chart can be extended to show values less than 1. Point out that the decimal point separates ones from values less than 1.

Display the decimal models. Emphasize that the model for tenth has larger parts than the model for hundredths.

Then link the language of fractions with denominators of 10 and 100 to the decimal form of a number. Point out the tenths and hundredths in the place-value chart.

Then have students look at Skill 15. Review each example, noting the place-value posi- tion of the digits that represent decimals.

Emphasize the role of the decimal point and note that the word “and” is reserved for the decimal point when reading numbers.

Skill

TRY THESE In Exercises 1 and 2 students write the standard form and word form of a number shown in a place-value chart.

• Exercise 1 Write 826.3

• Exercise 2 Write 4,351.22

PRACTICE ON YOUR OWN Review the example at the top of the page. Ask students to describe the value of each digit and tell you the fraction form of 8 tenths (₁⁸₀).

CHECK Determine if the students can write the word form of a number written in standard form. Success is indicated by 2 out of 2 correct responses.

Students who successfully complete the Practice on Your Ownand Check are ready to move to the next skill.

COMMON ERRORS

• Students may forget to write a zero as a placeholder in a number. For example, students may write 6 and 3 thousandths as 6.3.

• Students may be unable to express the word names of numbers written in standard form. For example, they might read 5.47 as “five and 47” or “five point four seven.”

Students who made more than 2 errors in the Practice on Your Own, or who were not successful in the Check section, may benefit from the Alternative Teaching Strategy on the next page.

Using Skill 15

OBJECTIVE Write and read decimals

15 Write and Read Decimals

20 Minute^s

Thousands hundreds tens ones • tenths hundredths

1000 100 10 1 1

1 0 or 0.1 1

1 00 or 0.01

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In this activity, students work with only ones, tenths, and hundredths to help focus on the place value of decimals.

Review these equivalent forms and display models of each.

one tenths hundreths

List the following on the flip chart.

1 and 5 tenths 1 and 2 hundredths 1 and 48 hundredths

Guide students to model and write the fraction form of each number.

For 1 and 5 tenths, students outline two 10 10 squares on the paper. To represent 1, they shade the entire grid; to represent 5 tenths, they outline 10 columns and shade 5.

Note that they can write 1 and 5 tenths as a mixed number.

Ask: What denominator will the fraction part of the mixed number have? Explain.

(10; the word name is 5 tenths, so the denominator is 10.)

Review decimal place-value positions and guide students to record the decimal form of the number (1.5).

Use a similar approach to help students represent 1 and 2 hundredths. Note that when recording the decimal form, students think:

hundredths means two decimal places.

Guide students to write the digit 2 in the hundredths place first, then record the zero in the tenths place.

1 and 2 hundredths Think: 1. ? ? 1. ? 2 1. 0 2 Then, focus on 1 and 48 hundredths.

Students may write this as 1.048; it is helpful to review the expanded forms of this

number:

Think: 48 hundredths

4 tenths 8 hundredths So: 1 and 48 hundredths

1 1 4

0 1

8

00 or 1 0.4 0.08 Guide students to model the number two ways:

Continue building conceptual understanding using other similar examples.

or

1 4

tenths 8 hundredths

1 48

hundredths

OBJECTIVE Model ones, tenths, and hundredths and write numbers in standard and word forms

Alternative Teaching Strategy

Write and Read Decimals

25 Minut^e

s

Optional

MATERIALS grid paper, flip chart

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Escribir y leer decimales

Ejemplo A Forma desarrollada: 6060.40.03 Forma estándar: 66.43 Con palabras: 66 y 43 centésimas Forma desarrollada: Forma estándar: 135.9 Con palabras: 135 y 9 décimas Forma desarrollada: Forma estándar: 5,301.8 Con palabras: 5 mil 301 y 8 décimas

decenasunidadesdécimas . unidades . unidades . centésimas 101 6640.10.01 ..3

15

Escribe el decimal en forma estándar y con palabras.

Ejemplo B 100 30 5 0.9

centenasdecenas décimas 10010 93

10.1 15

Ejemplo C 5,000 300 0 1 0.8

millares, ,

centenasdecenas décimas 1,0001001010.1 5 183 0.

Puedes usar una tabla de valor posicional para ayudarte a leer y escribir decimales. Razona: 800 20 6 0.3 En forma estándar: Con palabras:En forma estándar: Con palabras:y décimas

1 Razona: 4,000 300 50 1 0.2 0.02 mil ycentésimas

2 Ir a siguiente página

DestrezaDestreza

unidades . .

centenasdecenasdécimas 10010 3

10.1 862

unidades . millares, ,

centenascentésimasdecenasdécimas 1,0001001010.100.1 4 1223 5.

Inténtalo

Di “y” al leer el punto decimal.

usa una coma para separar los millares de las centenas

Nombre Destreza

(4)

Comprueba

Usa el valor posicional para ayudarte a escribir y leer decimales.

Usa la coma para separar los millares de las centenas.

Razona:

15

Practica por tu cuenta Destreza Destreza

Razona: 20 3 0.5 0.07

Forma estándar:

Con palabras: y

centésimas

800 90 0 0.3

Forma estándar:

Con palabras:

Razona: 100 70 7 0.6 0.08

Forma estándar:

Con palabras: y

centésimas

100,000 6,000 400 30 4 0.1 0.09

Forma estándar:

Con palabras:

4 2

3 1

169 y 45 centésimas

Forma estándar:

2 mil, 165 y 5 décimas

Forma estándar:

6 5

6,489.9

Word Form:

123,690.56

Word Form:

8 7

Forma desarrollada:

^600,000 10,000 1,000 300 40 5 0.8

Forma estándar:

611,345.8

Con palabras: 611 mil, 345 y 8 décimas

Recuerda decir

“y” al leer el punto decimal.

Escribe el decimal en forma estándar y con palabras.

Escribe el decimal con palabras.

Escribe el decimal en forma estándar.

centenas decenas

de millar de millar millares , centenas decenas unidades . décimas

100,000 10,000 1,000 100 10 1 0.1

6 1 1 , 3 4 5 . 8

Nombre Destreza

(5)

Have students read the definition of a multiple given above the examples.

Ask students to count by 2s beginning with 2. Tell them that the numbers they said are multiples of 2. Have them count by 5s beginning with 5.

Ask: The numbers you just said are multi- ples of what number? (5)

Direct the students’ attention to the first example.

Ask: What is the product of 1 and 4? (4) 2 and 4? (8) 3 and 4? (12) 4 and 4? (16) What do we call these products? (multiples of 4)

Guide students to understand that they can find multiples of 4 by multiplying a whole number by 4. Proceed in a similar manner with the other two examples in the lesson.

Help students understand that although they are writing the first 5 multiples for each number, they can find many more multiples.

TRY THESE In Exercises 1–3, students multiply to find the first five multiples of numbers.

• Exercise 1 Multiples of 3

Skill

PRACTICE ON YOUR OWN Review the example at the top of the page. Ask students why they multiply 1, 2, 3, 4, and 5 by 5.

Explain that although they can multiply any whole number except zero by 5 to get a multiple of 5, the example asks for the first five multiples only.

CHECK Determine if students know how to find the multiples of a number, and, given the first three multiples, can list the next three multiples in the sequence.

Success is indicated by 2 out of 2 correct responses.

COMMON ERRORS

• Students may list one multiple incorrectly and thus write all subsequent multiples incorrectly.

• Students may have forgotten the multiplication facts and give incorrect products.

Using Skill 7

OBJECTIVE Write the multiples of a number

7 ^Multiples

5 Minute^s

(6)

Have students use number lines to find multiples of given numbers. Define a multiple as the product of the number and any whole number except zero.

Demonstrate how to show multiples of 3.

Have students begin on the point for 0, count by threes, and draw equal jumps to the numbers as they count and name them.

Then suggest students circle all the numbers they landed on. Explain that when they count by threes, the numbers they name are the multiples of three.

Now ask students to write the multiplication expression for each multiple. Have them write 1 3 above the 3, 2 3 above the 6, and so forth.

Have students recall the definition of a multiple and determine that 0 is not a multiple and that 3 is the first multiple of the number 3. Guide them to see that the other numbers they circled are multiples also because they are the products of the whole numbers 1, 2, 3, 4, 5, 6, 7, 8, and the number 3.

Repeat the activity for multiples of 4 and 5.

When you feel confident that the students understand how to find the multiples of a number, have them find the first five multiples of other numbers using multiplication only.

OBJECTIVE Use the number line to find multiples

MATERIALS number lines 0–25

Alternative Teaching Strategy

Use a Number Line to Find Multiples

15 Minutes

Optional

4 6 8 10 12 14 16 18 25

2

0 3 5 7 9 11 13 15 17 19 20 21 22 23 24

1 x 3 2 x 3 3 x 3 4 x 3 5 x 3 6 x 3 7 x 3 8 x 3

0 x 3

1

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Múltiplos

3 , , , , ↑↑↑↑↑ 1323334353 Los cinco primeros múltiplos de 3 son:

321

Haz una lista con los cinco primeros múltiplos de 4. Multiplica 4 por los números 1, 2, 3, 4 y 5. 48121620 01424344454 Los cinco primeros múltiplos de 4 son: 4, 8, 12, 16 y 20.Los cinco primeros múltiplos de 7 son: 7, 14, 21, 28 y 35.Los cinco primeros múltiplos de 9 son: 9, 18, 27, 36 y 45. Ir a siguiente página

7

Haz una lista con los cinco primeros múltiplos de un número.

Haz una lista con los cinco primeros múltiplos de 7. Multiplica 7 por los números 1, 2, 3, 4 y 5.

Haz una lista con los cinco primeros múltiplos de 9. Multiplica 9 por los números 1, 2, 3, 4 y 5. 714212835 01727374757

918273645 01929394959

Un múltiplo es el producto de un número multiplicado por cualquier número cabal, excepto cero.

DestrezaDestreza Inténtalo

Nombre Destreza

(8)

Comprueba

Destreza

Destreza 7

Practica por tu cuenta

8

, , , ,

↑ ↑ ↑ ↑ ↑

1 8 2 8 3 8 4 8 5 8 Los cinco primeros múltiplos de 8 son:

11

Los cinco primeros múltiplos de 11 son:

11, , , ,

11 11 11 11 11

20

20, , , ,

10

, , , ,

↑ ↑ ↑ ↑ ↑

1 10 2 10 3 10 4 10 5 10 Los cinco primeros múltiplos de 10 son:

12

Los cinco primeros múltiplos de 12 son:

12, , , ,

12 12 12 12 12

30

30, , , , 6

4 2

5 3 1

Haz una lista con los tres múltiplos siguientes de cada número.

Haz una lista con los cinco primeros múltiplos de un número.

4

4, 8, 12, 16, 20, 24, , ,

7

7, 14, 21, 28, 35, , , 8

7

Haz una lista con los tres múltiplos siguientes de cada número:

15

15, 30, 45, , ,

25

25, 50, 75, , , 10

9

Haz una lista con los cinco primeros múltiplos de 5.

, , , ,

↑ ↑ ↑ ↑ ↑

1 5 2 5 3 5 4 5 5 5

Los cinco primeros múltiplos de 5 son:

5, 10, 15, 20 y 25.

25 20

15 10

Razona: Un múltiplo es 5 el producto de un número multiplicado

por cualquier número cabal, excepto cero.

Nombre Destreza

(9)

Direct students to Step 1. Ask: Does it mat- ter what values you choose for x?(No, any number will work, smaller numbers are easier to work with and graph.)

For Step 2: Which value comes first in an ordered pair?(x)

How do you plot an ordered pair?(The x-coordinate indicates how many units to move left or right and the y-coordinate indi- cates how many units to move up or

down.)

For Step 3: Why is the line extended past the plotted points?(The line represents all coordinates that are solutions to the equation and not just those points that can be plotted on the graph.)

TRY THESE In Exercise 1 students create a table of values, plot the ordered pairs, and draw the line for an equation.

• Exercise 1 x x 2 y (x, y)

2 2 2 0 (2, 0)

1 1 2 1 (1, 1)

0 0 2 2 (0, 2)

1 1 2 3 (1, 3)

- 2 - 1- 1 - 3

- 3 - 4

- 4 + 5

+ 5

x y

-5

- 5 + 1 + 2

+ 2 + 3

+ 3 + 4

+ 4 0

Skill

PRACTICE ON YOUR OWN Review the steps at the top of the page.

In Exercises 1–3, students graph a linear equation.

CHECK Determine that students know how to graph a linear equation. Success is indicated by 1 out of 1 correct responses.

Students who successfully complete the Practice on Your Ownand Check are ready to move on to the next skill.

COMMON ERRORS

• Students may switch the x- and y- coordinates. Stress that the x-coordinate moves left or right and the y-coordinate moves up or down.

• Students may not plot enough ordered pairs to ensure that their line is straight.

Using Skill 64

OBJECTIVE Graph linear equations

64 Graph Linear Equations

15 Minutes

(10)

Distribute graph paper and rulers to stu- dents. Write the equation x + y = 1 on the board.

Ask: How many points determine a line?

(2)

Have students determine the x- and y- intercepts of the equation.

Ask: When the graph crosses the y-axis, what is the value of x?(0)

To find the y-intercept, have students substitute 0 in for x and solve.

y 0 1; y 1. The ordered pair is written as (0, 1).

Ask: When the graph crosses the x-axis, what is the value of y?(0)

To find the x-intercept, have students substitute 0 in for y and solve.

x 0 1; x 1. The ordered pair is written as (1, 0).

Have students create a coordinate grid on their graph paper. Then have students plot the two ordered pairs on their grid: (0, 1) and (1, 0).

Ask: How do you plot the coordinates?

(The x-coordinate tells you how many units to move left or right, the y-coordinate tells you how many units to move up or down.) Point out that the order of the coordinates is important. Have students draw a line through the two points.

Repeat the activity several times with different equations.

When students show an understanding of the graphing process using whole numbers, change the equations to include fractions.

OBJECTIVE Graph a linear equation MATERIALS graph paper, ruler

Alternative Teaching Strategy

Graphing Linear Equations Using Intercepts

15 Minutes

Optional

(11)

Representar gráficamente ecuaciones lineales 64

La gráfica de una ecuación es la representación gráfica de todos los puntos cuyas coordenadas son las soluciones de la ecuación. Representa gráficamente la ecuacióny= x3. Paso 1: Elige valores de x y crea una tabla de valores.Paso 2: Representa gráficamente los pares ordenados.Paso 3: Dibuja una línea que atraviese los puntos. 0 - 2

- 1 - 1 - 2 - 3

- 4

+ 5 - 4

+ 5

x

y

- 5

+ 1 - 5

+ 1 + 2

+ 2+ 3

+ 4

00

- 2

- 1 - 1 - 2 - 3

- 4

+ 5 - 4

+ 5

x

y

- 5

+ 1 - 5

+ 1+ 2

+ 3

+ 4

0 Representa gráficamente la ecuación en un plano cartesiano. yx2 Crea una tabla de valores:

Marca los puntos y dibuja la línea. 0

- 2

- 1 - 1 - 2 - 3

- 4 - 3

+ 5 - 4

+ 5

x

y

- 5

+ 1 - 5

+ 1+ 2

+ 3

+ 4 + 3 + 2 + 4

0

1 Ir a siguiente página

xx3y(x, y) 00 33(0, 3) 11 34(1, 4) 33 30(3, 0) 22 31(2, 1) xx2y(x, y) 2(__, __) 1(__, __) 0(__, __) 1(__, __)

DestrezaDestreza Inténtalo

Nombre Destreza

(12)

Comprueba

Para representar gráficamente una ecuación lineal sigue estos pasos.

Paso 1: Haz una tabla de valores.

Paso 2: Marca los pares ordenados.

Paso 3: Dibuja una línea que atraviese los puntos.

64

Practica por tu cuenta

Representa gráficamente cada ecuación en un plano cartesiano.

y x 1

Crea una tabla de valores:

Marca los puntos y dibuja la línea.

- 4 - 4 - 2- 2 - 6

- 6 - 8

- 8 + 10

+ 10

x y

-10

- 10 + 2

+ 2 + 4

+ 4 + 6

+ 6 + 8

+ 8 0

1

y x 5 y 2x 1

- 4 - 4 - 2- 2 - 6

- 6 - 8

- 8 + 10

+ 10

x y

-10

- 10 + 2

+ 2 + 4

+ 4 + 6

+ 6 + 8

+ 8 0

3

- 4 - 4 - 2- 2 - 6

- 6 - 8

- 8 + 10

+ 10

x y

-10

- 10 + 2

+ 2 + 4

+ 4 + 6

+ 6 + 8

+ 8 0

2

y 2x 1 4

- 4 - 4 - 2- 2 - 6

- 6 - 8

+ 10

x y

-10

+ 2 + 2 + 4

+ 4 + 6

+ 6 + 8

+ 8 0

Representa gráficamente la ecuación en un plano cartesiano.

x x 1 y (x, y)

2 (__, __ )

1 (__, __ )

0 (__, __ )

1 (__, __ )

Nombre Destreza

Destreza

(13)

Begin by reviewing the meaning of factors:

Factors are two numbers that are multi- plied. The result is the product. Explain that in this activity students will be asked to find all the factors of a number.

Direct students’ attention to Step 1 and the statement that every counting number has at least two factors. (1 and itself) Provide other examples such as:

7 : 1 and 7 9 : 1 and 9 100 : 1 and 100

Point out that in this step, another important concept is introduced: A factor always divides the product without a remainder.

Direct the students’ attention to Step 2. The important point in this step is that the factors of 8 are numbers from 1 to 8. Explain that the statement means that the only numbers that are reasonable to test as factors are the numbers from 1 through 8.

Direct the students’ attention to Step 3.

Emphasize that when the factors repeat, then all the factors have been found.

Suggest to the students that they write the factors of a number as they find them. After they have found all the factors of a number, then they can order them from least to greatest to tell if any factors repeat. Remind students that 2 4 are the same factors as 4 2. Only the order has changed.

Skill

TRY THESE Exercises 1–3 model the type of exercise students will do on the Practice on Your Own page.

• Exercises 1–2 The number has 4 factors.

• Exercise 3 The number has 5 factors.

PRACTICE ON YOUR OWN Review the example at the top of the page. Ask the students to think of the division sentence for each example shown. For 2 ? 7, think 7 2 ?.

CHECK Determine if students can find all the factors of a number. Success is indicated by 2 out of 3 correct responses.

COMMON ERRORS

• Students may list multiples instead of factors.

• Students may omit some factors when writing the list.

• Students may lack proficiency with the basic multiplication and division facts and may write incorrect factors.

Using Skill 8

OBJECTIVE Find all the factors of a number

8 ^Factors

15 Minutes

(14)

You may wish to review division facts from 1 through 9 with the students.

Recall that one method for finding factors is to use multiplication. Another method involves division. Remind students that a factor of a number divides the number without leaving a remainder.

Start with the factors of 12. Display the following table. Explain that a table will help- students keep track of the factors they test.

Suggest that students systematically test factors starting with 1. With each division that has no remainder, students have found 2 factors: the divisor and the quotient. You might suggest that students circle the factors in each equation if they result in a quotient without a remainder.

Ask: For the factors of 12, what are the only possibilities that you need to test? (the whole numbers from 1 through 12) When students have tested factors, ask which numbers tested were not factors and why (5, 7, 8, 9, 10, and 11; the quotients all have remainders).

Continue with other examples, keeping the numbers less than 20.

If students continue to have difficulty finding factors, have them use graph paper to picture all the arrays or rectangles that are possible for a given number. When they have exhausted all possibilities, they have found the factors of the number.

OBJECTIVE Use division to find factors of a number

MATERIALS graph paper

Alternative Teaching Strategy

Divide to Find Factors

15 Minutes

Optional

4

2 3

12

Factors: 3 and 4 6

Factors: 2 and 6

Factors: 1 and 12 Possible

Factor Division Quotient

12 1 12 2 12 3 12 4 12 5 1

2 3 4 5

12 6 4 3 2 r 2

(15)

Factores

6 6 6 Los factores de 6 son:Los factores de 10 son: Los factores de 16 son:

10 10 10

16 16 16 16

321

Paso 1Usa las operaciones de multiplicación o división para hallar factores. Comienza por18. Todos los números de conteo tienen como mínimo dos factores, el 1 y el número mismo. Por lo tanto, 1 y 8 son factores de 8. 188←producto ↑ factoresUn factor siempre divide el producto sin que quede residuo. Ir a siguiente página

8

Halla los factores de los números cabales.

Paso 2Comprueba con otros pares de factores. Los únicos factores de 8 posibles que son números cabales son números del 1 al 8. 188 1 y 8 son factores. 2 y 4 son factores.248

Paso 3Continúa hasta que los factores se repitan. 1881 y 8 son factores. 2 y 4 son factores.248 3?83 no es un factor, porque 83 tiene residuo. 42Cuando los factores se repiten, has hallado todos los factores. Por lo tanto, los factores de 8 son 1, 2, 4 y 8.

Halla todos los números cabales que sean factores de 8.

Destreza Destreza

El número 2, ¿es un factor?

Inténtalo

Los factores son dos o más números que se multiplican.

Nombre Destreza

(16)

Comprueba

Haz una lista con los factores de 7.

Razona: Comienza con el número 1 y el número 7.

Luego prueba con el 2, luego el 3, luego el 4, etcétera. Si repites un

par de factores, has hallado todos los factores.

1 7 7 ← 1 y 7 son factores.

2 ? 7 ← 2 no es un factor.

7 1 7 ← Estos se repiten.

Has hallado todos los factores.

Los factores de 7 son 1 y 7.

2, 3, 4, 5 y 6 no son factores porque cuando 7 se divide entre cada uno de estos números, queda un residuo.

Destreza

Destreza 8

Practica por tu cuenta

9

Los factores de 9 son:

12

17

14

15

24

20

11

39

9 6 3

8 5 2

7 4 1

Escribe todos los factores de los números.

Escribe todos los factores de un número.

18 11 28 12 13

10

Nombre Destreza

Skill. 15 Write and Read Decimals. Using Skill 15 COMMON ERRORS. 69 Holt Matemáticas. MATERIALS place-value chart, base-ten blocks, decimal

Skill

Using Skill 15

15 Write and Read Decimals

Alternative Teaching Strategy

Write and Read Decimals

Optional

Escribir y leer decimales

15

DestrezaDestreza

Inténtalo

Comprueba

Usa el valor posicional para ayudarte a escribir y leer decimales.

Usa la coma para separar los millares de las centenas.

Razona:

15

Practica por tu cuenta Destreza Destreza

Forma estándar:

Con palabras: y

centésimas

Forma estándar:

Con palabras:

Forma estándar:

Con palabras: y

centésimas

Forma estándar:

Con palabras:

Forma estándar:

Forma estándar:

Word Form:

Word Form:

Forma desarrollada:

Forma estándar:

Con palabras: 611 mil, 345 y 8 décimas

Escribe el decimal en forma estándar y con palabras.

Escribe el decimal con palabras.

Escribe el decimal en forma estándar.

Skill

Using Skill 7

7 Multiples

Alternative Teaching Strategy

Use a Number Line to Find Multiples

Optional

Múltiplos

7

DestrezaDestreza Inténtalo

Comprueba

Destreza

Destreza 7

Practica por tu cuenta

Haz una lista con los tres múltiplos siguientes de cada número.

Haz una lista con los cinco primeros múltiplos de un número.

Haz una lista con los tres múltiplos siguientes de cada número:

Haz una lista con los cinco primeros múltiplos de 5.

, , , ,

Los cinco primeros múltiplos de 5 son:

5, 10, 15, 20 y 25.

Skill

Using Skill 64

64 Graph Linear Equations

Alternative Teaching Strategy

Graphing Linear Equations Using Intercepts

Optional

Representar gráficamente ecuaciones lineales 64

DestrezaDestreza Inténtalo

Comprueba

Para representar gráficamente una ecuación lineal sigue estos pasos.

Paso 1: Haz una tabla de valores.

Paso 2: Marca los pares ordenados.

Paso 3: Dibuja una línea que atraviese los puntos.

64

Practica por tu cuenta

Representa gráficamente cada ecuación en un plano cartesiano.

Representa gráficamente la ecuación en un plano cartesiano.

Destreza

Destreza

Skill

Using Skill 8

8 Factors

Alternative Teaching Strategy

7 ^Multiples

8 ^Factors