BLACKLINE MASTERS FOR THE COMMON CORE STATE STANDARDS FOR MATHEMATICS GRADE

Size: px
Start display at page:

Download "BLACKLINE MASTERS FOR THE COMMON CORE STATE STANDARDS FOR MATHEMATICS GRADE"

Transcription

1 BLACKLINE MASTERS

2 BLACKLINE MASTERS FOR THE COMMON CORE STATE STANDARDS FOR MATHEMATICS GRADE 6 PROVIDES Tier Intervention for Every Common Core Standard

3 Table of Contents Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. Lesson CC.6.RP. Model Ratios Lesson 2 CC.6.RP. Ratios and Rates Lesson 3 CC.6.RP.2 Find Unit Rates Lesson 4 CC.6.RP.3a Equivalent Ratios and Multiplication Tables Lesson 5 CC.6.RP.3a Problem Solving Use Tables to Compare Ratios Lesson 6 CC.6.RP.3a Algebra Use Equivalent Ratios Lesson 7 CC.6.RP.3a Algebra Equivalent Ratios and Graphs Lesson 8 CC.6.RP.3b Algebra Use Unit Rates Lesson 9 CC.6.RP.3c Model Percents Lesson 0 CC.6.RP.3c Write Percents as Fractions and Decimals Lesson CC.6.RP.3c Write Fractions and Decimals as Percents Lesson 2 CC.6.RP.3c Percent of a Quantity Lesson 3 CC.6.RP.3c Problem Solving Percents Lesson 4 CC.6.RP.3c Find the Whole from a Percent Lesson 5 CC.6.RP.3d Convert Units of Length Lesson 6 CC.6.RP.3d Convert Units of Capacity Lesson 7 CC.6.RP.3d Convert Units of Weight and Mass Lesson 8 CC.6.RP.3d Transform Units Lesson 9 CC.6.RP.3d Problem Solving Distance, Rate, and Time Formulas iii

4 LESSON Model Ratios OBJECTIVE Model ratios. CC.6.RP. Daniel is growing tulips and daffodils in a pot. For every 3 tulips he plants, he plants daffodil. How many daffodils will he plant if he plants 2 tulips? Step Make a model and write the ratio. The ratio of tulips to daffodils is 3:. = tulip = daffodil Step 2 Model the number of daffodils Daniel will plant if he plants 6 tulips. Step 3 Use the model and ratio to make a table. The table shows that for every 3 tulips, there is daffodil. Tulips Daffodils Step 4 Find 2 tulips on the table. The number of daffodils is 4. Step 5 Write the new ratio. The new ratio is 2:4. So, if Daniel plants 2 tulips, he will plant 4 daffodils. Write the ratio of triangles to squares.. : 2. : Draw a model of the ratio. 3. 5: 4. 3:4 Complete the table. 5. table for every 5 students 6. 7 pencils for every student Students 5 5 Tables 2 4 Students 2 3 Pencils 7 28 Ratios and Proportional Relationships

5 Model Ratios Write the ratio of gray counters to white counters. CC.6.RP gray:white 3:4 Draw a model of the ratio. 4. 5: 5. 6:3 Use the ratio to complete the table. 6. Marc is assembling gift bags. For every 2 pencils he places in the bag, he uses 3 stickers. Complete the table to show the ratio of pencils to stickers. 7. Singh is making a bracelet. She uses 5 blue beads for every silver bead. Complete the table to show the ratio of blue beads to silver beads. Pencils Stickers 3 Problem Solving 8. There are 4 quarts in gallon. How many quarts are in 3 gallons? Blue Silver 3 9. Martin mixes cup lemonade with 4 cups cranberry juice to make his favorite drink. How much cranberry juice does he need if he uses 5 cups of lemonade? 2 Lesson

6 LESSON 2 Ratios and Rates OBJECTIVE Write ratios and rates. CC.6.RP. A ratio is a comparison of two numbers by division. Ratios can compare parts of a whole or compare one part to the whole. A rate is a ratio that compares two numbers that have different units. The picture shows a group of school supplies. One part is pencils. The other part is notebooks. Write the ratio of pencils to notebooks. Write the ratio using words, as a fraction, and with a colon. Write the number of pencils first, and then write the number of notebooks. 2 to 4 number of to number of pencils notebooks 2 4 number of pencils number of notebooks 2:4 number of : number of pencils notebooks You could also write a ratio comparing part to whole. Write the ratio of notebooks to school supplies, three ways. 4 to 6 number of to number of notebooks school supplies Write each ratio three ways.. Write the ratio of circles to squares. to : 4 6 number of notebooks number of school supplies 4:6 number of : number of notebooks school supplies 2. Write the ratio of squares to shapes. to : Ratios and Proportional Relationships 3

7 Ratios and Rates Write the ratio in two different ways to 5 4: to : CC.6.RP. 5. 7: to There are 20 light bulbs in 5 packages. Complete the table to find the rate that gives the number of light bulbs in 3 packages. Write this rate in three different ways. Light Bulbs Packages Problem Solving 0. Gemma spends 4 hours each week playing soccer and 3 hours each week practicing her clarinet. Write the ratio of hours spent practicing clarinet to hours spent playing soccer three different ways.. Randall bought 2 game controllers at Electronics Plus for $36. What is the unit rate for a game controller at Electronics Plus? 4 Lesson 2

8 LESSON 3 Find Unit Rates OBJECTIVE Use unit rates to make comparisons. CC.6.RP.2 When comparing prices of items, the better buy is the item with a lower unit price. Determine the better buy by comparing unit rates. A 2-ounce box of Wheat-Os costs $4.08, and a 5-ounce box of Bran-Brans costs $5.40. Which brand is the better buy? Step Write a rate for each. Wheat-Os $ oz Since you are looking for the lower cost per ounce, write cost over ounce. Bran-Brans $ oz Step 2 Write each rate as a unit rate. $ oz 2 = $0.34 oz Divide the numerator and denominator by the number in the denominator. $ oz 5 = $0.36 oz Step 3 Choose the brand that costs less. $0.34 oz So, Wheat-Os are the better buy. $0.34 is less than $0.36. $0.36 oz Determine the better buy by comparing unit rates.. 20 pens for $.60 or 25 pens for $ berries for $2.60 or 7 berries for $3.06 a. Write a rate for each. a. Write a rate for each. and and b. Write each rate as a unit rate. b. Write each rate as a unit rate. and and c. Which is the better buy? c. Which is the better buy? Ratios and Proportional Relationships 5

9 Find Unit Rates Write the rate as a fraction. Then find the unit rate. CC.6.RP.2. A wheel rotates through,800º in 5 revolutions.,800º 5 revolutions,800º 5 5 revolutions 5 = 360º revolution 3. Bana ran 8.6 miles of a marathon in 3 hours. 2. There are 32 cards in 6 decks of playing cards. 4. Cameron paid $30.6 for 8 pounds of almonds. Compare unit rates. 5. An online game company offers a package that includes 2 games for $.98. They also offer a package that includes 5 games for $ Which package is a better deal? 6. At a track meet, Samma finished the 200-meter race in seconds. Tom finished the 00-meter race in 2.54 seconds. Which runner ran at a faster average rate? 7. Elmer Elementary School has 576 students and 24 teachers. Savoy Elementary School has 638 students and 29 teachers. Which school has the lower unit rate of students per teacher? 8. One cell phone company offers 500 minutes of talk time for $ Another company offers 480 minutes for $ Which company offers the better deal? Problem Solving 9. Sylvio s flight is scheduled to travel,792 miles in 3.5 hours. At what average rate will the plane have to travel to complete the trip on time? 0. Rachel bought 2 pounds of apples and 3 pounds of peaches for a total of $0.45. The apples and peaches cost the same amount per pound. What was the unit rate? 6 Lesson 3

10 LESSON 4 Equivalent Ratios and Multiplication Tables OBJECTIVE Use a multiplication table to find equivalent ratios. To find equivalent ratios, you can use a multiplication table or multiply by a form of. CC.6.RP.3a Write two ratios equivalent to 0:4. Use a multiplication table. Step Find 0 and 4 in the same row. Step 2 Look at the columns for 0 and 4. Choose a number from each column. Make sure that the numbers you choose are in the same row. 5 and 7 30 and 42 Step 3 Write the new ratios. 5:7 30: Use multiplication or division. Multiply Divide Step To multiply or divide by a form of, multiply or divide the numerator and denominator by the same number = Step 2 Write the new ratios = Solve Write a ratio that is equivalent to 6:6. a. Find 6 and 6 in the same row. b. Choose a pair of numbers from a different row, in the same columns as 6 and 6. c. Write the equivalent ratio. and 6:6 = : Write two ratios equivalent to Write two ratios equivalent to 8 6. Ratios and Proportional Relationships 7

11 Equivalent Ratios and Multiplication Tables Write two equivalent ratios. CC.6.RP.3a. Use a multiplication table to write two ratios that are equivalent to = 0 6, Determine whether the ratios are equivalent and and and and 3 4 Problem Solving 4. Tristan uses 7 stars and 9 diamonds to make a design. Write two ratios that are equivalent to 7_ There are 2 girls and 6 boys in Javier s math class. There are 26 girls and 4 boys in Javier s choir class. Is the ratio of girls to boys in the two classes equivalent? Explain. 8 Lesson 4

12 LESSON 5 Problem Solving Use Tables to Compare Ratios OBJECTIVE Solve problems involving ratios by using the strategy find a pattern. Use tables of equivalent ratios to solve the problem. Kevin s cookie recipe uses a ratio of 4 parts flour to 2 parts sugar. Anna s recipe uses 5 parts flour to 3 parts sugar. Do their recipes use the same ratio of flour to sugar? CC.6.RP.3a Read the Problem What do I need to find? I need to find out if the ratio of flour to sugar in Kevin s recipe is equivalent to the ratio in Anna s recipe. What information do I need to use? I will use the ratios of flour to sugar. Solve the Problem Make a table of equivalent ratios for each recipe. Kevin s Recipe Flour Sugar Anna s Recipe Flour Sugar Find an amount of flour that is in both tables. 20 How will I use the information? I will make ratios. tables to compare the. Sherona takes a 6-minute break after every 24 minutes of study. Benedict takes an 8-minute break after every 32 minutes of study. Are their ratios of study time to break time equivalent? Write the ratio for Kevin s recipe. 20 Write the ratio for Anna s recipe Are the ratios the same? no So, their recipes do not the same ratio of flour to sugar. 0 use 2. Micah buys 0 pens for every 2 pencils. Rachel buys 2 pens for every 3 pencils. Are their ratios of pens to pencils bought equivalent? Ratios and Proportional Relationships 9

13 Problem Solving Use Tables to Compare Ratios Read each problem and solve. CC.6.RP.3a. Sarah asked some friends about their favorite colors. She found that 4 out of 6 people prefer blue, and 8 out of 2 people prefer green. Is the ratio of friends who chose blue to the total asked equivalent to the ratio of friends who chose green to the total asked? Friends who chose blue Blue Total asked Friends who chose green Green Total asked Yes, 4 6 is equivalent to Lisa and Tim make necklaces. Lisa uses 5 red beads for every 3 yellow beads. Tim uses 9 red beads for every 6 yellow beads. Is the ratio of red beads to yellow beads in Lisa s necklace equivalent to the ratio in Tim s necklace? 3. Mitch scored 4 out of 5 on a quiz. Demetri scored 8 out of 0 on a quiz. Did Mitch and Demetri get equivalent scores? 4. Chandra ordered 0 chicken nuggets and ate 7 of them. Raul ordered 5 chicken nuggets and ate 2 of them. Is Chandra s ratio of nuggets ordered to nuggets eaten equivalent to Raul s ratio of nuggets ordered to nuggets eaten? 0 Lesson 5

14 LESSON 6 Algebra Use Equivalent Ratios OBJECTIVE Use tables to solve problems involving equivalent ratios. CC.6.RP.3a You can find equivalent ratios by using a table or by multiplying or dividing the numerator and denominator by the same number. Kate reads 5 chapters in 2 hours. At this rate, how many chapters will she read in 6 hours? Step Make a table of equivalent ratios Chapters read Time (hours) Step 2 Find 6 hours in the table. Find the number of chapters that goes with 6 hours: 5 Step 3 Write the new ratio: 5 6 The ratios 5 2 are 5 equivalent ratios. So, Kate will read 5 chapters in 6 hours. 6 Julian runs 0 kilometers in 60 minutes. At this pace, how many kilometers can he run in 30 minutes? Step Write equivalent ratios with a missing value = 30 Step 2 Divide the numerator and denominator by 2 to write the ratios using a common denominator. The denominators are the same, so the numerators are equal to each other. So, Julian can run 5 kilometers in 30 minutes. Use equivalent ratios to find the unknown value = = = = 30 2 = = = = = 6 Ratios and Proportional Relationships

15 Algebra Use Equivalent Ratios Use equivalent ratios to find the unknown value. CC.6.RP.3a. 4 0 = = = = = = 40 = = = = = = = = = 3 Problem Solving 3. Honeybees produce 7 pounds of honey for every pound of beeswax they produce. Use equivalent ratios to find how many pounds of honey are produced when 25 pounds of beeswax are produced. 4. A 3-ounce serving of tuna provides 2 grams of protein. Use equivalent ratios to find how many grams of protein are in 9 ounces of tuna. 2 Lesson 6

16 LESSON 7 Algebra Equivalent Ratios and Graphs OBJECTIVE Use a graph to represent equivalent ratios. CC.6.RP.3a Jake collects 2 new coins each year. Use equivalent ratios to graph the growth of his coin collection over time. Step Write an ordered pair for the first year. Let the x-coordinate represent the number of years:. Let the y-coordinate represent the number of coins: 2. Ordered pair: (, 2) Coins Year Step 2 Make a table of equivalent ratios. Step 3 Write ordered pairs for the values in the table. Step 4 Label the x-axis and y-axis. Step 5 Graph the ordered pairs as points. The point (, 2) represents the year Jake started his collection. It shows that he had 2 coins after year. (, 2), (2, 24), (3, 36), (4, 48), (5, 60) Coins y x Years Use the graph for 5.. Helen walks at a rate of 3 miles in hour. Write an ordered pair. Let the y-coordinate represent miles and the x-coordinate represent hours. (, ) 2. Complete the table of equivalent ratios. Miles 3 2 Hours Write ordered pairs for the values in the table. (, ), (, ), (, ), (, ), (, ) 4. Label the graph. Graph the ordered pairs. y x 5. What does the point (2, 6) represent on the graph? Ratios and Proportional Relationships 3

17 Algebra Equivalent Ratios and Graphs Christie makes bracelets. She uses 8 charms for each bracelet. Use this information for 4. CC.6.RP.3a. Complete the table of equivalent ratios for the first 5 bracelets. Charms Bracelets Write ordered pairs, letting the x-coordinate represent the number of bracelets and the y-coordinate represent the number of charms. (, 8 ), (2, 6 ), (, ), Number of Charms (, ), (, ) 0 3. Use the ordered pairs to graph the charms and bracelets. 4. What does the point (, 8) represent on the graph? y Christie s Bracelets Number of Bracelets x The graph shows the number of granola bars that are in various numbers of boxes of Crunch N Go. Use the graph for Complete the table of equivalent ratios. Bars Boxes Find the unit rate of granola bars per box. Problem Solving 7. Look at the graph for Christie s Bracelets. How many charms are needed for 7 bracelets? Number of Bars y Crunch N Go Granola Bars Number of Boxes 8. Look at the graph for Crunch N Go Granola Bars. Stefan needs to buy 90 granola bars. How many boxes must he buy? x 4 Lesson 7

18 LESSON 8 Algebra Use Unit Rates OBJECTIVE Solve problems using unit rates. CC.6.RP.3b You can find equivalent ratios by first finding a unit rate. Marcia makes bracelets to sell at craft fairs. She sold 4 bracelets for $54. How much could she expect to earn if she sells 25 bracelets? Step Write equivalent ratios. money bracelets $54 4 = 25 money bracelets Step 2 Since 25 is not a multiple of 4, use the known ratio to find a unit rate. $54 4 = Marcia earns $ $ per bracelet. = 25 Step 3 Write an equivalent ratio by multiplying the unit rate s numerator and denominator by the same value. Since 25 = 25, multiply by 25 over 25. $ = 25 Step 4 Since the denominators are equal, the numerators are also equal. $ = 25 So, Marcia would earn $275 if she sells 25 bracelets. Use a unit rate to find the unknown value = 300 a. Find the unit rate: = 300 b. = 300 c = = = = 54 = = = d. = Ratios and Proportional Relationships 5

19 Algebra Use Unit Rates Use a unit rate to find the unknown value = = 7 2 = = = 7 = = = 2 7 CC.6.RP.3b 4. 6 = 3 2 Draw a bar model to find the unknown value = = = = 2 0 Problem Solving 9. To stay properly hydrated, a person should drink 32 fluid ounces of water for every 60 minutes of exercise. How much water should Damon drink if he rides his bike for 35 minutes? 0. Lillianne made 6 out of every 0 baskets she attempted during basketball practice. If she attempted to make 25 baskets, how many did she make? 6 Lesson 8

20 LESSON 9 Model Percents OBJECTIVE Use a model to show a percent as a rate per 00. CC.6.RP.3c A percent is a ratio that compares a number to 00. It represents part of a whole. Model 54% on the 0-by-0 grid. Then write the percent as a ratio. Step The grid represents whole. It has 00 equal parts. To show 54%, shade 54 of the 00 equal parts. Step 2 A ratio can be written as a fraction. Write the number of shaded parts, 54, in the numerator. Write the total number of parts in the whole, 00, in the denominator. So, 54% is 54 out of 00 squares shaded, or shaded total Model the percent and write it as a ratio.. 9% 2. 80% 3. 66% ratio: 4. 3% ratio: 5. 3% ratio: 6. 25% ratio: ratio: ratio: Ratios and Proportional Relationships 7

21 Model Percents Write a ratio and a percent to represent the shaded part. CC.6.RP.3c ratio: 4 00 percent: 4% ratio: percent: ratio: percent: Model the percent and write it as a ratio % 5. 24% 6. 50% ratio: ratio: ratio: Problem Solving The table shows the pen colors sold at the school supply store one week. Write the ratio comparing the number of the given color sold to the total number of pens sold. Then shade the grid. 7. Black 8. Not blue Pens Sold Color Number Blue 36 Black 49 Red 5 8 Lesson 9

22 LESSON 0 Write Percents as Fractions and Decimals OBJECTIVE Write percents as fractions and decimals. CC.6.RP.3c You can write a percent as a decimal and a fraction. Write 40% as a decimal and as a fraction in simplest form. Step Write 40% as a decimal by dividing 40 by 00. This results in the decimal point moving two places to the left. Step 2 Write.40 as a fraction by writing the as a whole number and the decimal as a fraction. The 40 after the decimal point represents 40 hundredths. So, write 40 in the numerator and 00 in the denominator. Step 3 Simplify. So, 40% =.40 = % = 40 = = = 2 5 Write the percent as a decimal and as a fraction in simplest form.. 75% 2. 44% 3. 28% 4. 5% % 6. 38% 7. 7% % % %. 72% 2. 8% Ratios and Proportional Relationships 9

23 Write Percents as Fractions and Decimals Write the percent as a fraction or mixed number. CC.6.RP.3c. 44% 2. 32% 3. 6% % 44% = = % % 7..5% % Write the percent as a decimal % 0. 90%. 0% 2. 8% % % 5. 0.% % Problem Solving 7. An online bookstore sells 0.8% of its books to foreign customers. What fraction of the books are sold to foreign customers? 8. In Mr. Klein s class, 40% of the students are boys. What decimal represents the portion of the students that are girls? 20 Lesson 0

24 LESSON Write Fractions and Decimals as Percents OBJECTIVE Write fractions and decimals as percents. CC.6.RP.3c You can write fractions and decimals as percents. To write a decimal as a percent, multiply the decimal by 00 and write the percent symbol = 7.3% To multiply by 00, move the decimal point two places to the right. To write a fraction as a percent, divide the numerator by the denominator. Then write the decimal as a percent. To write 3 as a percent, first divide 3 by _ So, 3 8 = = 37.5% To write as a percent, multiply by 00 and write the percent symbol. Write the decimal or fraction as a percent Ratios and Proportional Relationships 2

25 Write Fractions and Decimals as Percents Write the fraction or decimal as a percent. CC.6.RP.3c = = = 35% Write the number in two other forms (fraction, decimal, or percent) Problem Solving 3. According to the U.S. Census Bureau, 3 of all adults in the United 25 States visited a zoo in What percent of all adults in the United States visited a zoo in 2007? 4. A bag contains red and blue marbles. Given that 7 of the marbles are red, 20 what percent of the marbles are blue? 22 Lesson

26 LESSON 2 Percent of a Quantity OBJECTIVE Find a percent of a quantity. CC.6.RP.3c You can use ratios to write a percent of a quantity. Find 0.9% of 30. Step Write the percent as a rate per % = Step 2 Multiply by a fraction equivalent to to = 9,000 get a whole number in the numerator. Step 3 Write the multiplication problem. Step 4 Multiply. So, 0.9% of 30 is , = 27, = 0.27 Find the percent of the quantity.. 8% of % of % of % of % of % of % of % of % of % of % of % of, James correctly answered 85% of the 60 problems on his math test. How many questions did James answer correctly? 4. A basketball player missed 25% of her 52 free throws. How many free throws did the basketball player make? Ratios and Proportional Relationships 23

27 Percent of a Quantity Find the percent of the quantity. CC.6.RP.3c. 60% of % of % of % of 82 60% = = % of 2, % of % of % of % of % of 2. 40% of % of 8.4 Problem Solving 3. The recommended daily amount of vitamin C for children 9 to 3 years old is 45 mg. A serving of a juice drink contains 60% of the recommended amount. How much vitamin C does the juice drink contain? 4. During a 60-minute television program, 25% of the time is used for commercials and 5% of the time is used for the opening and closing credits. How many minutes remain for the program itself? 24 Lesson 2

28 LESSON 3 Problem Solving Percents OBJECTIVE Solve percent problems by applying the strategy use a model. CC.6.RP.3c Use a model to solve the percent problem. Lucia is driving to visit her parents, who live 240 miles away from her house. She has already driven 5% of the distance. How many miles does she still have to drive? Read the Problem What do I need to find? I need to find the difference between the total distance and the distance already driven. What information do I need to use? The total distance is 240 miles and she has already driven 5% of the total distance. How will I use the information? I will draw a model to find the number of miles already driven and subtract that amount from the total distance.. At a deli, 56 sandwiches were sold during lunchtime. Twenty-five percent of the sandwiches sold were tuna salad sandwiches. How many of the sandwiches sold were not tuna salad? total distance distance driven Solve the Problem Use a bar model to help. Draw a bar to represent the total distance. Then draw a bar that represents the distance driven plus the distance left.? 5% 00% 240 miles The model shows that 00% = miles, so % of 240 = = miles. 5% of 240 = = 36 So, Lucia has already driven She still has to drive = 204 miles miles. 2. Mr. Brown bought a TV for $450. He has already paid 60% of the purchase price. How much has he already paid and how much does he have left to pay? Ratios and Proportional Relationships 25

29 Problem Solving Percents Read each problem and solve. CC.6.RP.3c. On Saturday, a souvenir shop had 25 customers. Sixty-four percent of the customers paid with a credit card. The other customers paid with cash. How many customers paid with cash? % of 25 = =.25 64% of 25 = = = 45 customers 2. A carpenter has a wooden stick that is 84 centimeters long. She cuts off 25% from the end of the stick. Then she cuts the remaining stick into 6 equal pieces. What is the length of each piece? 3. Mike has $36 to spend at the amusement park. He spends 25% of that money on his ticket into the park. How much does Mike have left to spend? 4. A car dealership has 240 cars in the parking lot and 7.5% of them are red. Of the other 6 colors in the lot, each color has the same number of cars. If one of the colors is black, how many black cars are in the lot? 5. The utilities bill for the Millers home in April was $32. Forty-two percent of the bill was for gas, and the rest was for electricity. How much did the Millers pay for gas, and how much did they pay for electricity? 6. Andy s total bill for lunch is $20. The cost of the drink is 5% of the total bill and the rest is the cost of the food. What percent of the total bill did Andy s food cost? What was the cost of his food? 26 Lesson 3

30 LESSON 4 Find the Whole from a Percent OBJECTIVE Find the whole given a part and the percent. CC.6.RP.3c You can use equivalent ratios to find the whole, given a part and the percent. 54 is 60% of what number? Step Write the relationship among the percent, part, and whole. The percent is 60%. The part is 54. The whole is unknown. Step 2 Write the percent as a ratio. percent = part whole 60% = = 54 Step 3 Simplify the known ratio. Find the greatest common factor (GCF) of the numerator and denominator. 60 = GCF = = = Divide both the numerator and denominator by the GCF = 54 Step 4 Write an equivalent ratio. Look at the numerators. Think: 3 8 = 54 Multiply the denominator by 8 to find the whole. So, 54 is 60% of 90. Find the unknown value. 3 5 = = = is 40% of 2. 5 is 25% of is 20% of is 50% of 5. 4 is 80% of 6. 2 is 5% of is 90% of 8. 2 is 75% of is 30% of Ratios and Proportional Relationships 27

31 Find the Whole from a Percent Find the unknown value. CC.6.RP.3c. 9 is 5% of is 75% of 3. 2 is 2% of 5 00 = = = is 50% of 5. 6 is 40% of is 28% of 7. 5 is 0% of is 6% of 9. 5 is 25% of 0. is 44% of. 9 is 95% of 2. 0 is 20% of Problem Solving 3. Michaela is hiking on a weekend camping trip. She has walked 6 miles so far. This is 30% of the total distance. What is the total number of miles she will walk? 4. A customer placed an order with a bakery for cupcakes. The baker has completed 37.5% of the order after baking 8 cupcakes. How many cupcakes did the customer order? 28 Lesson 4

32 LESSON 5 Convert Units of Length OBJECTIVE Use ratio reasoning to convert from one unit of length to another. CC.6.RP.3d To convert a unit of measure, multiply by a conversion factor. A conversion factor is a rate in which the two quantities are equal, but are expressed in different units. Convert to the given unit. 2,2 ft = Step Choose a conversion factor. mi mile = 5,280 feet, so use the conversion factor mile 5,280 feet. Step 2 Multiply by the conversion factor. 2,2 ft mi 5,280 ft So, 2,2 ft = 2_ 5 mi. = 2,2 ft mi 5,280 ft = 2,2 5,280 mi = 2_ 5 mi Customary Units of Length foot (ft) = 2 inches (in.) yard (yd) = 36 inches yard = 3 feet mile (mi) = 5,280 feet mile =,760 yards When converting metric units, move the decimal point to multiply or divide by a power of ten. 4 dm = hm Step Start at the given unit. Step 2 Move to the unit you are converting to. Step 3 Move the decimal point that same number of spaces in the same direction. Fill any empty place-value positions with zeros. So, 4 dm = 0.04 hm. Convert to the given unit miles = yards hectometers = millimeters inches = feet centimeters = dekameters Ratios and Proportional Relationships 29

33 Convert Units of Length Convert to the given unit. CC.6.RP.3d. 42 ft = yd 2. 2,350 m = km 3. 8 ft = in. conversion factor: yd 3 ft 42 ft yd 3 ft 42 ft = 4 yd m = dm 5. 5 mi = yd mm = cm Compare. Write <, >, or = dm,900 mm 8. 2 ft 4 yd cm 56,000 km in. 8 ft. 64 cm 630 mm 2. 2 mi 0,560 ft Problem Solving 3. The giant swallowtail is the largest butterfly in the United States. Its wingspan can be as large as 6 centimeters. What is the maximum wingspan in millimeters? 4. The 02nd floor of the Sears Tower in Chicago is the highest occupied floor. It is,43 feet above the ground. How many yards above the ground is the 02nd floor? 30 Lesson 5

34 LESSON 6 Convert Units of Capacity OBJECTIVE Use ratio reasoning to convert from one unit of capacity to another. CC.6.RP.3d Capacity is the measure of the amount that a container can hold. When converting customary units, multiply the initial measurement by a conversion factor. Convert to the given unit. 35 c = Step Choose a conversion factor. qt quart = 4 cups, so use the conversion factor 4 quart cups. Step 2 Multiply by the conversion factor. 35 c qt 4 c = 35 c 4 qt c = 35 4 qt = 8 3_ 4 qt You can rename the fractional part using the smaller unit. 8 3_ 4 quarts = 8 quarts, 3 cups So, 35 c = 8 3_ 4 qt, or 8 qt, 3 c. When converting metric units, move the decimal point to multiply or divide by a power of ten. 26 cl = hl Customary Units of Capacity 8 fluid ounces (fl oz) = cup (c) 2 cups = pint (pt) 2 pints = quart (qt) 4 cups = quart 4 quarts = gallon (gal) kilo- hecto- deka- liter deci- centi- milli- 0 0 Step Start at the given unit. 0 0 Step 2 Move to the unit you are converting to. 0 0 Step 3 Move the decimal point that same number of spaces in the same direction. Fill any empty place-value positions with zeros. So, 26 cl = hl. Convert to the given unit kiloliters = deciliters qt = gal, qt liters = hectoliters 4. 5 pints = cups Ratios and Proportional Relationships 3

35 Convert Units of Capacity Convert to the given unit. CC.6.RP.3d. 7 gallons = quarts liters = kiloliters conversion factor: 4 qt gal 7 gal 4 qt gal 7 gal = 28 qt Move the decimal point 3 places to the left. 5. liters = kiloliters qt = gal L = ml 5. 6 c = pt L = kl pt = qt pt cl = dal 9. 4 pt = fl oz kl = cl. 24 fl oz = pt c Problem Solving 2. A bottle contains 3.5 liters of water. A second bottle contains 3,750 milliliters of water. How many more milliliters are in the larger bottle than in the smaller bottle? 3. Arnie s car used 00 cups of gasoline during a drive. He paid $3.2 per gallon for gas. How much did the gas cost? 32 Lesson 6

36 LESSON 7 Convert Units of Weight and Mass OBJECTIVE Use ratio reasoning to convert from one unit of weight or mass to another. CC.6.RP.3d In the customary system, weight is the measure of the heaviness of an object. When converting customary units, multiply the initial measurement by a conversion factor. Convert to the given unit. 9 lb = Step Choose a conversion factor. 6 ounces = pound, so use the conversion factor oz Step 2 Multiply by the conversion factor. 9 lb 6 oz lb So, 9 lb = 304 oz. = 9 lb 6 oz lb = 304 oz = 304 oz 6 ounces pound. In the metric system, mass is the measure of the amount of matter in an object. When converting metric units, move the decimal point to multiply or divide by a power of ten. 3. dag = mg Customary Units of Weight pound (lb) = 6 ounces (oz) ton (T) = 2,000 pounds Step Start at the given unit. Step 2 Move to the unit you are converting to. Step 3 Move the decimal point that same number of spaces in the same direction. Fill any empty place-value positions with zeros. So, 3. dag = 3,000 mg. Convert to the given unit dg = hg 2. 4,500 pounds = tons grams = milligrams 4. 3 pounds = ounces Ratios and Proportional Relationships 33

37 Convert Units of Weight and Mass Convert to the given unit. CC.6.RP.3d. 5 pounds = ounces conversion factor: 6 oz lb 5 pounds = 5 lb 6 oz lb = 80 oz grams = hectograms Move the decimal point 2 places to the left grams = hectogram oz = lb g = dg 5. 5 T = lb hg = g lb = T 8. 38,600 mg = dag oz = lb oz kg = cg T = lb Problem Solving 2. Maggie bought 52 ounces of swordfish selling for $6.92 per pound. What was the total cost? 3. Three bunches of grapes have masses of,000 centigrams,,000 decigrams, and,000 grams, respectively. What is the total combined mass of the grapes in kilograms? 34 Lesson 7

38 LESSON 8 Transform Units OBJECTIVE Transform units to solve problems. CC.6.RP.3d To solve problems involving different units, use the relationship among units to help you set up a multiplication problem. Green peppers are on sale for $.80 per pound. How much would 2.5 pounds of green peppers cost? Step Identify the units. You know two quantities: pounds of peppers and total cost per pound. You want to know the cost of 2.5 pounds. $.80 per lb = $.80 lb Step 2 Determine the relationship among the units. The answer needs to be in dollars. Set up the multiplication problem so that pounds will divide out. Step 3 Use the relationship. So, 2.5 pounds of peppers will cost $4.50. $.80 lb 2.5 lb = $.80 lb 2.5 lb = $4.50 Solve.. If 2 bags of cherries cost $5.50, how much do 7 bags cost? a. What are you trying to find? 2. The area of a living room is 24 square yards. If the width is 2 feet, what is the length of the living room in yards? a. What is the width in yards? b. Set up the problem. c. What is the cost of 7 bags? b. Set up the problem. c. What is the length in yards? Ratios and Proportional Relationships 35

39 Transform Units Multiply or divide the quantities.. 62 g day 4 days 62 g day 4 days = 248 g sq yd 23 yd 322 sq yd 23 yd 322 yd yd = 4 yd 23 yd CC.6.RP.3d kg 0 hr sq km 8 km 5. hr 88 lb 2 days day sq mm mm 7. $50 20 sq ft sq ft 8 ft sq ft sq yd 9 yd km 20 gal. 225 sq dm 5 dm gal Problem Solving 2. Green grapes are on sale for $2.50 a pound. How much will 9 pounds cost? 3. A car travels 32 miles for each gallon of gas. How many gallons of gas does it need to travel 92 miles? 36 Lesson 8

40 LESSON 9 Problem Solving Distance, Rate, and Time Formulas OBJECTIVE Solve problems involving distance, rate, and time by applying the strategy use a formula. Use a formula to solve the problem. A bug crawls at a rate of 2 feet per minute. How long will it take the bug to crawl 25 feet? CC.6.RP.3d Read the Problem What do I need to find? I need to find the amount of time it will take the bug to crawl 25 feet. Solve the Problem Write the appropriate formula. t = d r What information do I need to use? Substitute the values for d and r. I need to use the distance the bug crawls t = 25 ft 2 min ft and the rate at which the bug crawls. How will I use the information? First I will choose the formula t = d r because I need to find time. Next I will 2 ft substitute 25 ft for d and min for r. Then I will divide to find the time. Rewrite the division as multiplication by the reciprocal. t = 25 ft min 2 ft = 2.5 min. A family drives for 3 hours at an average rate of 57 miles per hour. How far does the family travel? 2. A train traveled miles in 3.5 hours. What was the train s average rate of speed? Ratios and Proportional Relationships 37

41 Problem Solving Distance, Rate, and Time Formulas Read each problem and solve. CC.6.RP.3d. A downhill skier is traveling at a rate of 0.5 mile per minute. How far will the skier travel in 8 minutes? d = r t d = 0.5 mi 8 min min d = 9 miles 2. How long will it take a seal swimming at a speed of 8 miles per hour to travel 52 miles? 3. A dragonfly traveled at a rate of 35 miles per hour for 2.5 hours. What distance did the dragonfly travel? 4. A race car travels,22 kilometers in 4 hours. What is the car s rate of speed? 5. A cyclist travels at a rate of.8 kilometers per minute. How far will the cyclist travel in 48 minutes? 6. Kim and Jay leave at the same time to travel 25 miles to the beach. Kim drives 9 miles in 2 minutes. Jay drives 0 miles in 5 minutes. If they both continue at the same rate, who will arrive at the beach first? 38 Lesson 9

42 3 2 TIER LESSONS PROVIDES TIER INTERVENTION FOR EVERY COMMON CORE STANDARD The Houghton Mifflin Harcourt Response to Intervention program includes: Diagnostic Interviews for every Common Core Cluster Tier Lessons Tier 2 Prerequisite Skills Tier 3 Scaffolded Examples Plus, the Teacher Guide includes Tier - Tier 2 - Tier 3 correlations and answer keys. GRADE

TEACHER GUIDE INCLUDES. Tier 1 Tier 2 Tier 3 Correlations. Diagnostic Interviews for Every Common Core Cluster

TEACHER GUIDE INCLUDES. Tier 1 Tier 2 Tier 3 Correlations. Diagnostic Interviews for Every Common Core Cluster TEACHER GUIDE FOR THE COMMON CORE STATE STANDARDS FOR MATHEMATICS 3 2 INCLUDES Tier Tier 2 Tier 3 Correlations Diagnostic Interviews for Every Common Core Cluster Tier Lessons, Tier 2 Prerequisite Skills,

More information

THANK YOU FOR YOUR PURCHASE!

THANK YOU FOR YOUR PURCHASE! THANK YOU FOR YOUR PURCHASE! The resources included in this purchase were designed and created by me. I hope that you find this resource helpful in your classroom. Please feel free to contact me with any

More information

Course 1 Unit 4 Practice

Course 1 Unit 4 Practice Course 1 Unit 4 Practice Lesson 17-1 1. Use ratios to compare the shapes shown. a. black shapes to all shapes 4. Reason quantitatively. The number of ducks to geese in Miller s Pond last year was 2:3.

More information

UNIT 6 Ratios, Rates, Proportions and Measurement Conversions CCM6+7+ Name Teacher Estimated Test Date

UNIT 6 Ratios, Rates, Proportions and Measurement Conversions CCM6+7+ Name Teacher Estimated Test Date Page 1 UNIT 6 RATIOS RATES PROPORTIONS Meas. CONVERSIONS CCM6+7+ UNIT 6 Ratios, Rates, Proportions and Measurement Conversions CCM6+7+ Name Teacher Estimated Test Date Main Topics Page Number(s) Unit 7

More information

TEST NAME:Decimal Review TEST ID: GRADE:05 Fifth Grade SUBJECT: Mathematics TEST CATEGORY: My Classroom

TEST NAME:Decimal Review TEST ID: GRADE:05 Fifth Grade SUBJECT: Mathematics TEST CATEGORY: My Classroom TEST NAME:Decimal Review TEST ID:1123506 GRADE:05 Fifth Grade SUBJECT: Mathematics TEST CATEGORY: My Classroom Decimal Review Page 1 of 17 Student: Class: Date: 1. Which number line model represents the

More information

Ratios, Rates & Proportions Chapter Questions

Ratios, Rates & Proportions Chapter Questions Ratios, Rates & Proportions Chapter Questions 1. How are ratios simplified? 2. How are equivalent ratios written? 3. How are unit rates determined? 4. How can equivalent rates help to solve problems? 5.

More information

McRuffy Press Fourth Grade Color Math Test 7

McRuffy Press Fourth Grade Color Math Test 7 McRuffy Press Fourth Grade Color Math Test 7 Materials: Test pages (Resource pack, 3 sheets) Test Directions Page :. Problem solving: Solve the problems. 2. Fractions to decimals: Change the fractions

More information

Module 1. Ratios and Proportional Relationships Lessons 11 14

Module 1. Ratios and Proportional Relationships Lessons 11 14 Math 7 Module Lessons.notebook September, 05 Module Ratios and Proportional Relationships Lessons Lesson # September, 05 You need: pencil, calculator and binder. Do Now: Find your group and complete do

More information

Trimester 2 5 th Grade Name: Answer Key

Trimester 2 5 th Grade Name: Answer Key Trimester 2 th Grade Name: Answer Key..NBT.7 Fiona hiked along a trail in Glacier National Park that is 7.2 miles long. It took her hours to hike. What was her average speed per hour? 7.2 / =.3 (miles

More information

Grade 5 Mathematics Mid-Year Assessment REVIEW

Grade 5 Mathematics Mid-Year Assessment REVIEW Grade 5 Mathematics Mid-Year Assessment REVIEW The learning targets (Texas Essential Knowledge and Skill statements) are listed prior to sample items. The sample items are not an exhaustive list and only

More information

Lesson 10. Here are the first two worked out.

Lesson 10. Here are the first two worked out. Lesson 10 This page is on word problems. They will be using multiplication, division, addition, and subtraction. They will need to take multiple steps to find the answer to the question. They could use

More information

GRADE 6 WINTER REVIEW MATH PACKET

GRADE 6 WINTER REVIEW MATH PACKET Student Name: Date: Math Teacher: Period: GRADE 6 WINTER REVIEW MATH PACKET 2014-2015 Find the greatest common factor of each set of numbers. 1. 27, 36, 72 a. 216 b. 8 c. 9 d. 18 2. The table shows the

More information

Preview Library Built Test (Printable Worksheet)

Preview Library Built Test (Printable Worksheet) Page 1 of 10 Copyright 2015 Edmentum - All rights reserved. Ratio and Proportion 1. An item is priced at $13.56. If the sales tax is 5%, what does the item cost including sales tax? $0.68 $20.34 $14.24

More information

FINAL REVIEW m rounded to the nearest centimeter is _. Choose the correct answer, and write its number in the parentheses.

FINAL REVIEW m rounded to the nearest centimeter is _. Choose the correct answer, and write its number in the parentheses. FINAL REVIEW Choose the correct answer, and write its number in the parentheses. 1. What is the value of the digit 4 in 135.847? (1) 4 tenths (3) 4 hundredths 4 tens (4) 4 hundreds 2. What is the value

More information

Homework Week 1 Grade 5. Name

Homework Week 1 Grade 5. Name Homework Week 1 Grade 5 Name Week 1 Day 1 5 yards = feet 1) Draw an array to represent 3 2. 2) Point C is the center of the circle. What is the diameter of the circle? 20 in. C 1) 2) 3) 3) When you find

More information

Unit 7, Lesson 1: Exponent Review

Unit 7, Lesson 1: Exponent Review Unit 7, Lesson 1: Exponent Review 1. Write each expression using an exponent: a. b. c. d. The number of coins Jada will have on the eighth day, if Jada starts with one coin and the number of coins doubles

More information

amount base = percent 30% of the class 90% of the points 65% of the televisions

amount base = percent 30% of the class 90% of the points 65% of the televisions Free Pre-Algebra Lesson 41! page 1 Lesson 41 Solving Percent Equations A percent is really a ratio, usually of part to whole. In percent problems, the numerator of the ratio (the part) is called the, and

More information

Fraction Computation

Fraction Computation Name PMI th Grade Date Fraction Computation Adding Fractions with Common Denominators Classwork Solve the following problems. Simplify to lowest terms: ) + ) + ) + ) + ) + 6) + ) 0 + 0 8) 9 + 9 9) 6 +

More information

6-5 Solving Proportions

6-5 Solving Proportions Solve each proportion. 24 12.6 34 esolutions Manual - Powered by Cognero Page 1 2.4 29 55 esolutions Manual - Powered by Cognero Page 2 TELEVISION Aspect ratio is the ratio of width to height of a television

More information

6th Grade Advanced Topic II Assessment

6th Grade Advanced Topic II Assessment 1. The table shows the number of sport cards of each kind in Monique s collection. Monique s Sport Card Collection Kind of Card Baseball Basketball Football Hockey Total Number of Cards 36 28 20 16 100

More information

Mobile Math Teachers Circle The Return of the iclicker

Mobile Math Teachers Circle The Return of the iclicker Mobile Math Teachers Circle The Return of the iclicker June 20, 2016 1. Dr. Spock asked his class to solve a percent problem, Julia set up the proportion: 4/5 = x/100. She then cross-multiplied to solve

More information

Practice Test. 2. What is the probability of rolling an even number on a number cube? a. 1 6 b. 2 6 c. 1 2 d. 5 be written as a decimal? 3.

Practice Test. 2. What is the probability of rolling an even number on a number cube? a. 1 6 b. 2 6 c. 1 2 d. 5 be written as a decimal? 3. Name: Class: Practice Test. The elevation of the surface of the Dead Sea is -424. meters. In 2005, the height of Mt. Everest was 8,844.4 meters. How much higher was the summit of Mt. Everest? a. -9.268.7

More information

North Carolina Standard Course of Study - Mathematics

North Carolina Standard Course of Study - Mathematics A Correlation of To the North Carolina Standard Course of Study - Mathematics Grade 4 A Correlation of, Grade 4 Units Unit 1 - Arrays, Factors, and Multiplicative Comparison Unit 2 - Generating and Representing

More information

Uses of Fractions. Fractions

Uses of Fractions. Fractions Uses of The numbers,,,, and are all fractions. A fraction is written with two whole numbers that are separated by a fraction bar. The top number is called the numerator. The bottom number is called the

More information

3. Artemis bought a box of mini cookies in the shapes of hearts, stars, and circles. She laid out all the cookies on her plate.

3. Artemis bought a box of mini cookies in the shapes of hearts, stars, and circles. She laid out all the cookies on her plate. Summative Assessment 1. In which expression does g have a coefficient of 8? A. 8g B. g 8 C. 8 + g D. 2. Which number line correctly shows 7 and its opposite? A. B. C. D. 3. Artemis bought a box of mini

More information

[ 4TH GRADE MATH HOMEWORK] 5) Anibal used the model below to help find the sum of +. Does Anibal s model make sense? Explain your reasoning.

[ 4TH GRADE MATH HOMEWORK] 5) Anibal used the model below to help find the sum of +. Does Anibal s model make sense? Explain your reasoning. Week 4: Thursday 1) 7,643 x 8 = 2) + = 3) 6,523 6 = 4) 8,300 5,678 = 5) While working on a group project for homework three girls snacked on chocolate bars. Each girl had a chocolate bar of the same size.

More information

SEVENTH GRADE. Revised June Billings Public Schools Correlation and Pacing Guide Math - McDougal Littell Middle School Math 2004

SEVENTH GRADE. Revised June Billings Public Schools Correlation and Pacing Guide Math - McDougal Littell Middle School Math 2004 SEVENTH GRADE June 2010 Billings Public Schools Correlation and Guide Math - McDougal Littell Middle School Math 2004 (Chapter Order: 1, 6, 2, 4, 5, 13, 3, 7, 8, 9, 10, 11, 12 Chapter 1 Number Sense, Patterns,

More information

Talking REAL Maths. A resource to engage children in discussion based on common errors and misconceptions in mathematics.

Talking REAL Maths. A resource to engage children in discussion based on common errors and misconceptions in mathematics. Talking REAL Maths A resource to engage children in discussion based on common errors and misconceptions in mathematics. ALGEBRA Discussion mat Suggested year group/ks APP link Simple Sequence Lower KS2

More information

Unit 4 Proportional Reasoning: Ratio, Rate, and Proportion

Unit 4 Proportional Reasoning: Ratio, Rate, and Proportion Unit 4 Proportional Reasoning: Ratio, Rate, and Proportion Lesson Outline BIG PICTURE Students will: solve problems involving proportional reasoning. Grade 9 Applied Math Learning Goals Investigate ratio

More information

Unit 7, Lesson 1: Exponent Review

Unit 7, Lesson 1: Exponent Review Unit 7, Lesson 1: Exponent Review Let s review exponents. 1.1: Which One Doesn t Belong: Twos Which expression does not belong? Be prepared to share your reasoning. 8 1.2: Return of the Genie m.openup.org/1/8-7-1-2

More information

Fractions. Chapter NUMBER. Big Idea. Learning Goals. Essential Question. Important Words

Fractions. Chapter NUMBER. Big Idea. Learning Goals. Essential Question. Important Words NUMBER Fractions Chapter Big Idea Understanding improper fractions and mixed numbers can help me solve problems. Learning Goals I can relate improper fractions to mixed numbers. Essential Question How

More information

General Certificate of Secondary Education Foundation Tier

General Certificate of Secondary Education Foundation Tier Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Pages 3 Mark General Certificate of Secondary Education Foundation Tier 4 5 6 7 Mathematics (Linear) B Paper 1

More information

31 MARCH 1991 TM DEPARTMENT OF THE ARMY

31 MARCH 1991 TM DEPARTMENT OF THE ARMY TM 9-1370-206-10 31 MARCH 1991 DEPARTMENT OF THE ARMY WARNINGS SIGNALS CONTAIN HAZARDOS MATERIALS KEEP away from FIRE DON'T handle if damaged or parts are missing Handle CAREFLLY and use *GLOVES and FLL

More information

Draft last edited May 13, 2013 by Belinda Robertson

Draft last edited May 13, 2013 by Belinda Robertson Draft last edited May 13, 2013 by Belinda Robertson 97 98 Appendix A: Prolem Handouts Problem Title Location or Page number 1 CCA Interpreting Algebraic Expressions Map.mathshell.org high school concept

More information

Summer School: 5 th Grade Math Common Core Activities. Name:

Summer School: 5 th Grade Math Common Core Activities. Name: Summer School: 5 th Grade Math Common Core Activities Name: 2- DIGIT SUBTRACTION 3- DIGIT SUBTRACTION 2- DIGIT ADDITION 3- DIGIT ADDITION 4- DIGIT ADDITION PLACE VALUE 5,788-7,342-71,975-5,863-450,555-32,534-12,364-23,954-24,889-5,788-5,360-71,475-850,555-932,534-88,342-283,954-172,364-183,924

More information

GCSE Mathematics Practice Tests: Set 4

GCSE Mathematics Practice Tests: Set 4 GCSE Mathematics Practice Tests: Set 4 Paper 2F (Calculator) Time: 1 hour 30 minutes You should have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser,

More information

Student Name: Parent Signature:

Student Name: Parent Signature: Entering 5 th Grade Summer Packet Student Name: Parent Signature: Dear Parents, This packet is intended to help students stay strong in the academic material we have covered this year. It is an optional

More information

SPEED DRILL WARM-UP ACTIVITY

SPEED DRILL WARM-UP ACTIVITY SPEED DRILL WARM-UP ACTIVITY Name the operation representative of each of the following: percent left reduction total more half less twice off lower each double Write the equivalents: 20% as a decimal

More information

Table of Contents. Introduction...v. About the CD-ROM...vi. Standards Correlations... vii. Ratios and Proportional Relationships...

Table of Contents. Introduction...v. About the CD-ROM...vi. Standards Correlations... vii. Ratios and Proportional Relationships... Table of Contents Introduction...v About the CD-ROM...vi Standards Correlations... vii Ratios and Proportional Relationships... 1 The Number System... 10 Expressions and Equations... 23 Geometry... 27

More information

Correlation to the Common Core State Standards

Correlation to the Common Core State Standards Correlation to the Common Core State Standards Go Math! 2011 Grade 4 Common Core is a trademark of the National Governors Association Center for Best Practices and the Council of Chief State School Officers.

More information

Applications of Mathematics

Applications of Mathematics Write your name here Surname Other names Pearson Edexcel GCSE Centre Number Candidate Number Applications of Mathematics Unit 1: Applications 1 For Approved Pilot Centres ONLY Higher Tier Wednesday 6 November

More information

2016 Excellence in Mathematics Contest Team Project Level I (Precalculus and above) School Name: Group Members:

2016 Excellence in Mathematics Contest Team Project Level I (Precalculus and above) School Name: Group Members: 016 Excellence in Mathematics Contest Team Project Level I (Precalculus and above) School Name: Group Members: Reference Sheet Formulas and Facts You may need to use some of the following formulas and

More information

Creating Color Combos

Creating Color Combos THE 2016 ROSENTHAL PRIZE for Innovation in Math Teaching Creating Color Combos Visual Modeling of Equivalent Ratios Traci Jackson Lesson Plan Grades 5-6 Table of Contents Creating Color Combos: Visual

More information

1-1 Variables and Expressions

1-1 Variables and Expressions 1-1 Variables and Expressions Warm Up Lesson Presentation Lesson Quiz Warm Up Add or subtract. 1. 6 + 104 110 2. 12(9) 108 3. 23 8 15 4. Multiply or divide. 5. 324 18 18 6. 6 7. 13.5(10) 135 8. 18.2 2

More information

EOC FINAL REVIEW Name Due Date

EOC FINAL REVIEW Name Due Date 1. The line has endpoints L(-8, -2) and N(4, 2) and midpoint M. What is the equation of the line perpendicular to and passing through M? A. B. Y= C. Y= D. Y= 3x + 6 2. A rectangle has vertices at (-5,3),

More information

Sandwich. Reuben BLT. Egg salad. Roast beef

Sandwich. Reuben BLT. Egg salad. Roast beef 3.2 Writing Expressions represents an unknown quantity? How can you write an expression that 1 ACTIVITY: Ordering Lunch Work with a partner. You use a $20 bill to buy lunch at a café. You order a sandwich

More information

To calculate the estimated number of fish killed by shrimp trawlers every year in the Gulf of Mexico I will 9,400,000 by.

To calculate the estimated number of fish killed by shrimp trawlers every year in the Gulf of Mexico I will 9,400,000 by. Blue - Divide by Whole Numbers and Powers of 10 Metric Conversions 1. The thickness of a book, including the covers, is 2.1 cm. The front and back cover are each 0.5 cm thick. The book has 230 pages, numbered

More information

TeeJay Publishers. Curriculum for Excellence. Course Planner - Level 1

TeeJay Publishers. Curriculum for Excellence. Course Planner - Level 1 TeeJay Publishers Curriculum for Excellence Course Planner Level 1 To help schools develop their courses, TeeJay Publishers has produced a Course Planner for CfE Level 1. This Planner from TeeJay provides

More information

8.3. Start Thinking! Warm Up. Find the area of the triangle Activity. Activity. 4 m. 14 in. 7 m. 9 in. 12 yd. 11 yd. 1 mm. 5.

8.3. Start Thinking! Warm Up. Find the area of the triangle Activity. Activity. 4 m. 14 in. 7 m. 9 in. 12 yd. 11 yd. 1 mm. 5. Activity Start Thinking! For use before Activity You know how to find the area of squares, rectangles, triangles, trapezoids, and parallelograms. Describe three different methods you could use to estimate

More information

- 1. Name : Score : Teacher : Date : Mixed Problems with Fractions 1 ) = = = 2 ) 3 ) 4 ) 5 ) = 1 5 x 1 2 = 6 )

- 1. Name : Score : Teacher : Date : Mixed Problems with Fractions 1 ) = = = 2 ) 3 ) 4 ) 5 ) = 1 5 x 1 2 = 6 ) Name : Score : Teacher : Date : Mixed Problems with Fractions ) ) ) 4 ) ) 6 ) 7 ) 8 ) 9 ) 0 ) ) ) - 4 0 6 0 + 4 4 + 0 x + 0 x 4 x 4-4 7 0-4 Math-Aids.Com Name : Score : Teacher : Date : Mixed Problems

More information

(1) + 1(0.1) + 7(0.001)

(1) + 1(0.1) + 7(0.001) Name: Quarterly 1 Study Guide The first quarterly test covers information from Modules 1, 2, and 3. If you complete this study guide and turn it in on Tuesday, you will receive 5 bonus points on your Quarterly

More information

Astronomy Lab - Lab Notebook and Scaling

Astronomy Lab - Lab Notebook and Scaling Astronomy Lab - Lab Notebook and Scaling In this lab, we will first set up your lab notebook and then practice scaling. Please read this so you know what we will be doing. BEFORE YOU COME TO THIS LAB:

More information

Math Conversation Starters

Math Conversation Starters Math Conversation Starters How do you define? (You can fill this with anything) When do you use it in real life? I am thinking of a number that is less than 100. It s a square number. The sum of the digits

More information

Unit Four Answer Keys

Unit Four Answer Keys Multiplication, Division & Fractions Unit Four Unit Four Answer Keys Session Blacklines A.., Unit Four Pre-Assessment Responses will vary. example example a b Sketches will vary. Example: a, Sketches will

More information

CALIFORNIA STANDARDS TEST CSM00433 CSM01958 A B C CSM02216 A 583,000

CALIFORNIA STANDARDS TEST CSM00433 CSM01958 A B C CSM02216 A 583,000 G R E Which of these is the number 5,005,0? five million, five hundred, fourteen five million, five thousand, fourteen five thousand, five hundred, fourteen five billion, five million, fourteen LIFORNI

More information

Learning fun with.

Learning fun with. Learning fun with #1 #4 Milton Hershey was born in 1857. How many years ago was he born? Milton Hershey opened his first candy shop in 1876. It closed six years later. What year did his candy shop close?

More information

Unit 07 PC Form A. 1. Use pencil and paper to answer the question. Plot and label each point on the coordinate grid.

Unit 07 PC Form A. 1. Use pencil and paper to answer the question. Plot and label each point on the coordinate grid. 1. Use pencil and paper to answer the question. Plot and label each point on the coordinate grid. A (5,2) B (2,2) C (0,0) D (1,3) E (2,4) 2. Use pencil and paper to answer the question. Write two fractions

More information

Ratios. How are the numbers in each ad compared? Which ads are most effective?

Ratios. How are the numbers in each ad compared? Which ads are most effective? 5 and part to part, part to whole versions of ratios There are different ways to compare numbers. Look @ these advertisments. How are the numbers in each ad compared? Which ads are most effective? 1 5

More information

Professor Weissman s Algebra Classroom

Professor Weissman s Algebra Classroom Combine Like Terms Unit #12 2007 Prof Weissman s Software Tel: 1-347-528-7837 mathprof@hotmail.com Professor Weissman s Algebra Classroom Martin Weissman, Jonathan S. Weissman, Tamara Farber, & Keith Monse

More information

Distribution of Data and the Empirical Rule

Distribution of Data and the Empirical Rule 302360_File_B.qxd 7/7/03 7:18 AM Page 1 Distribution of Data and the Empirical Rule 1 Distribution of Data and the Empirical Rule Stem-and-Leaf Diagrams Frequency Distributions and Histograms Normal Distributions

More information

Time available for students to complete test: 40 minutes

Time available for students to complete test: 40 minutes national assessment program literacy and numeracy NUMERACY NOn-CALCULATOR year 7 2008 0:0 SESSION Time available for students to complete test: 0 minutes Use 2B or HB pencil only Curriculum Corporation,

More information

Student Guide. 1. A.* batches B.* 8 batches; Copyright Kendall Hunt Publishing Company. 2. A.* less than 1 B.* cups C.* 2 5. cups;

Student Guide. 1. A.* batches B.* 8 batches; Copyright Kendall Hunt Publishing Company. 2. A.* less than 1 B.* cups C.* 2 5. cups; Answer Key Lesson 0: Student Guide Mrs Murphy s Bakery Draw pictures and use invented strategies, repeated subtraction, rectangles, fraction circle pieces, and number lines to solve the problems Mrs Murphy

More information

3/31/2014. BW: Four Minute Gridding Activity. Use a pencil! Use box # s on your grid paper.

3/31/2014. BW: Four Minute Gridding Activity. Use a pencil! Use box # s on your grid paper. Monday, /1 You Need: On your desk to be checked during bellwork: Extra Credit Assignment if you did it Math Notebook Table of Contents Assignment Title # 9 Bellwork /17-/20 40 4.2 Rates 41 4.2 Practice

More information

A place for everything, and everthing in its place. - Samuel Smiles ( ) Unit Summary

A place for everything, and everthing in its place. - Samuel Smiles ( ) Unit Summary Unit : Place Value, Comparing and Ordering A place for everything, and everthing in its place. - Samuel Smiles ( - 0) Unit Summary Overview: The Concept of place value has been around since 000 B.C.E.

More information

How would the data in Tony s table change if he recorded the number of minutes he read during a 20 day period instead of a 15 day period?

How would the data in Tony s table change if he recorded the number of minutes he read during a 20 day period instead of a 15 day period? ? Name 17.1 Essential Question Unlock the Problem A frequency table is a table that uses numbers to record data about how often something happens. The frequency is the number of times the data occurs.

More information

How can you determine the amount of cardboard used to make a cereal box? List at least two different methods.

How can you determine the amount of cardboard used to make a cereal box? List at least two different methods. Activity Start Thinking! For use before Activity How can you determine the amount of cardboard used to make a cereal box? List at least two different methods. Activity Warm Up For use before Activity Evaluate

More information

12.1 Creating Systems of Linear Equations

12.1 Creating Systems of Linear Equations Name Class Date 12.1 Creating Sstems of Linear Equations Essential Question: How do ou use sstems of linear equations to model and solve real-world problems? Resource Locker Eplore Creating Linear Sstem

More information

Lesson 25: Solving Problems in Two Ways Rates and Algebra

Lesson 25: Solving Problems in Two Ways Rates and Algebra : Solving Problems in Two Ways Rates and Algebra Student Outcomes Students investigate a problem that can be solved by reasoning quantitatively and by creating equations in one variable. They compare the

More information

Delta College Middle School Math Competition Practice Test A 2018

Delta College Middle School Math Competition Practice Test A 2018 Delta College Middle School Math Competition Practice Test A 208 ) In the Noveo music group there are 4 times as many flutes as there are bassoons. The number of clarinets is 8 more than triple the number

More information

Comparing Areas of Rectangles

Comparing Areas of Rectangles Activity Overview In this activity, students discover the relationship between a change in the dimensions of a rectangle and the change in the corresponding area. Topic: Problem Solving Understand measurable

More information

First Grade. Real World Subtraction with Manipulatives. Slide 1 / 188 Slide 2 / 188. Slide 3 / 188. Slide 4 / 188. Slide 5 / 188.

First Grade. Real World Subtraction with Manipulatives. Slide 1 / 188 Slide 2 / 188. Slide 3 / 188. Slide 4 / 188. Slide 5 / 188. Slide 1 / 188 Slide 2 / 188 First Grade Subtraction to 20 Part 1 2015-11-23 www.njctl.org Slide 3 / 188 Slide 4 / 188 Table of Contents Pt. 1 click on the topic to go to that section Table of Contents

More information

First Grade. Slide 1 / 188. Slide 2 / 188. Slide 3 / 188. Subtraction to 20 Part 1. Table of Contents Pt. 1

First Grade. Slide 1 / 188. Slide 2 / 188. Slide 3 / 188. Subtraction to 20 Part 1. Table of Contents Pt. 1 Slide 1 / 188 Slide 2 / 188 First Grade Subtraction to 20 Part 1 2015-11-23 www.njctl.org Table of Contents Pt. 1 click on the topic to go to that section Slide 3 / 188 - Real World Subtraction with Manipulatives

More information

Algebra I Module 2 Lessons 1 19

Algebra I Module 2 Lessons 1 19 Eureka Math 2015 2016 Algebra I Module 2 Lessons 1 19 Eureka Math, Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be reproduced, distributed, modified, sold,

More information

Dot Plots and Distributions

Dot Plots and Distributions EXTENSION Dot Plots and Distributions A dot plot is a data representation that uses a number line and x s, dots, or other symbols to show frequency. Dot plots are sometimes called line plots. E X A M P

More information

3.1 Decimal Place Value

3.1 Decimal Place Value 3.1. Decimal Place Value www.ck12.org 3.1 Decimal Place Value Introduction The Ice Cream Stand Julie and her friend Jose are working at an ice cream stand for the summer. They are excited because in addition

More information

2.2. Multiplying and Dividing Powers. INVESTIGATE the Math

2.2. Multiplying and Dividing Powers. INVESTIGATE the Math . Multipling and Dividing Powers GOAL Develop and appl exponent principles to multipl and divide powers. INVESTIGATE the Math Amir thought there was a wa to simplif 1 6 1 9 1 without using a calculator.?

More information

Globe Academy Mathematics Department

Globe Academy Mathematics Department Globe Academy Mathematics Department Home Learning Booklet Year 10 Aut II Name: Teacher: Develop a passion for learning. If you do, you will never cease to grow. Anthony J. D'Angelo Week 1 1. Here is a

More information

ACCELERATED MATHEMATICS CHAPTER 3 FRACTIONS TOPICS COVERED:

ACCELERATED MATHEMATICS CHAPTER 3 FRACTIONS TOPICS COVERED: ACCELERATED MATHEMATICS CHAPTER FRACTIONS TOPICS COVERED: Divisibility Rules Primes & Prime Factorization Greatest Common Factor Least Common Multiple Fraction sense Adding and subtracting fractions and

More information

Please fax your students rhythms from p.7 to us AT LEAST THREE DAYS BEFORE the video conference. Our fax number is

Please fax your students rhythms from p.7 to us AT LEAST THREE DAYS BEFORE the video conference. Our fax number is Class Materials 1 Dear Educator, Thank you for choosing the. Inside this packet, you will find all of the materials your class will need for your upcoming Math and Music video conference. There are lessons

More information

Guidelines for Preparing a Paper from a Mini-Workshop Presentation For the Proceedings of the Association for Biology Laboratory Education (ABLE)

Guidelines for Preparing a Paper from a Mini-Workshop Presentation For the Proceedings of the Association for Biology Laboratory Education (ABLE) Guidelines for Preparing a Paper from a Mini-Workshop Presentation For the Proceedings of the Association for Biology Laboratory Education (ABLE) This document provides presenters of mini-workshops with

More information

Bite Size Brownies. Designed by: Jonathan Thompson George Mason University, COMPLETE Math

Bite Size Brownies. Designed by: Jonathan Thompson George Mason University, COMPLETE Math Bite Size Brownies Designed by: Jonathan Thompson George Mason University, COMPLETE Math The Task Mr. Brown E. Pan recently opened a new business making brownies called The Brown E. Pan. On his first day

More information

1. The trail around Lenape Lake is 0.8 mile long. What fraction is equivalent to 0.8? a. 0/8 b. 1/8 c. 8/10 d. 8/100

1. The trail around Lenape Lake is 0.8 mile long. What fraction is equivalent to 0.8? a. 0/8 b. 1/8 c. 8/10 d. 8/100 4.NF.5 1. The trail around Lenape Lake is 0.8 mile long. What fraction is equivalent to 0.8? a. 0/8 b. 1/8 c. 8/10 d. 8/100 2. Melissa lives 0.6 kilometer from her school. Which fraction is equivalent

More information

Answers. Chapter 9 A Puzzle Time MUSSELS. 9.1 Practice A. Technology Connection. 9.1 Start Thinking! 9.1 Warm Up. 9.1 Start Thinking!

Answers. Chapter 9 A Puzzle Time MUSSELS. 9.1 Practice A. Technology Connection. 9.1 Start Thinking! 9.1 Warm Up. 9.1 Start Thinking! . Puzzle Time MUSSELS Technolog Connection.. 7.... in. Chapter 9 9. Start Thinking! For use before Activit 9. Number of shoes x Person 9. Warm Up For use before Activit 9.. 9. Start Thinking! For use before

More information

Section A Using the n th Term Formula Grade D / C

Section A Using the n th Term Formula Grade D / C Name: Teacher Assessment Section A Using the n th Term Formula Grade D / C 1. The first term of a sequence is 2. The rule for continuing the sequence is What is the second term of the sequence? Add 7 then

More information

Histograms and Frequency Polygons are statistical graphs used to illustrate frequency distributions.

Histograms and Frequency Polygons are statistical graphs used to illustrate frequency distributions. Number of Families II. Statistical Graphs section 3.2 Histograms and Frequency Polygons are statistical graphs used to illustrate frequency distributions. Example: Construct a histogram for the frequency

More information

What is a Sentence? The rabbit that is hopping around. the horse track. The bunch of red roses. in their bee hives. is in a purple vase.

What is a Sentence? The rabbit that is hopping around. the horse track. The bunch of red roses. in their bee hives. is in a purple vase. What is a Sentence? Use colours to match a sentence beginning (the first column of boxes) with a sentence ending (the second column of boxes). Make a meaningful sentence. The rabbit that is hopping around

More information

7 th Grade 20 Day Homework Day 1

7 th Grade 20 Day Homework Day 1 7 th Grade 20 Day Homework Day 1 1) Two hundred and twenty people applied to work at Ernest Educational Concepts. After Ms. Ernest reviewed their applications, one-fourth of the people could not pass the

More information

See what happens when you mix baking soda and vinegar. Build a model ecosystem with playdough or clay.

See what happens when you mix baking soda and vinegar. Build a model ecosystem with playdough or clay. Science See what happens when you mix baking soda and vinegar. Build a model ecosystem with playdough or clay. Make and organize a collection. Rocks, leaves, shells, bottle caps, rubber bands, coins...or

More information

Green Valley Public School, Ahmedgarh

Green Valley Public School, Ahmedgarh Green Valley Public School, Ahmedgarh Holidays Home Work (2018-19) Name: Class IV ENGLISH Sec.: Q1. Read the following poem carefully and answer the following questions: The Beautiful Sunset A yawn came

More information

MA 15910, Lesson 5, Algebra part of text, Sections 2.3, 2.4, and 7.5 Solving Applied Problems

MA 15910, Lesson 5, Algebra part of text, Sections 2.3, 2.4, and 7.5 Solving Applied Problems MA 15910, Lesson 5, Algebra part of text, Sections 2.3, 2.4, and 7.5 Solving Applied Problems Steps for solving an applied problem 1. Read the problem; carefully noting the information given and the questions

More information

Countable (Can count) uncountable (cannot count)

Countable (Can count) uncountable (cannot count) Countable (Can count) uncountable (cannot count) I have one cat. ( I have a cat. ) I have one milk. I have one of milk (I have a of milk) I have three cats I have three milk s (I have three of milk) examples

More information

Overview. Teacher s Manual and reproductions of student worksheets to support the following lesson objective:

Overview. Teacher s Manual and reproductions of student worksheets to support the following lesson objective: Overview Lesson Plan #1 Title: Ace it! Lesson Nine Attached Supporting Documents for Plan #1: Teacher s Manual and reproductions of student worksheets to support the following lesson objective: Find products

More information

Chapter 8 Review/Test

Chapter 8 Review/Test Name Chapter Review/Test Personal Math Trainer Online Assessment and Intervention. What are the next four multiples of _? Personal Math Trainer. SMARTER Marta is making servings of fruit salad. She adds

More information

cl Underline the NOUN in the sentence. gl Circle the missing ending punctuation. !.? Watch out Monday Tuesday Wednesday Thursday you are in my class.

cl Underline the NOUN in the sentence. gl Circle the missing ending punctuation. !.? Watch out Monday Tuesday Wednesday Thursday you are in my class. Name: My Language Homework Q1:1 Week 1 May 1-4 Due: 5/5 Color am words blue. Color ad words green. bad ham jam Sam dad fad had yam mad Circle the letters that should be capitalized. you are in my class.

More information

GCSE Mathematics Practice Tests: Set 1

GCSE Mathematics Practice Tests: Set 1 GCSE Mathematics Practice Tests: Set 1 Paper 2F (Calculator) Time: 1 hour 30 minutes You should have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser,

More information

1 TG Grade 4 Unit 8 Lesson 10 Answer Key. Answer Key Lesson 10: Multiplying Fractions by a Whole

1 TG Grade 4 Unit 8 Lesson 10 Answer Key. Answer Key Lesson 10: Multiplying Fractions by a Whole Answer Key Lesson 0: Multiplying Fractions by a Whole Student Guide Multiplying Fractions by a Whole Using Area Models Use fraction strips, fraction circle pieces, or number lines to solve Questions. Be

More information

Anglia ESOL International Examinations. Preliminary Level (A1) Paper CC115 W1 [5] W3 [10] W2 [10]

Anglia ESOL International Examinations. Preliminary Level (A1) Paper CC115 W1 [5] W3 [10] W2 [10] Please stick your candidate label here W R R1 [] Anglia ESOL International Examinations Preliminary Level (A1) CANDIDATE INSTRUCTIONS: For Examiner s Use Only R2 R3 R4 R5 [] [] [] [] Paper CC115 Time allowed

More information

percents Common Core Standard 7.RP3 Use proportional relationships to solve multistep ratio and percent problems.

percents Common Core Standard 7.RP3 Use proportional relationships to solve multistep ratio and percent problems. Intro All right, welcome to class everybody I need you guys to come in, take your seat Take out everything you need Put it on top of your desk I have something real special planned for you Now make sure

More information

STYLE. Sample Test. School Tests for Young Learners of English. Form A. Level 1

STYLE. Sample Test. School Tests for Young Learners of English. Form A. Level 1 STYLE School Tests for Young Learners of English Level 1 Sample Test Form A Hellenic American University, Office for Language Assessment. Distributed by the Hellenic American Union. FREE OF CHARGE LISTENING

More information

Jumpstarters for Math Word Problems

Jumpstarters for Math Word Problems Jumpstarters for Math Word Problems Short Daily Warm-ups for the Classroom By ANNE STEELE COPYRIGHT 2007 Mark Twain Media, Inc. ISBN 978-1-58037-400-2 Printing No. CD-404059 Mark Twain Media, Inc., Publishers

More information