Student Name: Date: How Many? The table shows the number of different base-ten model pieces it takes to represent each place value position.

How Many? The table shows the number of different base-ten model pieces it takes to represent each place value position. How Many? Thousand cubes Hundred Thousand Thousands Ten Thousand Units Thousand Hundred Ten One 1 Flats 10 1 Longs 1,000 100 1 Unit cubes 100,000 10,000 100 1 1 Use the base-ten model and the pattern shown to complete the table. 2 Describe how the place values change as you move from right to left in the table. 3 Describe how the place values change as you move from left to right in the table. How could you describe the value of the millions place as compared to value of the hundred-thousands place? 3 2015 Region 4 Education Service Center

Place Value: Find Someone Who... Find a student who can answer one of the problems below. Ask him or her to record his or her thinking along with an answer and to sign his or her name. Continue the process until each problem is answered. Each student may only answer one problem on your paper. After each problem is answered, make any corrections needed on your own paper. 1 2 3 4 Expanded Notation (2 x 100,000,000) + (3 x 10,000,000) + (9 x 1,000,000) + (4 x 100,000) + (7 x 10,000) + (5 x 1,000) + (1 x 100) + (8 x 1) (5 x 10,000,000) + (4 x 1,000,000) + (2 x 100,000) + (8 x 10,000) + (7 x 1,000) + (3 x 10) + (7 x 1) (7 x 100,000,000) + (3 x 1,000,000) + (5 x 100,000) + (4 x 10,000) + (1 x 1,000) + (8 x 100) + (6 x 10) + (2 x 1) (8 x 100,000,000) + (3 x 10,000,000) + (7 x 100,000) + (1 x 10,000) + (2 x 1,000) + (4 x 100) + (5 x 1) can record the standard notation of the number and who can answer the question. standard notation: What is the value of the digit 9? signature: standard notation: What is the value of the digit 2? signature: standard notation: What is the value of the digit 7? signature: standard notation: What is the value of the digit 3? signature: Explain how to determine the value of a digit in any given whole number. 5 2015 Region 4 Education Service Center

What is the Value? 1 Place one Digit Card in each of the place-value positions on the Place Value Chart to represent a multi-digit number. Place Value Chart Millions Thousands Ones H T O H T O H T O 2 Record the created number and represent the value of the number using expanded notation. Example: 35,204 = (3 x 10,000) + (5 x 1,000) + (2 x 100) + (4 x 1) 3 Repeat steps 1 and 2 two more times. The expanded form of 40,040 is 40,000 + 40. How might you use the expanded form of 40,040 to write its expanded notation? 7 2015 Region 4 Education Service Center

Digit Cards Cut along the bold dotted lines. Three sets of cards are provided. 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 2015 Region 4 Education Service Center 8

Place Value Match Match four sets of Place Value Cards that represent the same value in word form and expanded notation. Note: Not all cards will be used. Fill in the blank on each card with the appropriate standard form. Attach the four matched sets of cards below. Words and Standard Notation Expanded Notation Select one of the unmatched cards. Create the card that would be its match. Explain your card to a partner. 11 2015 Region 4 Education Service Center

Place Value Cards Cut along the bold dotted line. Two sets of cards are provided. (2 x 1) + (7 x 0.1) + (8 x 0.01) (2 x 10) + (8 x 1) + (7 x 0.1) (8 x 10) + (2 x 0.1) + (7 x 0.01) (8 x 1) + (7 x 0.1) + (2 x 0.01) (7 x 10) + (8 x 1) + (2 x 0.1) (7 x 10) + (2 x 1) + (0 x 0.1) + (8 x 0.01) (2 x 1) + (7 x 0.1) + (8 x 0.01) (2 x 10) + (8 x 1) + (7 x 0.1) (8 x 10) + (2 x 0.1) + (7 x 0.01) (8 x 1) + (7 x 0.1) + (2 x 0.01) (7 x 10) + (8 x 1) + (2 x 0.1) (7 x 10) + (2 x 1) + (0 x 0.1) + (8 x 0.01) is the sum of 8 tens, 0 ones, 2 tenths, and 7 hundredths is the sum of 7 tens, 8 ones, and 2 tenths is the sum of 7 tens, 2 ones, and 8 tenths is the sum of 2 tens, 8 ones, and 7 hundredths is the sum of 8 ones, 7 tenths, and 2 hundredths is the sum of 2 ones, 7 tenths, and 8 hundredths is the sum of 8 tens, 0 ones, 2 tenths, and 7 hundredths is the sum of 7 tens, 8 ones, and 2 tenths is the sum of 7 tens, 2 ones, and 8 tenths is the sum of 2 tens, 8 ones, and 7 hundredths is the sum of 8 ones, 7 tenths, and 2 hundredths is the sum of 2 ones, 7 tenths, and 8 hundredths 2015 Region 4 Education Service Center 12

Complete the Comparison 1 Record the missing comparison symbols needed to make the comparison statements true. 2 Record a number with at least 5 digits that will make each comparison statement true. 93,123,238 184,143,659 < 236,012 1,392,203 1,203,201 329,235,257 = 81,210 18,201 47,396 < 425,124,059 421,542,509 < 832,252,913 3 Circle one of the pair of numbers above that is not equal. Write a number that has a value between these two numbers. Justify how you know the number you wrote for question 3 is between the two values you selected. 15 2015 Region 4 Education Service Center

Paper Recycling The table below shows the total number of pounds of paper Blue Skies, Texas recycled over a five year time period. Use the information in the table to answer the questions. Year Total Number of Pounds of Paper Recycled 2013 71,252,325 2012 65,235,523 2011 71,592,498 2010 65,239,831 2009 71,045,946 1 Which year had the least total number of pounds of paper recycled? What is the value of the digit in the ten-millions place? 2 Which year had the greatest total number of pounds of paper recycled? What is the value of the digit in the hundred-thousands place? 3 Use >, <, or = to create a comparison statement about the greatest total number of pounds of paper recycled and the next to greatest total number of pounds of paper recycled. 4 Order the five total number of pounds of paper from greatest to least. When comparing the data for 2010 and 2012, which place value indicates which number is larger? Why? 17 2015 Region 4 Education Service Center

Follow the directions on display. Rounding Road Trip Round 124,142 to the nearest 10 Round 523,951 to the nearest 100 Round 97,094 to the nearest 10,000 Round 943,638 to the nearest 1,000 START Initials: Initials: Initials: Initials: Comparison Spinner Number Spinner Round 863,253 to the nearest 100,000 Initials: Finish Round 72,397 to the nearest 10 Round 655,815 to the nearest 10,000 Round 317,412 to the nearest 100 Round 27,386 to the nearest 1,000 Initials: Initials: Initials: Initials: Do you predict the sum of the rounded numbers with your initials will be greater than or less than the actual sum? Explain your thinking. 19 2015 Region 4 Education Service Center

Rounding Road Trip Directions The Rounding Road Trip is completed in pairs. Each player chooses a different color counter. Take turns using a paperclip and pencil to spin the Number Spinner. Move the counter that number of spaces. Complete the task for that space by: rounding the number as described, recording the rounded number in the space provided, and recording your initials. If you land on a space already completed, spin the spinner again. Continue spinning until each player reaches Finish. After both players have made it to Finish, each player adds up all of the rounded numbers he/she rounded. Spin the Comparison Spinner to determine the winner. 2015 Region 4 Education Service Center 20

Representing Decimals 1 Use base-ten blocks to model the decimals shown below. 0.03 0.3 2 Use base-ten blocks to model two different decimals between the 0.03 and 0.3. Record the two decimals. Justify your answer. 3 A) Use the Blank Grids to represent 0.03 and 0.3. B) Use the open number line to explain how you know the statement below is true by placing the decimals 0.03 and 0.3 on the number line. 0.3 is further from zero than 0.03 on a number line What connections do you see between the base-ten blocks and a number line for modeling decimals? 23 2015 Region 4 Education Service Center

Blank Grids Cut along the bold dotted line. Two sets of cards are provided. 2015 Region 4 Education Service Center 24

Decimal Model Match Follow the instructions on Decimal Model Match Rules to complete the activity. Decimal Base-ten Model Money Model Describe how you and your partner determined where to place the cards on the game board. 27 2015 Region 4 Education Service Center

Decimal Cards Cut along the dotted line. 2015 Region 4 Education Service Center 28

Decimal Model Match Rules 1 Mix up the cards and place them face down. 2 Player A turns over two cards, chooses one of the cards to place on the game board, and turns the other card back over. 3 Player B turns over two cards, chooses one of the cards to place on the game board, and turns the other card back over. Note: As a player places cards on the game board, he or she needs to place cards that represent the same decimal on the same row. 4 Players A and B will continue taking turns until all cards have been placed. 5 Players A and B are to work together to record the decimal that represents the models. 29 2015 Region 4 Education Service Center

Decimal Comparisons: Justified True/False Determine if each statement is true or false by using base-ten blocks. Justify your answer by conecting the statement to the base-ten blocks. Statement True/False Justify Your Answer. 1.7 < 1.07 1.26 < 1.9 2.3 = 2.03 1.08 = 1.80 2.6 > 2.48 Choose one of the comparisons that is false. Draw a picture of the base-ten blocks to prove that the comparison is false. 31 2015 Region 4 Education Service Center

Ordering Decimals: Fan and Pick With your partner, decide who will be partner A and who will be partner B. Partner A: o Turn over the Decimal Cards. o Fan them out. Partner B: o Choose four cards. o Use base-ten blocks to represent each decimal. o Use your models to help you place the cards in order from least to greatest in the rectangles below. Partner A: Check your partner s work. Switch roles and repeat the process. Continue until each person has ordered two sets of cards on his or her paper. Set 1 Set 2 How is using the base-ten blocks to order decimals similar to ordering whole numbers? How is it different? 33 2015 Region 4 Education Service Center

Decimal Cards Cut along the bold dotted line. Three sets of cards are provided. 0.07 1.25 2.8 0.14 1.02 2.08 1.52 0.7 0.4 1.15 2.68 0.41 2.06 2.6 1.2 0.17 0.47 1.5 2.86 1.71 0.07 1.25 2.8 0.14 1.02 2.08 1.52 0.7 0.4 1.15 2.68 0.41 2.06 2.6 1.2 0.17 0.47 1.5 2.86 1.71 0.07 1.25 2.8 0.14 1.02 2.08 1.52 0.7 0.4 1.15 2.68 0.41 2.06 2.6 1.2 0.17 0.47 1.5 2.86 1.71 2015 Region 4 Education Service Center 34

Make a Fraction a Decimal Choose a Paper Strip to represent each fraction and then shade the Paper Strip to represent the fraction. Use the model to determine and record the equivalent decimal. Fraction Model Decimal 2 10 25 100 7 10 56 100 How are fractions and decimals similar? How are they different? 37 2015 Region 4 Education Service Center

Paper Strips Cut along the bold dotted line. Two sets of paper strips are provided. 2015 Region 4 Education Service Center 38

Student Name: Date: Decimal to Fraction: Find Someone Who... Find a student who can describe the model as a decimal and as a fraction. Ask him or her to record his or her thinking along with an answer and to sign his or her name. Continue the process until your paper is complete. Each student may only answer one problem on your paper. After each problem is answered, make any corrections needed on your own paper. can describe the model as a decimal and as a fraction. can describe the model as a decimal and as a fraction. Decimal: Decimal: Fraction: Fraction: Signature: Signature: can describe the model as a decimal and as a fraction. can describe the model as a decimal and as a fraction. Decimal: Decimal: Fraction: Signature: Fraction: Signature: What is the relationship between the denominators of the fractions and the place value of the equivalent decimals? Justify your answer. 41 2015 Region 4 Education Service Center

Fraction and Decimal: Agree or Disagree Mr. Thomas wanted to buy a piece of lumber that was 2 12 10 meters. The salesperson gave Mr. Thomas a piece of lumber that was 12.02 meters. Did the salesperson give Mr. Thomas the correct length? No, because the fraction and the decimal should represent twelve and two-tenths of a meter of lumber and the decimal should be written Joe Sam Yes, because the fraction and the decimal both represent twelve and two-tenths of a foot of lumber. With which student do you agree? Explain why you agree with this student, and why you disagree with the other student. Sketch a model for 2 and 0.02 using the same model for one whole. How do 10 your sketches justify your answer? 43 2015 Region 4 Education Service Center

Locating Decimals Determine the decimal represented by the point on each number line. Decimal Number Line Representation 1 2 3 4 5 6 7 8 9 10 Choose one of the number lines above that has more than one length for partition lines. How did you determine the value of each partition line? 45 2015 Region 4 Education Service Center

Two hexagons represent 1 whole. Putting the Pieces Together 1 Use pattern block pieces to represent 4 6 of the whole. 2 How many sixths are in 4? 6 3 Write an addition equation to show how many sixths are in 4. 6 4 Use pattern block pieces to represent 5 How many fourths are in 1 1? 4 1 1 4 of the whole. 6 Write an addition equation to show how many fourths are in 1 1. 4 Explain why 5 4 is equivalent to 1 1 4 using unit fractions and a model or a picture. 47 2015 Region 4 Education Service Center

Fraction Sums Match the Fraction Sum Card(s) that represent the sum of the unit fractions. Note: Some cards will remain without a match. Expression Fraction Sum Card(s) 1 1 1 1 1 1 1 1 1 5 5 5 5 5 5 5 5 1 1 1 1 2 5 5 5 5 1 1 1 1 1 1 3 5 5 5 5 5 5 1 1 1 1 1 4 3 3 3 3 3 1 1 1 1 1 1 1 5 3 3 3 3 3 3 3 1 1 1 6 3 3 3 Draw a picture to represent how you know the number of thirds or the number of fifths that are equal to one whole. 49 2015 Region 4 Education Service Center

Fraction Sum Cards Cut along the bold dotted line. Five sets of cards are provided. 1 3 1 1 1 5 5 5 4 6 5 1 3 1 1 1 5 5 5 4 6 5 1 3 1 1 1 5 5 5 4 6 5 1 3 1 1 1 5 5 5 4 6 5 1 3 1 1 1 5 5 5 4 6 5 5 3 2 3 1 3 3 5 3 2 3 1 3 3 5 3 2 3 1 3 3 5 3 2 3 1 3 3 5 3 2 3 1 3 3 7 3 8 5 1 4 2 3 5 7 3 8 5 1 4 2 3 5 7 3 8 5 1 4 2 3 5 7 3 8 5 1 4 2 3 5 7 3 8 5 1 4 2 3 5 2015 Region 4 Education Service Center 50

Decomposing Fractions: Who Is Correct? Ms. Murray asked her students to use fraction circle pieces to represent 6. 5 Next, she asked them to decompose the fraction 6 5 and record how they decomposed the fraction using symbolic notation. Use your fraction circle to help you determine which student correctly decomposed the fraction 6 5. Circle the work of the correct student(s). Justify your answers using words or pictures. Brian Carlos Sam Jayden 1 1 1 1 1 2 1 5 1 1 1 3 1 5 1 1 1 1 1 5 5 5 5 5 5 Choose a student who decomposed the fraction incorrectly. Explain to this student what he did wrong. 53 2015 Region 4 Education Service Center

Same Fraction, Different Representations: Round Robin Pass your paper to the person seated at your right. Determine the process you will use to decompose a paper strip to represent the fraction 5. Draw a strip diagram 3 and the related expression to represent your decomposed fraction. You may work with your group to solve the problem. Upon completing the first representation, pass your paper to the right again. Determine the process you will use, and decompose 5 in a second way. 3 Continue this process two more times using a different strategy from those that have already been recorded. Strip Diagram that represents 5 3 Expression 1 2 3 4 When decomposing fractions, how are the strip diagram representations and expressions related? 55 2015 Region 4 Education Service Center

Paper Strips Cut along the bold dotted line. Two sets of paper strips are provided. ` 2015 Region 4 Education Service Center 56

Equivalent Fractions: True or False Determine if the two fractions are equivalent. Justify your answer using words or a diagram. Fractions True or False Justification 3 12 4 16 3 10 2 5 5 4 6 6 9 2 3 3 8 How did you determine if the two fractions are equivalent? 59 2015 Region 4 Education Service Center

Proving Fraction Equivalence Ms. Peterson stated that the two fractions in each set below are equivalent. 3 9 = 5 15 4 8 = 12 24 Prove 3 9 = 5 15 Trade papers with a partner and prove 3 9 = 5 15 differently than your partner. Method 1: Method 2: Prove 4 8 = 12 24 Trade papers with a partner and prove 4 8 = 12 differently than your partner. 24 Method 1: Method 2: 3 5 How are the two strategies used to prove similar? How are they different? 9 15 61 2015 Region 4 Education Service Center

Fraction Comparisons Problem A Problem B Ms. Hernandez s family ate 3 4 of a pan Ms. Hernandez s family ran 1 2 of a mile of brownies. Ms. Johnson s family ate 5 8 of a pan of brownies. Both pans of brownies were equal in size. 1 Create a model that compares the portion of a pan of brownies eaten by each family. together as a family. Ms. Johnson s family ran 3 of a mile together as a 10 family. 1 Create a model that compares the distance that each family ran. 2 Which family ate the largest portion of a pan of brownies? 2 Which family ran the shorter distance? 3 Record a comparison statement using both fractions and the symbols <, >, or =. 3 Record a comparison statement using both fractions and the symbols <, >, or =. How did your models help you compare fractions with unlike denominators? 63 2015 Region 4 Education Service Center

Making Fraction Comparisons Identify the Fraction Card that will make each comparison statement true. Tape or glue the cards in the appropriate places to make each comparison statement true. 2 3 < > 4 10 = 1 6 5 7 > < 2 10 Choose one comparison statement. Sketch a model to justify the statement as true. 65 2015 Region 4 Education Service Center

Fraction Cards Cut along the bold dotted lines. Eight sets of cards are provided. 5 3 1 2 1 6 5 6 12 2 5 3 1 2 1 6 5 6 12 2 5 3 1 2 1 6 5 6 12 2 5 3 1 2 1 6 5 6 12 2 5 3 1 2 1 6 5 6 12 2 5 3 1 2 1 6 5 6 12 2 5 3 1 2 1 6 5 6 12 2 5 3 1 2 1 6 5 6 12 2 2015 Region 4 Education Service Center 66

Fraction Addition and Subtraction 1 Represent each problem using a paper strip. Use your model to determine a solution. Attach your model below the problem it represents. 1 2 = 4 4 2 7 4 = 8 8 3 5 7 = 8 8 4 4 1 = 2 2 Which problems are represented with more than one paper strip? Why? 69 2015 Region 4 Education Service Center

Paper Strips Cut along the bold dotted lines. Two sets of paper strips are provided. ` 2015 Region 4 Education Service Center 70

The Family Garden Each member of the Kennedy family was given a portion of the garden in their backyard to plant their favorite vegetable or fruit. The table below shows the portions given to each family member: Family Member Mr. Kennedy Mrs. Kennedy Jake Kate Portion of Garden 1 12 3 12 4 12 4 12 Represent how much more of the garden Jake and Kate have planted than Mr. and Mrs. Kennedy. Use the strip diagrams shown below. How did you partition the strip diagram into twelfths? 73 2015 Region 4 Education Service Center

Practice Time Use Cuisenaire Rods to represent and solve each problem. Create pictorial models to show how you used the Cuisenaire Rods to represent and solve each problem. Problem A During football practice Juan ran 3 4 of a mile on Monday and 6 4 of a mile on Wednesday. How many miles did Juan run on these two days? Pictorial Model: Answer: Problem B Macy goes to dance class every week for an hour. During dance class she spends 3 6 of the time practicing ballet and 2 of the time practicing jazz. The rest of the 6 time is spent exercising. What part of the hour does Macy spend exercising? Pictorial Model: Answer: Choose one of the problems above and represent it and its solution using a number line. 75 2015 Region 4 Education Service Center

Adding and Subtracting Fractions: Whose Strategy Is Most like Mine? Solve Problem A and Problem B below. Include the strategy that you use to solve the problem. Problem A: Candace had 1 3 8 pizzas to share with her friends after school. Before her friends got to her house, her brother ate 6 of one pizza. How 8 many pizzas were left for Lisa and her friends? Work Space: Problem B: After Freddy s party there 3 were 2 hamburger pizzas and 6 5 4 6 pepperoni pizzas left over. How many pizzas were left over from Freddy s party? Work Space: Which strategy did you not circle for Problem A? Is it an appropriate solution strategy? Why or why not? 77 2015 Region 4 Education Service Center

Examine the two students procedures for solving these two problems. Circle the procedure that is most similar to your procedure and process. Use the space provided to explain your selection. Problem A: Candace had 1 3 8 pizzas to share with her friends after school. Before her friends got to her house, her brother ate 6 of one pizza. How 8 many pizzas were left for Lisa and her friends? Problem B: After Freddy s party there 3 were 2 hamburger pizzas and 6 5 4 6 pepperoni pizzas left over. How many pizzas were left over from Freddy s party? 1 25 3 8 8 25 6 8 8 25 5 1 ( ) 8 8 8 25 5 1 ( ) 8 8 8 20 1 19 3 2 8 8 8 8 1 6 3 8 8 1 1 5 3 ( ) 8 8 8 1 1 5 (3 ) 8 8 8 5 3 8 8 5 3 2 2 8 8 8 3 5 2 4 6 6 3 3 2 2 4 ( ) 6 6 6 3 3 2 2 4 ( ) 6 6 6 2 2 4 1 6 2 1 7 7 6 3 3 5 2 4 6 6 3 5 6 6 6 3 3 2 6 ( ) 6 6 6 3 3 2 6 ( ) 6 6 6 2 2 1 6 1 7 7 6 6 3 2015 Region 4 Education Service Center 78

Estimating Sums and Differences Use benchmark fractions to determine the best estimate for each addition and subtraction problem. Problem 6 4 10 9 Best Estimate 1 2 1 1 1 2 Justify your response 11 2 12 5 3 7 16 12 17 14 18 20 0 1 2 1 1 2 3 4 1 1 4 1 2 1 Create a number line or strip diagram to justify one of your estimates. 81 2015 Region 4 Education Service Center

Wooden Jewelry Box The list below shows the materials Matthew needs to build a wooden jewelry box for his mother. 3 He needs two pieces of wood that are 11 inches each. 8 He needs one piece of wood that is He needs one piece of wood that is 7 5 8 inches long. 5 2 8 inches long. 1 Estimate each value in the above problem to the nearest 1 -inch. Estimate the 2 length of wood Matthew needs to buy in order to build the wooden jewelry box. Estimated Amount: 2 Determine the actual length of wood Matthew needs to buy in order to build the wooden jewelry box. Actual Amount: 3 What do you notice as you compare the estimated amount of wood needed to the actual amount of wood needed? Is your estimate reasonable? Why or why not? 83 2015 Region 4 Education Service Center

How Far From Zero? 1 Represent each fraction and decimal on the number line. 3 1 10 5 2 Number Line 2 5 1.8 0.7 2 Label each decimal with an equivalent fraction on the number line. 3 Label each fraction with an equivalent decimal on the number line. 4 How could the fraction 40 100 your thinking. be represented on the number line above? Explain How did you determine where to place 5 and 1.8 in relationship to zero? 2 85 2015 Region 4 Education Service Center

Who Is Winning? Six friends were competing in a race. The fractions below tell how much of the race they have completed. Zero represents the starting point, and 1 represents the distance of the entire race. Place the racers on the number line according to how much of the race each runner has completed. Maggie 5 8 Henry 1 2 Daniel 2 3 Joey 5 6 Tiffany 4 9 Karen 11 12 0 1 1 Which friend is currently winning the race? Explain how you know. 2 Which friend is currently in last place? Explain how you know. How might benchmark fractions help you determine if your placement of each racer is reasonable? 87 2015 Region 4 Education Service Center

Solve each problem below. Solving Problems Problem A Problem Answer A local dress shop has 2,407 dresses in stock. There are 837 short dresses and 958 long dresses. The remaining dresses are children s dresses. How many dresses are children s dresses? Problem B Luke is 9 years older than Bria. Bria is 15 years younger than Samantha. Samantha is twice as old as Xavier. Xavier is 12 years old. What is the combined age of these four people? Problem C Ms. Chavez collected 1,653 books during June, 929 books during July, and 1,585 books during August. In September, Ms. Chavez donated 1,498 books to one local charity and 1,674 books to another local charity. How many books does Ms. Chavez have left in her collection? Describe the process you used to solve Problem B. 89 2015 Region 4 Education Service Center

Adding and Subtracting Decimals: Who Is Correct? Solve the problem below. Include the procedure that you used to solve the problem. Miguel received $86.50 for his birthday. He spent $16.35 on an action figure. He also spent $21.48 on a DVD. How much money does Miguel have after buying an action figure and DVD? 91 2015 Region 4 Education Service Center

Examine Michael s, Jasmine s, Antonio s, and Zoe s procedure for solving this problem. Circle the student that has a solution that matches your solution. Identify the other students mistakes. Michael Jasmine Antonio Zoe 1 16.35 21.48 37.83 16.35 21.48 37.73 1 16.35 21.48 37.83 410 86.50 16.35 70.15 7 15 15 86.50 37.83 7 15 14 10 86.50 37.73 7 15 14 10 86.50 37. 83 6 10 10 15 70.15 21.48 48.73 48.77 48.67 49.67 What suggestions do you have for the students who made mistakes? 2015 Region 4 Education Service Center 92

Addition and Subtraction: Three in a Row Choose one row from the table below. Solve each of the three problems in that row. Record your answers. Problem A Bryce spent a total of $29.22 on apps for his phone during June and July. During June, he spent $12.98 on apps. How much money did Bryce spend on apps during July? Problem B Daylen started with $28.31. He spent $9.02 on books and $3.04 on snacks. He put the rest of his money in savings. How much money did Daylen put in savings? Problem C Micah bought 3.2 pounds of oranges and 5.48 pounds of apples. How many pounds of fruit did Micah purchase? Problem D Angelica has $83.45 in her checking account. She paid a phone bill using $61.13 from her checking account. What is the remaining balance in her checking account? Problem E Gary started the day with $41.72. He spent some money to buy a movie ticket and spent $8.18 to buy snacks. At the end of the day, Gary had $24.79 remaining. How much did Gary spend on a movie ticket? Problem F Sherry started with a full tank of gas in her car. She used 6.75 gallons over the weekend and has 9.15 gallons of gas remaining. With how many gallons of gas did Sherry start? Problem: Problem: Problem: Answer: Answer: Answer: Describe how you know your answer to Problem B or Problem E is reasonable using estimation. 95 2015 Region 4 Education Service Center

Addition and Subtraction: Loop 1 Solve each problem on the Addition and Subtraction Loop Cards in the workspace provided below. 2 Tape the top of the card that contains the correct answer to the bottom of the card with the matching word problem. 3 Continue this process for the remaining problems. 4 When complete, the taped cards should form a loop. Work Space How is adding and subtracting decimals similar to and different from adding and subtracting whole numbers? 97 2015 Region 4 Education Service Center

Addition and Subtraction Loop Cards Cut along the dotted lines. Do not cut along the solid lines. $87.38 $57.85 Chase had 14 dollars in his jacket pocket. He spent $10.77 downloading music. How much money does Chase have now? Maria had some money in her purse on Monday. She spent $5.89 on Tuesday and $4.30 on Wednesday. She now has $5.82 in her purse. How much money did Maria have in her purse on Monday? $16.01 $3.23 Last week, Lyla spent $43.90 on groceries, $27.48 on clothes, and $16.00 on entertainment. How much money did Lyla spend? Alex had $63.01. He cashed a check for $15.99. Then he spent $21.15 on a new shirt. How much money does Alex now have? 2015 Region 4 Education Service Center 98

Multiplying by 10 or 100: Loop 1 Solve each problem on the Multiplication Loop Cards in the work space provided below. Record the answer on the card. 2 Tape the top of the card that contains the correct expression to the bottom of the card that contains matches its expression. 3 Continue this process for the remaining problems. 4 When complete, the taped cards should form a loop. Work Space Explain how you could use properties of operations and place value to solve one of these problems. 101 2015 Region 4 Education Service Center

Cut along the dotted lines. Multiplying by 10 or 100 Loop Cards (3,000 10) + (400 10) + (50 10) + (9 10) (3,000 100) + (500 100) + (40 100) + (9 100) (3,000 100) + (900 100) + (40 100) + (5 100) A local zoo is selling season passes for $100 each. So far, they have sold 3,594 season passes. How much money has the zoo earned from season passes? Every hat at The Hat Shop is $10 with tax. They have a total of 3,954 hats in the store. If they sold all of the hats, how much money they would receive from sales? Jazzy Music sold all of their CDs for $10, including tax, during the month of June. During this time, they sold 3,459 CDs. How much money did they receive from this CD sale? Answer: Answer: Answer: (3,000 10) + (400 10) + (90 10) + (5 10) (3,000 10) + (900 10) + (50 10) + (4 10) (3,000 100) + (500 100) + (90 100) + (4 100) Jack s Apples sells containers of apples with 100 apples in each container. In May, they sold 3,549 containers of apples. How many apples did they sell in May? Answer: Each of the 3,945 students at Joy Elementary read 100 books this year. How many books were read by the Joy Elementary students this year? Answer: The Best Bank has 3,495 dimes. What is the value of these dimes in cents? Answer: 2015 Region 4 Education Service Center 102

Multiplying by 10: Who Is Correct? Aubrey and Blaine both solved the problem below. They both determined the answer to be $5,450. However, they provided different explanations. A local pizza place sold large pizzas for $10 during the month of October. A total of 546 large pizzas was sold during October. What was the total cost of these large pizzas? Aubrey s Explanation To solve the problem I needed to multiply 546 by 10, which means that each value from the expanded form is being multiplied by 10, so 10 546 = 10 (500 + 40 + 6) (10 500) + (10 40) + (10 6) 5,000 + 400 + 60 5,460 Blaine s Explanation To solve the problem I needed to multiply 546 by 10. When I multiplied by 10, I knew the product needed to be 10 times larger than the value of each digit; 500, 40, and 6. This means the product is the sum of 5,000 + 400 + 60. Is Aubrey correct? Justify your answer. Is Blaine correct? Justify your answer. Which explanation makes the most sense to you mathematically? Justify your answer. 105 2015 Region 4 Education Service Center

Model My Product Match the Factor and Product Cards to each array model. Use the remaining cards to complete the multiplication equation that represents the array. = = = = Which one of these array models might represent a perfect square? Justify your answer. 107 2015 Region 4 Education Service Center

Factor and Product Cards Cut along the bold dotted lines. Nine sets are provided. 12 19 13 195 13 11 13 15 204 17 169 209 12 19 13 195 13 11 13 15 204 17 169 209 12 19 13 195 13 11 13 15 204 17 169 209 12 19 13 195 13 11 13 15 204 17 169 209 12 19 13 195 13 11 13 15 204 17 169 209 12 19 13 195 13 11 13 15 204 17 169 209 12 19 13 195 13 11 13 15 204 17 169 209 12 19 13 195 13 11 13 15 204 17 169 209 12 19 13 195 13 11 13 15 204 17 169 209 2015 Region 4 Education Service Center 108

Complete the Model Complete the models below to represent the product of each problem. Complete the equation to determine the sum of the each partial product. Record the product above each model. 1 34 27 = 2 32 15 = 20 + 7 10 + 5 30 210 30 + 4 80 + 80 + 210 + = 3 14 14 = 10 + 4 10 + 4 40 + + 40 + = + 2 10 + + + 10 = 4 12 23 = 20 + 3 10 + 2 + + + = Describe how the model for 12 23 is related to place value. 111 2015 Region 4 Education Service Center

Multiplication: Whose Strategy Is Most like Mine? Determine the product: 27 13 Include the strategy that you use to solve the problem. Choose two of the multiplication procedures. How are they are alike? How are they are different? 113 2015 Region 4 Education Service Center

Examine Rose s, Patti s, and Gary s procedures for solving this problem. Circle the procedure that is most similar to your procedure and process. Use the space provided to explain why each procedure does or does not make sense mathematically. Rose 27 x10 270 2 27 x 3 81 1 270 81 351 Does this procedure make sense mathematically? Why or why not? Patti 2 27 x13 1 81 270 351 Does this procedure make sense mathematically? Why or why not? Gary 27 x 1 3 21 60 70 1 200 351 Does this procedure make sense mathematically? Why or why not? 2015 Region 4 Education Service Center 114

Multiplication: Find Someone Who Find a student who can answer one of the problems below. Ask him or her to record his or her thinking along with an answer and to sign his or her name. Continue the process until each problem is answered. Each student may only answer one problem on your paper. After each problem is answered, make any corrections needed on your own paper. can solve the following problem. A local business plans to give away 8 cash prizes of $450 and 4 cash prizes of $225 at its grand opening. What is the total amount of money the business will give away at the grand opening? Answer: can solve the following problem. Rachel is arranging chairs for a program. She needs a total of 2,146 chairs. She has already arranged 48 rows of chairs with 36 chairs in each row. How many chairs does Rachel need to complete her arrangement? Answer: Signature: can solve the following problem. A school is purchasing a class set of laptops for each of their 35 teachers. Each class set contains 24 laptops. How many laptops will the school purchase? Answer: Signature: can solve the following problem. Alex rode the same route on her bike four times. One lap of the route is 5,375 meters. How many meters did Alex ride during the four laps? Answer: Signature: Signature: Choose one problem from above. How can you use estimation to determine if the answer is reasonable? 117 2015 Region 4 Education Service Center

Modeling Division Problem Open Array Model Quotient 25 20 1 184 4 4 100 80 4 46 Use an open array to model the solution for each division problem. 1,024 4 2,125 5 147 3 Choose one problem and describe how the open array represents the dividend, divisor, and quotient of the division problem. 119 2015 Region 4 Education Service Center

Division Model Mistake Jayden was asked to determine the quotient of 492 6 using the model provided below. 2 12 10 60 10 60 50 + 10 + 10 + 2 = 72 492 6 = 72 50 300 6 Jayden s teacher asked her to identify a mistake in her work. Describe the mistake Jayden made when determining the quotient. Explain how Jayden can correct the error. How can starting with a model of the dividend help you determine the quotient of a division problem? 121 2015 Region 4 Education Service Center

Division Completion Number Bank 70 35 25 100 100 125 775 25 24 28 70 25 37 Determine where to place each number from the Number Bank in order to complete the solution process for each problem. Each number will only be used once. Malcolm ran for 168 minutes last week. He ran the same number of minutes for each of the seven days. How many minutes did Malcolm run each day? Lakeside Independent School District needs 3,875 elementary registration packets for back-to-school night. Five people plan to make an equal number of packets. How many packets must each person make to complete the project? Kelly saved $375 in three months. She saved the same amount each month. How much money did Kelly save per month? 7 168 10 5 3,875 375 3 300 3 98 75 3 28 10 35 + = 4 25 0 0 123 2015 Region 4 Education Service Center

What connections do you see among the three solution processes? 2015 Region 4 Education Service Center 124

Solving Division Problems Solve each problem on your own. With a partner, compare your answers and make corrections as needed. Problem A There are 3,681 students at West Elementary School. Three grades attend the school. There are an equal number of students in each grade. How many students are in each grade? Work: Problem B The public library has 1,845 new books and 4,527 old books. Micah placed an equal number of books on 9 bookcases in the library. How many books did he place on each bookcase? Work: Problem C A local football team collected $2,385 this week and $2,805 last week in ticket sales. Tickets were $5 per person. How many tickets were sold? Work: Problem D Sunnyside Elementary school read 7,784 books in eight months. They read an equal number of books each month. How many books were read each month? Work: Another student solved Problem B by dividing 6,300 by 9, dividing 72 by 9, and adding the two results. How does this compare to your method? 127 2015 Region 4 Education Service Center

Estimating with Whole Numbers: Odd One Out Circle the expression in each set that does NOT show how to appropriately use rounding or compatible numbers as an estimation strategy. Justify why the odd one out is not an appropriate estimation strategy. Problem Estimation Strategy Justify the Odd One Out A B C Marc mowed 53 lawns this summer. He earned $28 for each lawn mowed. About how much money did Marc earn this summer? Today, a local printing shop printed 678 boxes of cards to ship to 6 different card stores. Each store receives an equal amount. Approximately how many cards will each store receive? The Nguyen family traveled 1,298 miles for vacation. On day one they traveled 481 miles, and on day two they traveled 326 miles. They finished traveling on day three. How many miles did they travel on day three? 50 30 50 25 60 20 680 10 675 5 660 6 1,300 (475 + 325) 1,000 (400 300) 1,300 500 300 When does rounding to the nearest 10 prove to be an inappropriate estimation strategy? Why? 129 2015 Region 4 Education Service Center

Comparing Estimates James was given the following problems to solve in math class. Estimate the answer to each problem. Compare your estimate to James estimate. 1 Karen earned $120 last week and $100 this week. She worked a total of 6 hours. Approximately how much money did she earn per hour? My Estimate: James said Karen earns approximately $40 per hour. Explain why James answer represents an appropriate estimation. 2 Gainer Elementary School is selling t-shirts for a fundraiser. The fourth graders have bought 63 t-shirts. The third graders have bought 28 t-shirts. The school receives $18 for each t-shirt sold. Approximately how much money has the school received? My Estimate: James said the school will raise approximately $1,800. Explain why James answer represents an appropriate estimation. Could your estimates and James estimates be different and still be appropriate estimations? Why or why not? 131 2015 Region 4 Education Service Center

Solve each problem. Justify your answer. School Fundraisers Problem 1 Ms. Seymour s class is participating in a walk-a-thon fundraiser. Each of her 22 students walked 52 laps around the track. During the 4 hours of the fundraiser, the students walked the same number of laps each hour. How many laps did the 22 students walk altogether in one hour? Work: Problem 2 The craft club is making friendship bracelets to sell for a fundraiser. They need to make 351 red bracelets and 354 blue bracelets this week. They plan to make an equal number of bracelets Monday through Friday. How many bracelets should they make each day? Work: Answer: Answer: How are Problem 1 and Problem 2 alike? How are they different? 133 2015 Region 4 Education Service Center

Interpreting Solutions Solve each problem. Record your solution strategy and answer. Problem Solution Strategy Answer A fruit stand owner is putting together orange baskets that contain 8 oranges each. The owner begins with 185 oranges. How many complete baskets can be made? A fourth-grade class of 185 students is going on a field trip. The students are taking vans that can each hold 8 students. How many vans are needed for the trip? A sewing class has 185 yards of fabric to make quilts. Each quilt requires 8 yards of fabric. How much fabric will remain after all the quilts are made? How is each answer present in your solution strategy? 135 2015 Region 4 Education Service Center

Solve the Problem Solve the problems below. Justify your answer. Problem 1 Sebastian and his two brothers read an equal amount each week. They read for a combined total of 135 minutes each week. They read the same amount of time each week. How many minutes will each boy have read in 6 weeks? Work: Problem 2 Alan earned $1,284 a month for the past four months. He shared these earnings equally among his savings, his checking account, and his wallet. During the past four months, how much money did Alan put in his savings account? Work: Answer: Problem 3 Jasmine plans to save $25 a month for four years. If she does this, how much money will she have saved at the end of four years? Work: Answer: Problem 4 Rosa has 96 beads to make necklaces for her friends. Half of these beads are purple. She uses 8 purple beads for each necklace. How many complete necklaces can Rosa make? Work: Answer: Answer: Choose one of the problems. How did you solve the problem? 137 2015 Region 4 Education Service Center

Multiplication and Division: Find Someone Who... Find a student who can answer one of the problems below. Ask him or her to record his or her thinking along with an answer and to sign his or her name. Continue the process until each problem is answered. Each student may only answer one problem on your paper. After each problem is answered, make any corrections needed on your own paper. can solve the following problem. 1 Each student at Parkside Elementary will get 3 pencils from the principal. There are 16 classes with 25 students in each class. How many pencils will the principal need to purchase? Answer: can solve the following problem. 2 Marcus earns the same amount of money each week. He earned $2,480 after working four weeks. How much money would Marcus earn after working 9 weeks? Answer: Signature: can solve the following problem. 3 Six friends each raised $310 to donate to charity. They plan to donate half of the money to a children s hospital and half to a local shelter. What is the total amount of money the friends will donate to the children s hospital? Answer: Signature: can solve the following problem. 4 Kayla and her two sisters have a total of 1,080 minutes of designated computer time a week. If they share the computer time equally, how much computer time will each girl receive in six weeks? Answer: Signature: Signature: How do you know the answer to Problem 3 is reasonable? 139 2015 Region 4 Education Service Center

Kelly s Shopping Spree Complete the strip diagram and write an equation that could be used to solve the problem. Kelly spent $134 on a pair of pants and 3 shirts. She spent $56 on the pants, and each shirt was the same price. How much did Kelly spend on each shirt? Strip diagram: $ $ Pants $ Shirt $ Shirt $ Shirt $ Equation: How did you use the strip diagram to solve the problem? 141 2015 Region 4 Education Service Center

Dinner and a Movie Use colored pencils and the diagram to create a strip diagram for each problem. Dinner: Yang s family of three went to dinner at a buffet. The total cost of the buffet was $42. The soft drinks were a separate charge. Yang s family spent $51. How much money, m, did they spend per person on soft drinks? Movie: After dinner, Yang s family went to see a movie. At the theater, the family paid $42 for the movie tickets. They bought 3 soft drinks for $5 each and shared a large tub of popcorn that cost $9. Yang s family paid with $70. How much money, m, did they receive back? How are your strip diagrams similar? How are they different? 143 2015 Region 4 Education Service Center

Cupcakes by the Dozen Use the Number and Operation Cards to write an equation that can be used to represent the situation below. Use the equation to determine the answer to the problem. Equation: Ms. Rogers baked 5 dozen cupcakes. Her son ate two of the cupcakes. How many cupcakes remain? Let c represent the remaining number of cupcakes. Answer: Draw a strip diagram that represents this situation. Explain how it represents the situation. 145 2015 Region 4 Education Service Center

Number and Operation Cards Cut along the bold dotted lines. Nine sets of cards are provided. 5 12 2 c = 5 12 2 c = 5 12 2 c = 5 12 2 c = 5 12 2 c = 5 12 2 c = 5 12 2 c = 5 12 2 c = 5 12 2 c = 2015 Region 4 Education Service Center 146

Step 1 Representing Multi-Step Problems Create a strip diagram to represent the problem. Frances bought 2 video games for $62 each, a new gaming system for $352, and various accessories for his new gaming system. Frances spent $546 at Games-R-Us on all of his purchases. How much money, m, did Frances spend on the various accessories for his gaming system? Strip Diagram: Step 2 Equation: Trade papers with a partner. Represent the problem using an equation with a variable standing for the unknown quantity. Step 3 Answer: Trade papers with a partner. Use your partner s equation and/or strip diagram to solve the problem. Describe how your equation and strip diagram represent the situation. 149 2015 Region 4 Education Service Center

Output to the Input Jacob earns $124 each week. He saves all of his money. He created a table to represent the total value of his savings, as shown in the sequence below. 1 Complete Jacob s table below. 124, 248, 372, 496,... Input, Position (Weeks) Process Output, Value (Total Savings) 1 1 124 2 2 3 3 4 5 6 2 How much money will Jacob have saved at nine weeks? How did you determine the total savings at nine weeks? 151 2015 Region 4 Education Service Center

Sequence Match Determine where to place each of the Sequence Match Cards. Complete the missing information for each set. Output Values Input-Output Table Numerical Process input + 23 252 input input 23 252 input How did you determine the placement of the cards? 153 2015 Region 4 Education Service Center

Sequence Match Cards Cut along the bold dotted line. Two sets of cards are provided. Input Output 1 2 25 3 26 4 Input Output 1 2 46 3 4 92 Input Output 1 251 2 250 3 4 Input Output 1 252 2 3 4 63, 46,,,..., 25,,,... 251,,,,...,,, 63,... Input Output 1 2 25 3 26 4 Input Output 1 2 46 3 4 92 Input Output 1 251 2 250 3 4 Input Output 1 252 2 3 4 63, 46,,,..., 25,,,... 251,,,,...,,, 63,... 2015 Region 4 Education Service Center 154

Determining the Area Use the model of the rectangle below to answer the following questions. width length = 1 square unit 1 What is the length and width of the rectangle? 2 What is the area of the large rectangle in square units? 3 How did you determine the area of the rectangle? 4 What relationship do you notice between the length, width, and area of this rectangle? 5 Do you think this will be true for all rectangles? Why? Sketch a diagram to show how the length and width are related to the array of square units. 157 2015 Region 4 Education Service Center

Highlighting Dimensions Use a ruler to measure the side lengths of the rectangle below to the nearest inch. Use different colored highlighters to highlight side lengths with the same measure. Answer the questions below. inches inches inches inches 1 What do you notice about the side lengths of the rectangle? 2 What is the perimeter of the rectangle? 3 How is this relationship seen in the expression 2l + 2w where w represents the width and l represents the length of the rectangle? Describe the relationship between the attributes of a rectangle and the formula for the perimeter of a rectangle, P = 2l + 2w. 159 2015 Region 4 Education Service Center

Perimeter and Area: Agree or Disagree? Martha, Jeremy, and Joel were asked to describe a way to determine the perimeter of the following figure. Their work is shown below. Martha s Statement Jeremy s Statement Joel s Statement I would measure the length and width of the figure. Then, I would determine the sum of twice the length and twice the width, following the formula 2l + 2w. I would measure the length and width of the figure. Then, I would determine the sum of all four sides of the figure, following the formula l + w + l + w. I would measure one side of the figure. Then, I would multiply the side length by four, following the formula 4s. I agree disagree with (circle one) Martha because... I agree disagree with (circle one) Jeremy because... I agree disagree with (circle one) Joel because... Whose procedure are you most likely to use if you were to determine the perimeter of the figure above. Why? 161 2015 Region 4 Education Service Center

Perimeter and Area: Find Someone Who... Find a student who can answer one of the problems below. Ask him or her to record his or her thinking along with an answer and to sign his or her name. Continue the process until each problem is answered. Each student may only answer one problem on your paper. After each problem is answered, make any corrections needed on your own paper. can define area. Definition: can define perimeter. Definition: Signature: Signature: use a formula to determine the area of a rectangular game board that is 14 inches long and 15 inches wide. Work: use a formula to determine the perimeter of a rectangular game board that is 14 inches long and 15 inches wide. Work: Signature: Signature: How is determining the area of a rectangle similar to determining its perimeter? How is it different? 163 2015 Region 4 Education Service Center

Complete the table below. Perimeter and Area Problem Situation Which Formula? Circle the correct formula(s). Answer Jack is marking field lines for a playing field. The field is 26 yards wide and 60 yards long. What is the perimeter of the field? 2 l + 2w l + w + l + w 4s Carrie is cutting rectangular pieces of stained glass for her art project. Each piece is 9 inches by 12 inches. How many square inches does each piece of stained glass cover? l w l + w + l + w 4s Marsha is making a baby blanket for her sister. The blanket is a square that has side lengths of 36 inches. If she sews pink ribbon along the edge, how much ribbon will Marsha need? l w 2 l + 2w 4s Pick a problem situation that can be solved using two different formulas. Explain why both formulas apply. 165 2015 Region 4 Education Service Center

Mani s Art Project Mani is painting a rectangular canvas with a length of 50 cm. He will need 160 cm of wood trim to frame the canvas. Mani s Canvas 50 cm What is the width of the canvas? What is the area of the canvas? What are the known parts of the problem? What are the unknown parts of the problem? What is your plan for solving the problem? Carry out your plan to solve the problem. The width of the canvas is. The area of the canvas is. How do you know your answer is reasonable? 167 2015 Region 4 Education Service Center

Patty Paper Trace Fold a sheet of patty paper into four equal sections as shown to the right. Number the sections 1 4. Place the patty paper over the figure below to trace one of the following in each section of your patty paper. 1 A point 2 A line 3 A line segment 4 A ray 1 2 3 4 I M L S E How is the ray you drew different from the line segment you drew? 169 2015 Region 4 Education Service Center

Parallel or Perpendicular? Cut out the Parallel or Perpendicular Cards. Determine if the card represents parallel lines or perpendicular lines. Attach the cards in the appropriate column. Parallel Lines Perpendicular Lines Draw a picture that includes both parallel and perpendicular lines. Use colored pencils to highlight the parallel lines with one color and the perpendicular lines with a different color. 171 2015 Region 4 Education Service Center

Parallel or Perpendicular Cards Cut along the bold dotted line. Two sets of cards are provided. Two or more lines that never intersect because the lines are always the same distance apart. The lines have no points in common. m p s t The boards on top of an electric pole. Lines that intersect to form a right angle. The lines have one point in common. The yard lines on a football field. 10 20 30 40 50 40 30 20 10 Two or more lines that never intersect because the lines are always the same distance apart. The lines have no points in common. m p s t The boards on top of an electric pole. Lines that intersect to form a right angle. The lines have one point in common. The yard lines on a football field. 10 20 30 40 50 40 30 20 10 2015 Region 4 Education Service Center 172

Lines of Symmetry 1 Draw the line or lines of symmetry for each figure if one exists. 2 Which figure in each set is the odd one out? Circle the figure that has a different number of lines of symmetry than the other 2 figures. 3 Examine the figures that are not circled. How many lines of symmetry do they have? 4 Draw another shape that has the same number of lines of symmetry as the two figures that are not circled. Using your own words, describe the attributes of a line of symmetry. 175 2015 Region 4 Education Service Center

Angle Me Triangle The corner of an index card models a right angle. Use the corner of an index card to determine if each angle of the triangle is acute, obtuse, or right. Classify each angle and record it on the line next to the angle. B E A G Triangle ABC H C Triangle DEF F Triangle GHI D I How did you classify the angles in each of the triangles? 177 2015 Region 4 Education Service Center

Classifying Figures: Odd One Out Circle the figure in each set that is different from the other two figures. Justify your choice. Set 1 A B C I choose figure. This figure is a. It does not match because. Set 2 A B C I choose figure. This figure is a. It does not match because. Set 3 50 A 65 65 60 60 B 60 32 C 130 18 I choose figure. This figure is a. It does not match because. Look at set 2. What different attribute could be used to re-classify the figures? Explain how your answer could now be different from your first answer. 179 2015 Region 4 Education Service Center

Tri-Angles Use the examples and non-example provided to define each type of triangle. 1 Examples Non-examples Yes or No? These are acute triangles. 35 72 73 65 58 57 This is not an acute triangle. 45 45 Is this an acute triangle? 72 73 35 YES NO These are obtuse triangles. This is not an obtuse triangle. Is this an obtuse triangle? YES 50 66 50 NO 2 102 42 57 57 95 28 100 38 35 3 These are right triangles. 90 33 57 45 This is not a right triangle. 35 Is this a right triangle? YES 47 NO 105 72 73 28 45 181 2015 Region 4 Education Service Center

4 Use the examples and non-examples to complete the following sentences. An acute triangle has. A right triangle has. An obtuse triangle has. 5 Compare your definitions with a partner s definitions. Discuss any differences, and make any additions or corrections to your definitions. How does your knowledge about 90 angles help you determine whether a triangle is an acute, obtuse, or right triangle? 2015 Region 4 Education Service Center 182

Polygon!: Justified True/False Read each statement. Determine if the statement is either always true, sometimes true, or never true. Justify your answer. Statement Always Sometimes Never Justification A rectangle has parallel sides. Always Sometimes Never A pentagon has perpendicular sides. Always Sometimes Never A triangle has parallel sides. Always Sometimes Never A rhombus has perpendicular sides. Always Sometimes Never Create another Always, Sometimes, Never statement with a different polygon using parallel sides and/or perpendicular sides. Give your statement to a partner to answer and justify. 185 2015 Region 4 Education Service Center

Circle Folding Work with your group members to complete steps 1 5. Step 1: Cut your circle from Circle Template along its curved edge. Step 2: Fold the circle in half, fold it in half again, and then fold in half again. Do not unfold the first folds. Once the three folds have been completed, unfold the circle and mark the center. Step 3: Cut the circle into pieces using the fold lines as cutting lines. Use a colored pencil to shade three of the pieces. Distribute one piece of your circle to each member of the group. Step 4: Attach the largest piece to the circle below so that the vertex of the piece aligns to the center of the circle. Step 5: Layer and attach the medium size piece and then the smallest piece on top of the largest piece. How are the angles formed by the 3 pieces similar? How are they different? Draw another angle that would fit in this set. Draw an angle that would NOT fit in this set. 187 2015 Region 4 Education Service Center

Circle Template Cut along the dotted lines and give one circle to each member of your group. Follow the directions on Circle Folding to complete the activity. 2015 Region 4 Education Service Center 188

Sections of a Circle Any circle can be divided into 360 equally-sized sections. The tick marks around the circles below illustrate these sections. Each circle models a 360 protractor. An angle whose vertex is the center of the circle represents a fraction of the circle bounded by its rays. 1 of a circle is 1. 360 Degrees are used to measure angles. 1 What fraction represents the shaded portion of the protractor? 360 A Identify the measurement for angle A. 2 What fraction represents the shaded portion of the protractor? 360 B Identify the measurement for angle B. 191 2015 Region 4 Education Service Center

3 Shade 45 360 of this circle to create angle C. Identify the measurement for angle C. 4 Shade 155 360 of this circle to create angle D. Identify the measurement for angle D. Sketch a diagram to represent a different way to shade 90 360 90 angle. of a circle or a 2015 Region 4 Education Service Center 192

Who am I? My shape is a. I am divided into equal parts. Each part is called a. I am used to measure. I am a! 195 2015 Region 4 Education Service Center

I am divided into equal parts. Each part is called a. I am used to measure. I am a! How are the two tools similar? How are they different? 2015 Region 4 Education Service Center 196

Measuring Angles: Round Robin Pass your paper to the person seated at your right. Determine the process you will use, and measure angle A on the paper you have received. You may work with your group to solve the problem. Upon completing the first problem, pass the papers to the right again. Determine the process you will use, and measure Angle B problem. Continue this process for the remaining angles. Angle A Angle B A B ma = mb = Angle C Angle D mc = C D md = 199 2015 Region 4 Education Service Center

Describe the process you used to measure each angle using a protractor. 2015 Region 4 Education Service Center 200

Pass it Please! Shuffle the Pass it Please! Cards. Distribute one card to each member of the group. Place any additional cards in a pile. Each member of the group is to use a protractor to determine the measure of the angle on his/her card. Record the measure and initial the card in the solution box. Trade cards with any member of the group. Each member of the group is to verify that the angle on his/her new card was measured correctly. o If the angle was measured correctly, place a check mark in the verified box and initial the card. o If the angle was not measured correctly, consult with the member of the group that initially measured the angle and come to an agreement on its measure. Make any necessary changes to the solution box and place a check mark in the verified box and initial the card. Trade cards again and repeat the process. Attach one of the cards below. How could you check your measurement for reasonableness without measuring a second time? 203 2015 Region 4 Education Service Center

Pass it Please! Cards Cut along the dotted lines. Card 1 A Card 2 ma = Verified Initials: Initials: Verified Initials: D Verified md = Initials: Initials: Verified Initials: 2015 Region 4 Education Service Center 204

Card 3 E me = Initials: Card 4 Verified Initials: C Verified Initials: Verified mc = Initials: Initials: Verified Initials: 205 2015 Region 4 Education Service Center

Measuring Angles! Determine the measure of each angle to the nearest degree. Problem 1 Measure of BEC B C A E D Problem 2 C E Measure of CKG G A I K 207 2015 Region 4 Education Service Center

Problem 3 Measure of T T Problem 4 Measure of P P Describe the process you used to determine the measure of angle P. 2015 Region 4 Education Service Center 208

Ray AB has been drawn below. Draw ray AC so that BAC measures 37. Sketching Angles A B Ray MN has been drawn below. Draw ray MO so that NMO measures 153. N M How did you determine where to draw the second ray? 211 2015 Region 4 Education Service Center

Angles That Are Greater Than and Less Than A Determine the measure of A. m A = Draw an Angle That Is Greater Than Angle A Draw an Angle That Is Less Than Angle A My angle measures. My angle measures. Classify each angle. Justify your classification. 213 2015 Region 4 Education Service Center

Angles Distribute one Angle Card to each member of the group. Use the card to answer the questions. Angle AMT 1 Use a highlighter to highlight the two rays that form AMT and the interior space between them. 2 What is the measure of AMT? Angle TMH 3 Use a different highlighter to highlight the two rays that form TMH and the interior space between them. 4 What is the measure of TMH? Angle AMH 5 Use your measurements foramt and TMH above to predict the measure of AMH. I predict that mamh. 6 Measure AMH. Is your prediction correct? Justify. Compare your card to your group members cards. Draw a picture of another pair of angles that would fit in the set. Justify your drawing. 215 2015 Region 4 Education Service Center

Angle Cards Cut along the dotted lines. Card A A T M H Card B A T M H 2015 Region 4 Education Service Center 216

Card C T A M H Card D T A M H 217 2015 Region 4 Education Service Center

Adjacent Angles: Who Is Correct? Nancy and Paula were asked to solve the following problem: Angle BAD has a measure of 72. Determine the measure of angle BAC. B A 26 C D Nancy and Paula each solved the problem and came up with different answers. Their work is shown below. Nancy s Work x = measure of angle BAC 72 + 26 = x 72 + 26 = 98 So, BAC measures 98. Is Nancy correct? Justify your answer. Paula s Work m ABC = x 26 + x = 72 26 + 46 = 72 So, BAC measures 46. Is Paula correct? Justify your answer. Describe the process you used to determine who was correct. 219 2015 Region 4 Education Service Center

Which Is The More Reasonable Unit? Circle the unit that is more reasonable for each situation. Use the letters below each circled unit to complete the word puzzle. 1 2 Situation Jorge wants to know how far he will run in the next marathon. Sebastian is planning to measure the water in his aquarium. Best Unit Yard or Mile C S Gallon or Quart I E 3 Tamaryn wants to know how heavy her dog is. Ounce or Pound O I 4 5 6 7 8 A carpenter needs to know the height of a door frame. A baker is measuring the amount of sugar to bake a cake. A zoo veterinarian records the total of three elephant s weights. Emmanuel needs to repaint the outside of his house. Mrs. Oliver is measuring the length of her classroom. Inch or Foot H G Cup or Fluid Ounce E K Ton or Ounce L P Pint or Gallon S M Yard or Inch B G 1 7 3 6 5 8 2 4! How did you determine the more reasonable unit for Situation 2? 221 2015 Region 4 Education Service Center

Fill In The Blanks Use your reference materials and the Word Bank below to complete the following statements. Some words will remain unused. Word Bank Centimeter Grams Less Meters Millimeter Equal Kilogram Liter Milligram Millimeters Gram Kilometer Meter Milliliters Greater 1 A is smaller than centimeter. 2 There are 100 centimeters in a. 3 A gram is than a kilogram. 4 There are 1,000 in a kilometer. 5 A liter is than a milliliter. 6 One thousand milligrams is equal to a. 7 A is larger than a meter. 8 One liter is to 1,000 milliliters. 9 A centimeter is equal to 10. 10 One kilogram is equal to 1,000. The prefixes kilo-, centi-, and milli- are used in the metric system. How did they help you determine which unit of measure is larger or smaller in each statement? 223 2015 Region 4 Education Service Center

It s A Boy! Duncan the elephant was born on February 7 at the Houston Zoo. He weighed 385 pounds. Elephants drink approximately 50 gallons of water and eat about 700 pounds of food per day. 1 Complete the table below to determine comparisons of gallons to quarts. Gallons to Quarts Gallons Process Quarts 1 1 4 5 10 25 50 2 What do you notice about the relationship between gallons and quarts and the process column? 3 Complete the table below to determine comparisons of pounds to tons. Pounds to Tons Pounds Process Tons 2,000 2000 1 4,000 6,000 8,000 Draw a picture that illustrates the relationship between gallons and quarts and a picture that illustrates the relationship between pounds and tons. 225 2015 Region 4 Education Service Center

Measurement Conversions: Who Is Correct? Rachael and George were asked to use a table to solve the following problem: Jackson saw a centipede that was 90 millimeters long on the internet. How many centimeters is equal to 90 millimeters? Rachael and George each solved the problem using a table but came up with different answers. Their work is shown below. Rachael s Work mm cm 10 1 20 2 30 3 60 6 90 9 The centipede is 9 centimeters long. Is Rachael correct? Justify your answer. George s Work cm My Process mm 1 1 10 10 90 90 10 900 The centipede is 900 centimeters long. Is George correct? Justify your answer. Draw a picture to illustrate the relationship between centimeters and millimeters. 227 2015 Region 4 Education Service Center

Conversion Puzzle Use the clues below and Puzzle Clues to complete the puzzle. 1 2 3 4 5 6 8 Across Down 2 centimeters = 260 millimeters 1 3 feet = inches 3 65 meters = centimeters 2 2 kilometers = meters 5 1 centimeter = millimeters 4 cups = 26 pints 6 4 kilograms = grams 5 ounces = 64 pounds 8 2 years = months 6 quarts = 11 gallons Describe the process you used to convert measures with smaller units into an equivalent measure with larger units. 229 2015 Region 4 Education Service Center

Across 2 cm mm 10 100 15 150 20 200 25 250 Puzzle Clues Down 1 ft in. 1 12 2 24 4 48 5 60 3 m cm 10 1,000 20 2,000 35 3,500 75 7,500 2 km m 1 1,000 3 3,000 5 5,000 7 7,000 5 cm mm 2 20 3 30 4 40 7 70 4 c pt 10 5 24 12 50 25 60 30 6 kg g 1 1,000 2 2,000 3 3,000 5 5,000 5 oz lb 16 1 160 10 480 30 960 60 8 Years Months 3 36 4 48 6 72 10 120 6 qt gal 12 3 20 5 28 7 36 9 2015 Region 4 Education Service Center 230

Pass the Paper, Please! After completing each step, initial the paper and pass the paper to the person on your right. Figure 1 Figure 2 Use a ruler to measure the side lengths of the figures above to the nearest tenth of a centimeter. Record the side lengths on the figures. What is the perimeter of each figure in centimeters? Initials: Figure 1: Figure 2: Initials: Complete the sentence below. The perimeter of figure is greater than the perimeter of figure. Initials: What is the difference between the perimeters of these figures in centimeters? Initials: Describe a real-world situation where you might need to compare the perimeters of two different figures. 233 2015 Region 4 Education Service Center

Oh, No! I Am Late! Zake is always late to the family dinner! He wants to use the open number line below to determine what time he needs to leave his home. He wants to be at the restaurant 10 minutes early. The family dinner starts at 6:45. It takes him 3 hours and 30 minutes to drive from his home to the restaurant. Determine the times and the times intervals that may best represent Zake s thinking. Time Intervals 6:45 Time 1 At what time should Zake leave home to be at the restaurant 10 minutes before dinner starts? 2 At what time will Zake arrive at the restaurant? How is using an open number line to model time intervals similar to using an open number line to model addition and subtraction? 235 2015 Region 4 Education Service Center

Cups and Ounces: Round Robin Pass your paper to the person seated at your right. Determine the process you will use, and solve the first problem on the paper you have received. You may work with your group to solve the problem. Upon completing the first problem, pass the papers to the right again. Determine the process you will use, and solve the second problem. Continue this process for the remaining problems. Problem 1 The pastry chef at Ariel s Sweets is making fudge brownies. The recipe calls for 36 ounces of sweetened condensed milk. The chef begins by using 4 cups of sweetened condensed milk. What amount of condensed milk is still needed to complete the recipe? Problem 2 Cathy mixes bottles of powdered baby formula with water each day. She uses 6 cups of water to fill four 4-ounce bottles, three 5-ounce bottles and two 8-ounce bottles. How many fluid ounces of water will remain from the original 6 cups of water? Answer: Problem 3 Jaxon drinks one 32-ounce soft drink and two 16-ounce glasses of water each day. How many cups of liquid does Jaxon drink each day? Answer: Problem 4 David is making punch. He needs 3 fluid ounces of fresh grapefruit juice and 9 fluid ounces of apple juice for each serving. David needs to serve 12 people. How many cups of punch will he need? Answer: Answer: Draw a diagram that can be used to solve Problem 4. Explain your drawing. 237 2015 Region 4 Education Service Center

The Missing Dots Dilemma The table shows the number of blocks stacked by students. Stacking Blocks Number of Blocks Stacked 20 21 22 23 24 Frequency Complete the dot plot using the data in the table. Number of Blocks Stacked per Student 20 22 24 Key = 2 students Describe the relationship between the data in the frequency table and its graph. 239 2015 Region 4 Education Service Center

Organizing the Leaves Moe measured the height in centimeters of bean plants for his science project. Sort the Plant Height Cards. Use the data from the cards to complete the stem-and-leaf plot. Plant Height (centimeters) Stem Leaves 1 2 3 4 5 6 7 1 2 means 12 centimeters 1 How many plants were measured? 2 How many plants are less than 19 centimeters tall? How do you know? 3 How many plants are over 50 centimeters tall? How do you know? How did you organize the leaves of the stem-and-leaf plot? 241 2015 Region 4 Education Service Center

Plant Height Cards Cut along the bold dotted line. Two sets of cards are provided. 62 74 19 40 77 12 32 39 12 30 61 63 68 43 12 62 74 19 40 77 12 32 39 12 30 61 63 68 43 12 2015 Region 4 Education Service Center 242

Distance Traveled Ms. Reese recorded the distance each of her students travels in one round trip between school and home each day. The data are shown in the stem-and-leaf plot. Round Trip Distance Traveled Between School and Home (miles) Stem Leaves 0 1, 1, 1, 2, 2, 2, 2, 2, 4, 4, 5, 6, 7, 7, 7, 8 1 1, 3, 5, 5, 6, 6, 7, 9 2 0, 1, 2 1 3 means 13 miles 1 Use the stem-and-leaf plot to write the distance traveled by each student in Ms. Reese s class. Round Trip Distance Traveled Between School and Home (miles) 2 How many students travel less than 15 miles each day? Write two questions that can be answered by the data. 245 2015 Region 4 Education Service Center

Class Shoe Size Each of Mr. Garcia s students recorded the length of his or her foot. The dot plot shows the foot lengths of his students. Student Foot Length (Inches) 1 1 1 1 1 6 7 8 9 10 2 2 2 2 2 Key: =2 students Statement True or False Justify your answer. 1 Only one student s foot measures 1 6 2 inches. True False 2 3 Eight students have a foot that is 9 inches or longer. The number of students with feet 1 that measure 7 inches is twice as 2 many as the number of students with feet that measure 7 inches. True False True False Select a statement that was false. Explain to a partner how to rewrite the statement so that it is true. Record the corrected statement. Statement 247 2015 Region 4 Education Service Center

Stem-and-Leaf Plot The stem-and-leaf plot shows the number of seconds it takes to download an app. Download Time 1 2 1, 1, 5, 6, 9 3 0 4 1, 4, 8 5 6 2, 3, 7, 9 2 1 means 2.1 seconds 1 2 3 4 5 Statement Solution Justification How much longer is the longest download time than the shortest download time? How many apps took between 4.0 seconds and 5.0 seconds to download? How many apps took longer than 4.5 seconds to download? What is the total of the longest three download times? Are there more apps with download times between 3.0 seconds and 5.0 seconds or between 6.0 seconds and 7.0 seconds? Does a leaf of zero have the same meaning as a stem with no leaves? Why or why not? 249 2015 Region 4 Education Service Center

Fixed and Variable Expenses Place the words from the Word Bank in the appropriate expense category. Complete any remaining spaces with your own examples. Justify each of your answers to a partner. Fixed Expenses Variable Expenses Word Bank auto loan payment mortgage water bill groceries magazine subscription electric bill How is a variable expense different from a fixed expense? 251 2015 Region 4 Education Service Center

Profit Comparisons Profit: The difference between the amount of money earned and the expenses required to earn the money. Match each company with the description that best describes its profit. Calculate each company s profit. Carol s Homemade Burgers Carol made a total of $283.30 selling burgers today. The supplies to make the burgers cost Carol $89.20. What was Carol s profit? Miguel s Photography Miguel spent $38.90 on supplies and $15.28 on props for three photo shoots. He received a total of $446.34 in payments for the shoots. What was Miguel s profit? Kali s Lawn Service Kali mowed 15 lawns for $25 each. She spent $16.08 on fuel for her lawn mower. What was Kali s profit? Barker s Baseball Supplies Mr. Barker s supplier charged him $353.35 for an order of baseball bats. He paid $32.75 for shipping. He sold the bats for $661.50. What was Mr. Barker s profit? Description Company Name Profit This company has the greatest profit. This company has the least profit. This company s profit is between $350 and $390. This company s profit is close to $275. Describe the difference between the amount of money collected by a business and its profit. 253 2015 Region 4 Education Service Center

Savings Options Using your Savings Options Chart, name one advantage and one disadvantage for each savings option for each of Connor s goal statements. 1. Connor wants to buy a bicycle in one year. Advantages Disadvantages Savings Account Certificate of Deposit (CD) Money Market Account Individual Retirement Account 2. Connor is a fourth grader and wants to start saving for college. Advantages Disadvantages Savings Account Certificate of Deposit (CD) Money Market Account Individual Retirement Account Choose one of the statements from above. What advice would you give Connor about which savings option to use for his goal? 255 2015 Region 4 Education Service Center

Savings Options Chart Savings Account Deposit and withdrawal at anytime No time restrictions on how long money may stay in account No minimum amount of money to keep in account Most banks do not charge withdrawal penalties Very low interest rate Certificate of Deposit (CD) Money must stay in account for an agreed amount of time; usually 1 month to 5 years Early withdrawal penalties Locked interest rate higher than savings account Lower interest rate than a money market account Money Market Account Individual Retirement Account (IRA) Minimum amount to open No time restrictions on how long money can stay in account Minimum amount must remain in account No penalty for early withdrawal up to four times a month. Higher interest rates than savings accounts if minimum amount is over $2,500. Minimum amount to open Penalties for early withdrawals before retirement age Tax advantages Higher interest rates than money market account or certificate of deposit 1 Required to withdraw at age 70 2 2015 Region 4 Education Service Center 256

Spending My Allowance The students in Ms. Umbach s class used a strip diagram to represent how they would each allocate a weekly allowance of $10. Kevin Spending $2.50 Savings for Car $2.50 Savings for College $2.50 Sharing $2.50 Fran Spending $5.00 Savings $2.50 Sharing $2.50 Jack Spending $7 Savings $2 Sharing $1 Tasha Spending $5 Savings for Vacation $2 Savings for College $2 Sharing $1 Use the strip diagram to represent how you would allocate a weekly allowance of $10. Me Which student could more wisely allocate his or her weekly allowance? Explain your thinking. 259 2015 Region 4 Education Service Center