# NCTM Content Standard/National Science Education Standard

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Title: BASE-ic Space Travel Brief Overview: This unit introduces the concepts of bases and exponents (or powers) in order to gain a deeper understanding of place value. Students will assume the role of intergalactic space travelers. Traveling in crews of four, they will journey to galaxies that use number systems other than base 10, including base 5 and base 2. To facilitate this travel, they must purchase fuel by learning about these bases, compare them to one another, and convert numbers between bases. NCTM Content Standard/National Science Education Standard Understand numbers, ways of representing numbers, relationships among numbers, and number systems: Understand the place value structure of the base-ten number system and be able to represent and compare whole numbers and decimals Recognize equivalent representations for the same number and generate them by decomposing and composing numbers Compute fluently and make reasonable estimates: Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools Grade/Level: Grade 5 (Accelerated Program) Duration/Length: 3 days (60 minutes per day) Student Outcomes: Students will: Distinguish between base and exponent (or power) Understand that in the base 10 system, each place value increases by the power of 10 Represent numbers using base subscript and exponent superscript Convert base 10 numbers to base 5 and numbers in base 5 to base 10 Explore conversions between bases other than base 5 and base 10

2 Materials and Resources: Day 1 Spacecraft Design (Student Resource 1) Base 10 materials (cubes, flats, units) for each group to have at least one of each Board/Overhead Example (Teacher Resource 1) Place Value Pocket Chart Directions (Teacher Resource 2A-B) You might want to make a pocket chart to use as a visual reference for students. Colored construction paper Glue sticks Scissors Markers 3 x 5 Index cards 10 per student (You may want to make a set of digit cards and trim to 2 x 5.) I Have/Who Has with Exponents (Teacher Resource 3) Cut apart each card to make 1 set per group of 12 students. Boarding Pass Day 1 exit ticket (Student Resource 2) Boarding Pass Day 1 Key (Teacher Resource 4) Day 2 Quintopian Creature (Teacher Resource 5) 40 colored chips per group (10 each of 4 different colors: white, red, blue, yellow) Additional Place Value Pocket Charts (Teacher Resource 7) Board/Overhead Example (Teacher Resource 6A-C) Other base 5 information can be found at: o htm o o Galaxy Quintopia (Student Resource 3A-B) Galaxy Quintopia Key (Teacher Resource 8A-B) Boarding Pass Day 2 exit ticket (Student Resource 4) Boarding Pass Day 2 Key (Teacher Resource 9) Day 3 Biaculean Creature (Teacher Resource 10) Venn Diagram (Student Resource 5) Venn Diagram Key (Teacher Resource 11) Additional Place Value Pocket Charts (Teacher Resource 6 from Day 2) Make an eight-column chart by taping two charts together and labeling with base 2 notation. Board/Overhead Example (Teacher Resource 12A-D) Galaxy Biaculus (Student Resource 6A-C) Galaxy Biaculus Key (Teacher Resource 13)

3 Quintopian Practice (Student Resource 7) Quitopian Practice Key (Teacher Resource 14) Ticket Home Summative Assessment (Student Resource 8A-B) Ticket Home Key (Teacher Resource 15A-B) Development/Procedures: Day 1 o Pre-assessment On an overhead or chalkboard, write a 3-digit number (i.e. 743) and have students identify the place value and the digit value. Ex: What place is the 4 in? The 7 has what value? Have students verbally give their answers and explain how they know. Repeat with other three- or four-digit numbers as necessary. o Engagement Ask: What do you think about the possibility of life on other planets? Have students share responses. Say: Today we are going to start on a journey to visit other beings, on other planets, in other galaxies! Let s pretend that you and your group members are a space crew. You will travel together in an imaginary space craft. Starting today, we will begin our three-day voyage to other galaxies to observe the life forms and number systems there. Divide students into groups of four. Say: With your group, decide on a creative name for your spacecraft. Have one group member write that name on your spaceship illustration sheet (Student Resource 1) and the names of all group members as well. Decorate as you see fit! o Exploration Ask students on what number our own number system is based? (10) Distribute base 10 materials to each group. Tell students that you want them to use the base 10 materials to identify how each place is similar and different (ones, tens, hundreds, thousands). Possible observations may include that as you move to the left, a 0 is added to each place or that each place is multiplied by 10. Lead students to also recognize that in the base 10 materials, the dimensions increase by 1 (units have no side length of 10, rods have 1 side length of 10, flats are square with 2 side lengths of 10, and cubes have 3 side lengths of 10.

4 o Explanation Explain that our number system is based on 10 and is called the base 10 system. Use an overhead or chalkboard to explain that each place can be expressed as a power of ten. See Board/Overhead Example for teaching directions (Teacher Resource 1). Have students follow along with you as you give the directions on the board. This could be having students record notes in their math journals and write down two important facts learned on a sticky note, etc. o Application Tell students that they are about to make a place value pocket chart for base 10. Distribute to each student a sheet of construction paper, a glue stick, scissors, and a marker. Guide them through making their chart using yours as an example (see Teacher Resource 2A-B). Have them label each pocket with the correct place in base 10 notation. Discuss each place to reinforce new vocabulary: base, exponent, power. Ask: What is the value of any number raised to the zero power? (1) Distribute index cards to each student. Have them trim the cards to about 2 x 5. Use your example as a reference. Have them write one digit on each card for digits, 0-9. Give examples of 3-digit and 4-digit numbers and have students place the corresponding digits in their pocket charts, with students justifying their answers. Ask groups to identify the exponential expression corresponding to each digit s place (i.e. in 2,453, the 2 is in the 10 to the third power place.) Continue in this way, asking questions about identifying the value of digits, bases and exponents or powers. Tell students that they are about to play a game using their new knowledge of bases and powers. Divide the students into groups of 12. Distribute one set of I Have/Who Has cards made from Teacher Resource 3 to each group. (If there are more cards than students, give some students a second card.) To begin play, each group selects one student to begin by reading their card. Students should listen for their number and respond by reading their card. Play ends when each person has read their card. Guide students as they play, giving hints where needed. Students having trouble remembering their facts may benefit from the reteaching activity below.

5 o Differentiation Reteach Have students create cards with an exponential expression (i.e. 4 2 ) on one side and the numerical value (i.e. 16) on the other side. They can use these to play a matching game of Concentration. Enrich Give students an additional sheet of construction paper. They should make another chart for the next four places in base 10. They should identify the places independently (i.e. 10 4, 10 5, 10 6, 10 7 ) and tape these to their first chart. o Assessment Distribute Boarding Pass #1 exit ticket (Student Resource 2) to board the spacecraft and travel to Galaxy Quintopia. Say: It s time to travel! Let s blast off! Tomorrow we will land at our first destination, Galaxy Quintopia. Read over these exit tickets to determine levels of attainment and adjust next day s instruction. Answer key can be found on Teacher Resource 4. Day 2 o Engagement The class is about to enter their first galaxy: Quintopia. Say: Space crews, prepare for entry ! We re here. We are now in the galaxy of Quintopia. Ask students what they think is different about this galaxy. Show them the picture of the Quintopian (Teacher Resource 4). Ask: What do you know about the prefix, quint? Lead them to the idea of quint meaning 5. Ask: How do you think the number 5 will impact our journey? Tell them that the Quintopians are different creatures that have 5 antennae. Ask: What number system do you think they use? (5) How do you think the base five system is different than base 10? o Exploration Tell students that the Quintopians count everything in groups of five and use the base 5 system. That means that they don t use the numerals 5, 6, 7, 8, or 9! Display the base 10 pocket chart from yesterday. Say: Yesterday, we used base 10 materials. What do you think base 5 materials would look like? (Wait for responses.) Today we will create our own base 5 materials using chips.

6 Distribute about 40 chips (10 each of white, red, blue, yellow) to each group. Tell them that each color should represent a different numerical value for the base 5 system. They should explore using the chips. You can provide them with a hint. Say: You may want to think about the base 10 pocket charts you made yesterday. Why do you want 4 different colors? Lead them to understand that the 4 colors should represent the first 4 places of the new system. Tell them that the first place is always units or ones and choose white. The next place is fives, or 5 to the first power and choose red. Ask what the next place should be. Guide them to 5 to the second power or twentyfives and choose blue. Ask what the last place should be. Students should recognize the pattern and respond with one hundred twenty-fives for 5 to the third power and choose yellow. Now, tell students that you will be using the chips to create a base 5 number. Direct students to make piles of 4 blue chips, 2 red chips, and 4 white chips. Explain that in the base 5 system this number is: 424 in base 5. Ask students if they can tell what that number is in the base 10 system. (Answer: 114 in base x 25 = 100, 2 x 5 = 10, 4 x 1 = 4; =114.) A model of this process can be found at htm o Explanation Use an overhead or chalkboard to explain that each place in the base five system can be expressed as a power of five. See Board/Overhead Example for teaching directions (Teacher Resource 6A-B). Have students follow along with you as you give directions on the board. This could be having students record notes math journals, write down 2 important facts learned on a sticky note, etc. o Application Tell students that they will have to convert Earth s base 10 numbers to base 5 to survive on Quintopia. They will make a place value pocket chart for base 5 to help them. Distribute materials to make another place value chart for base 5. This time it should be labeled as directed on Additional Place Value Pocket Charts (Teacher Resource 7). You might want to make another chart with the base 5 labeling and display.

7 Guide them through making their chart using yours as an example. Discuss each place to reinforce new vocabulary: base, exponent, power. Ask: What is the value of any number raised to the zero power? (1) Using their digit cards from the day before, write a 3-digit base 10 number and have students convert it to base 5. Do one example with the whole group and then write another number to be converted independently. Now explain how to convert base 5 numbers to base 10. Convert 234 in base 5 to base 10. Have students place their 2, 3 and 4 digit cards in their base 5 pocket charts. Ask: What is the value of the 2? (2 x 25 = 50) Record the number 50 on the board. Ask: What is the value of the 3? (3 x 5 = 15) Record the number 15 under the 50 on the board. Ask: What is the value of the 4? (4 x 1 = 4) Record the number 4 under the 15 and add all three addends. The sum should be 69; the answer is 69 in base 10. Repeat conversions as necessary. Distribute Galaxy Quintopia (Student Resource 3A-B). Circulate as students work in groups to make the conversions. Students having trouble may benefit from the reteaching activity below. Answer key can be found on Teacher Resource 8A-B. o Differentiation Reteach Have students do the base five counting activity on website: Have students practice in pairs converting 2-digit base 10 numbers to base 5 using pocket charts. Enrich Have students answer the following: Why will you never reach the number 6 in base 5? What are the first 20 counting numbers in base 5? Have students create their own 4-digit base 10 numbers and convert them to base 5. o Assessment Distribute Boarding Pass #2 exit ticket (Student Resource 4) to board the spacecraft and travel to Galaxy Biaculus. Say: It s time to travel! Let s blast off! Tomorrow we will land at our second destination, Galaxy Biaculus. Read over these exit tickets to determine levels of attainment and adjust next day s instruction. Answer key can be found on Teacher Resource 9.

8 Day 3 o Engagement The class is about to enter their second galaxy: Biaculus. Say: Space crews, prepare for entry ! We re here. We are now in the galaxy of Biaculus. Ask students what they think is different about this galaxy. Show them the picture of the Biaculean (Teacher Resource 10). Lead them to the meaning of the prefix, bi being 2. Ask: How do you think the number 2 will impact our journey? Tell them that the Biaculeans are different creatures that have 2 antennae. Ask: What number system do you think they use? (base 2 or binary) How do you think the base 2 system is different than base 10? How is it different than base 5? Tell students that the Biaculeans count everything in groups of two and use the base 2 system. That means that they only use numerals 0 and 1! o Exploration Say: Yesterday, we used base 10 and base 5. Today we will compare base 5 to base 10. Distribute Venn Diagram (Student Resource 5). Display both pocket charts and have students complete the diagram comparing the base 5 and base 10 systems. Students share their thoughts. Record on board (see Teacher Resource 11 for the answer key) and discuss. o Explanation Use an overhead or chalkboard to explain that each place in the base two system can be expressed as a power of two. See Board/Overhead Example for teaching directions (Teacher Resource 12A-D). Repeat with additional examples as necessary. Have students follow along with you as you give directions on the board. This could be having students record notes in math journals or write down two important facts learned on a sticky note, etc. Ask students why so many places are needed when converting to base 2. Lead them to understand that the lower the base the higher the number of digits in the number, since there are a limited number of digits available for use. Ask which conversion seems easier and have students share their answers.

9 o Application Tell students that they will have to convert Quintopia s base 5 numbers and Biaculus base 2 numbers back to base 10 for survival and safe travel home. They will make a place value pocket chart for base 2 to help them. Distribute materials to make another place value chart for base 2. They will make two and tape them together for an 8-column chart. This time it should be labeled as directed on Additional Place Value Pocket Charts (Teacher Resource 7). Guide them through making their chart using yours as an example. Discuss each place to reinforce new vocabulary: base, exponent, power. Ask: What is the value of any number raised to the zero power? (1) Using their digit cards from the day before, write a 3-digit base 5 number and have students convert it to base 10, then to base 2. Do one example with the whole group and then write another number to be converted independently. Now explain how to convert base 2 numbers to base 10. Convert 1110 in base 2 to base 10. Have students place their digit cards in their base 2 pocket charts. They may have to write additional ones and zeros on the backs of other digit cards. Ask: What is the value of the first 1? (1 x 8 = 8) Record the number 8 on the board. Ask: What is the value of the second 1? (1 x 4 = 4) Record the number 4 under the 8 on the board. Ask: What is the value of the third 1? (1 x 2 = 2) Record the number 2 under the 4. Ask: What is the value of the 0? (1 x 0 = 0) Add all three addends. The sum should be 14; the answer is 14 in base 2. Repeat conversions with larger numbers. Distribute Galaxy Biaculus (Student Resource 6A-B). Circulate as students work in groups to make the conversions. Students having trouble may benefit from the reteaching activity below. Answer key can be found on Teacher Resource 13A-B. o Differentiation Reteach Students can review conversions step by step in Quintopian Practice (Student Resource 7). Enrich Have students convert base 10 to other bases, including base 3, 4, or 6.

10 Summative Assessment: Authors: Distribute A Ticket Home Summative Assessment (Student Resource 8A-B) to board the spacecraft and travel back home to the Milky Way. Say: It s time to travel! You need to purchase fuel to get to your home base! In order to do that, you must make conversions from base 10 to base 5 to base 2 and back to base 10. Good luck on your mission. Graded assessments (see Teacher Resource 15A-B) will determine the level of performance. Marian Dingle Guilford Elementary School Howard County Public Schools Cheryl D. Madden Eastwood Center Baltimore County Public Schools

11 Student Resource 1 Name of Spacecraft Crewmembers

12 Student Resource 2 Boarding Pass #1 Day 1 Complete this boarding pass in order to board your spacecraft and travel to our first destination: Use the number 6,475 to answer the following questions: 1. What is the value of the digit 4? 2. In what place is the 4? 3. Write that place in exponential form. 4. What is the value of the digit 7? 5. In what place is the 7? 6. Write that place in exponential form. 7. In what place is the digit 6? 8. Write that place in exponential form. Use the expression 6 3 to answer the following questions: 9. Which digit is the base? 10. Which digit is the exponent? It s time to travel! Let s blast off! Tomorrow we will land at our first destination, Galaxy Quintopia!

13 Student Resource 3A Galaxy Quintopia Today our spacecraft arrived in the Galaxy of Quintopia. The inhabitants of Quintopia use the Base 5 place value system. You and your spacecrew need to translate Quintopian numbers into Planet Earth s Base 10 system! Look at the following example: 5 3 = = = = x 25 = 75 4 x 5 = 20 3 x 1 = 3 So, = = Now you try! Use the Base 5 Place Value Chart shown above to help you = x 25 + x 5 + x = = x x 25 + x 5 + x = = x 25 + x 5 + x = = = = 10

14 Now try converting from Base 10 into Base 5! Look at this example: = 5 Student Resource 3B Page Two Think There is one group of 125 in = 47. There is one group of 25 in = 22. There are four groups of 5 in = 2. There are two groups of 1 in = 1 x x x x 1 = = x x 25 + x 5 + x 1 = = x 25 + x 5 + x 1 = = x x 25 + x 5 + x 1 = 5

15 Student Resource 4 Boarding Pass #2 Day 2 Complete this boarding pass in order to board your spacecraft and travel to our next destination. Use the place value chart to help you. Be sure to show your work! 5 3 = = = = x 25 = 75 4 x 5 = 20 3 x 1 = 3 Convert this Base 5 number to Base = x x 25 + x 5 + x = 10 Convert this Base 10 number to Base = x x 25 + x 5 + x 1 = 5 It s time to travel! Let s blast off! Tomorrow we will land at our next destination, Galaxy Biaculus!

16 Base 5 Base 10 Student Resource 5

17 Student Resource 6A Galaxy Biaculus Today our spacecraft arrived in the Galaxy of Biaculus. The inhabitants of Biaculus use the Base 2 place value system. Since we just came from Galaxy Quintopia, you and your space crew need to translate Quintopian base 5 numbers into Biaculean base 2 numbers! Example: Convert to base x 125 = x 25 = 0 2 x 5 = 10 3 x 1 = First convert to base 10: 1 x x x x 1 = 3 = = Now convert to base x128=128 0x64=0 0x32=0 0 x 16 = 0 1 x 8 = 8 0 x 4 =0 1 x 2 = 2 0x 1 = Think There is one group of 128 in = 10. There are zero groups of 64, zero groups of 32, and zero groups of 16 in 10. There is one group of 8 in = 2. There are zero groups of 4 in 2, one group of 2 in 2, and zero groups of 1. Answer: Now you try, using the above charts to help you.

18 Student Resource 6B Galaxy Biaculus (page 2) Convert these numbers from base 5 to base = x 25 + x 5 + x = = x x 64 + x 32 + x 16 + x 8 + x 4 + x = = x x 25 + x 5 + x = = x x 64 + x 32 + x 16 + x 8 + x 4 + x = 2

19 Student Resource 6C Galaxy Biaculus (page 3) Almost home! In order to get there, you and your space crew should practice converting Biaculean numbers back into Earth s base 10 numbers! Look at the following example: x 16 = 16 1 x 8 = 8 0 x 4 =0 1 x 2 = 2 1 x 1 = So, = = Now you try! Use the Base 2 Place Value Chart shown above to help you = x x 64 + x 32 + x 16 + x 8 + x 4 + x 2 x = = x x 64 + x 32 + x 16 + x 8 + x 4 + x 2 x = 10 CHALLENGE: Can you convert to a base 5 number?

20 Student Resource 7 Quintopian Practice Use the chart to convert 4321 in base 5 to base 10. Base 5 Places Step Step 2 4 x 125 = x 25 =75 2 x 5 = 10 1 x 1 = 1 Step Step Write the digits in the chart. 2. Multiply the digit by the place. 3. Add the values of each place. 4. The sum is the number in base 10. Now, use the chart to help convert from base 5 to base Step 1 Step 2 Step 3 Step 4 Base 5 Places Step 1 Step 2 Step 3 Step 4 Base 5 Places

21 Student Resource 8A A Ticket Home Day 3 In order to train future space cadets in BASE-ic space travel, please complete the following to show all that you have learned. Good luck on your mission. 1. The following number is written in base 10. What does the digit 4 represent? A 4 B 40 C 400 D 4, In the base 10 number below, the 3 is in what place? 3, A ones B tens C hundreds D thousands 3. In the following number, the digit 3 is called the: 2 3 A base B exponent C square D cube 4. The number 100 can be represented by which expression? A 10 0 B 10 1 C 10 2 D 10 3

22 Student Resource 8B A Ticket Home Day 3 Brief Constructed Response Complete this boarding pass in order to board your spacecraft and travel back to our home base, Planet Earth: Part A Convert the following base 5 number to base 10: = 10 Part B Use what you know about place value to explain why your answer is correct. Use numbers and/or words in your explanation. Let s go home!!

23 Teacher Resource 1A Board/Overhead Example Day 1 Write a 4-digit number on the board, as below: 3562 Ask students to identify places and record underneath each digit thousand hundred ten one Then write the numeral of each place thousand hundred ten one Ask students to help you represent each number using the number 10. You will eventually have this: thousand hundred ten one x 10 x x (leave blank) Explain that there is another way to represent numbers that are multiplied by themselves. Define base as a number that is multiplied by itself and exponent or power as the number of times it is multiplied. It is written like this: base exponent or base power Ask the class these questions: How many times is the 10 multiplied in the thousands place? (3) How many times is the 10 multiplied in the hundreds place? (2) How many times is the 10 multiplied in the tens place? (1) How many times is the 10 multiplied in the ones place? (0) Since 10 multiplied by itself 0 times in the ones place, it is written as Add that any base raised to the zero power is one.

24 Teacher Resource 1B Board/Overhead Example Day 1 Add each exponential expression underneath each place, so it looks like this: thousand hundred ten one x 10 x x (leave blank) Ask: How do we write the ones place? (10 to the zero power.) How do we write the tens place? (10 to the first power.) How do we write the hundreds place? (10 to the second power.) How do we write the thousands place? (10 to the third power.)

25 Teacher Resource 2A Place Value Pocket Chart Directions Student Materials: one piece of 9 x 12 construction paper glue stick marker index cards scissors Directions: 1. Holding the construction paper horizontally, fold approximately one-half of the bottom portion upward. 2. Crease the fold so that it lies flat and forms a pocket at the bottom. pocket 3. Fold the paper horizontally in half, then in half again, so that three creases are formed, dividing the sheet into fourths. Unfold. Glue pockets at outer edges. glue glue

26 Teacher Resource 2B 4. Use a marker to draw lines on the place value pocket chart over each vertical crease. 5. Label the bottom of each pocket with the appropriate base and power and corresponding word name. (for Base 10 charts: 10 0 ones; 10 1 tens; 10 2 hundreds; 10 3 thousands; for Base 5 charts: 5 0 ones; 5 1 fives; 5 2 twentyfives; 5 3 one hundred twenty-fives etc.) 10 3 thousands 10 2 hundreds 10 1 tens 10 0 ones 6. Have students trim 10 index cards to approximately 2 x 5 (trim off about one inch so that the cards fit easily into each pocket). Have students label each card with a digit from 0 through 9. The cards will be inserted into the pockets to demonstrate place value of digits in various bases.

27 I Have Who Has with Exponential Numbers Teacher Resource 3 I have 100. Who has 2 2? I have 4. Who has 3 2? I have 9. Who has 4 2? I have 16. Who has 5 2? I have 25. Who has 6 2? I have 36. Who has 9 2? I have 81. Who has 7 2? I have 49. Who has 8 2? I have 64. Who has 2 3? I have 8. Who has 3 3? I have 27. Who has 5 3? I have 125. Who has 10 2?

28 Teacher Resource 4 Boarding Pass #1 Day 1 Answer Key Complete this boarding pass in order to board your spacecraft and travel to our first destination: Use the number 6,475 to answer the following questions: 1. What is the value of the digit 4? 2. In what place is the 4? 3. Write that place in exponential form. 400 hundreds What is the value of the digit 7? 5. In what place is the 7? 70 tens 6. Write that place in exponential form In what place is the digit 6? 8. Write that place in exponential form. Use the expression 6 3 to answer the following questions: 9. Which digit is the base? 10. Which digit is the exponent? thousands It s time to travel! Let s blast off! Tomorrow we will land at our first destination, Galaxy Quintopia!

29 Quintopian Creature Teacher Resource 5

30 Teacher Resource 6A Board/Overhead Example Day 2 Write a 2-digit number on the board, as below: Explain: The number reads, seventy-two, base 10. The base is written as a subscript. Since we have always dealt with base 10 numbers, we have dropped the base notation until now. Now, write the first four places for the base 5 system. Remember, each digit increases by a power of 5, and that the digit to the right is always the unit or one, which is five to the zero power. Now, explain that the next place has a value of 5, which is 5 to the first power. one 1 five one 5 1 The next place has a value of 25, which is five to the second power. Similarly, the next place has a value of 125, which is five to the third power. one hundred twenty-five twenty-five five one x 5 x 5 5 x Base System Conversions: Our next challenge is to convert our base 10 number to base 5. Step 1: What is the highest place in base 5 that is less than or equal to 72? (25) How many groups of 25 are in 72? (2)

31 Teacher Resource 6B Board/Overhead Example Day 2 So, we write a 2 in the 25 place. 2 one hundred twenty-five twenty-five five one Since we have 2 groups of 25 which makes 50, subtract 50 from 72 to get 22. Step 2: Now go to the next place to the right, which is the 5 place. How many groups of 5 are in 22? (4) So, we write a 4 in the 5 place. 2 4 one hundred twenty-five twenty-five five one Since we have 2 groups of 5 which makes 20, subtract 20 from 22 to get 2. Step 3: Now go to the next place to the right, which is the 1 place. How many groups of 1 are in 2? (2) So, we write a 2 in the 1 place one hundred twenty-five twenty-five five one So, = 242 5

32 Teacher Resource 7 Additional Place Value Pocket Charts Base Five 5 3 one hundred 5 2 twenty- 5 1 fives 5 0 ones twenty-fives fives Base Two 2 7 one hundred 2 5 thirtyseconds twentyeighths 2 6 sixtyfourths 2 4 sixteens 2 3 eights 2 2 fours 2 1 twos 2 0 ones

33 Teacher Resource 8A Galaxy Quintopia Answer Key Today our spacecraft arrived in the Galaxy of Quintopia. The inhabitants of Quintopia use the Base 5 place value system. You and your spacecrew need to translate Quintopian numbers into Planet Earth s Base 10 system! Look at the following example: 5 3 = = = = x 25 = 75 4 x 5 = 20 3 x 1 = 3 So, = = Now you try! Use the Base 5 Place Value Chart shown above to help you = 1 x x 5 + 4x = = 4 x x x 5 + 0x = = 3 x x x = = = = 66 10

34 Teacher Resource 8B Now try converting from Base 10 into Base 5! Look at this example: = 5 Think There is one group of 125 in = 47. There is one group of 25 in = 22. There are four groups of 5 in = 2. There are two groups of 1 in = 1 x x x x 1 = = 1 x x x x = = 2 x x x = = 2 x x x x =

35 Teacher Resource 9 Boarding Pass #2 Day 2 Complete this boarding pass in order to board your spacecraft and travel to our next destination. Use the place value chart to help you. Be sure to show your work! 5 3 = = = = x 25 = 75 4 x 5 = 20 3 x 1 = 3 Convert this Base 5 number to Base = 3 x x x x = Convert this Base 10 number to Base = 1 x x x x = It s time to travel! Let s blast off! Tomorrow we will land at our next destination, Galaxy Biaculus!

36 Biaculean Creature Teacher Resource 10

37 Venn Diagram Answer Key Base 5 Base 10 Sample Answers: five digits, 0 5 places are ones, fives, twentyfives, one hundred twenty-fives, etc. Sample Answers: digits 0 5 places for different values values grow exponentially Sample Answers: ten digits, 0 9 places are ones, tens, hundreds, thousands, etc. Teacher Resource 11

38 Teacher Resource 12A Board/Overhead Example Day 3 Write a 3-digit base 5 number on the board, as below: Convert base 5 to base 2 in two parts. First, convert base 5 to base 10, then base 10 to base 2. Write the digits in their base 5 places. Remember, each digit increases by a power of 5, and that the digit to the right is always the unit or one, which is five to the zero power twenty-five five one Convert to base 10: Add: = 93 3 x 25 = 75 Answer: x 5 = 15 3 x 1 = 3 Now convert this number to base 2 by writing the place values for base 2. You ll need more places because the denominations increase at a slower rate. Start with the one place and add each place to the left by multiplying by 2, one at a time (as in Day 1 and Day 2). sixty-four thirty-two sixteen eight four two one x2x2x2x2x2 2x2x2x2x2 2x2x2x2 2x2x2 2x Step 1: What is the highest place in base 2 that is less than or equal to 93? (64) How many groups of 64 are in 93? (1)

39 Teacher Resource 12B Board/Overhead Example Day 3 So, we write a 1 in the 64 place. 1 sixty-four thirty-two sixteen eight four two one Since we have 1 group of 64 which makes 64, subtract 64 from 93 to get 29. Step 2: Now go the next place to the right which is the 32 place. How many groups of 32 are in 29? (0) So, we write a 0 in the 32 place. 1 0 sixty-four thirty-two sixteen eight four two one Since we have 0 groups of 32 which makes 0, subtract 0 from 29 to get 29. Step 3: Now go the next place to the right which is the 16 place. How many groups of 16 are in 29? (1) So, we write a 1 in the 16 place sixty-four thirty-two sixteen eight four two one Since we have 1 group of 16 which makes 16, subtract 16 from 29 to get 13. Step 4: Now go the next place to the right which is the 8 place.

40 Teacher Resource 12C Board/Overhead Example Day 3 How many groups of 8 are in 13? (1) So, we write a 1 in the 8 place sixty-four thirty-two sixteen eight four two one Since we have 1 group of 8 which makes 8, subtract 8 from 13 to get 5. Step 5: Now go the next place to the right which is the 4 place. How many groups of 4 are in 5? (1) So, we write a 1 in the 4 place sixty-four thirty-two sixteen eight four two one Since we have 1 group of 4 which makes 4, subtract 4 from 5 to get 1. Step 6: Now go the next place to the right which is the 2 place. How many groups of 2 are in 1? (0) So, we write a 0 in the 2 place sixty-four thirty-two sixteen eight four two one Since we have 0 groups of 4 which makes 0, subtract 0 from 1 to get 1.

41 Teacher Resource 12D Board/Overhead Example Day 3 Step 7: Now go the next place to the right which is the 1 place. How many groups of 1 are in 1? (1) So, we write a 1 in the 1 place sixty-four thirty-two sixteen eight four two one So, Observation: = = The process of conversion to base 2 may seem tedious, but when deciding how many groups are in a given place, the choices are either 0 or 1. Thus, the mental math is simpler than in other base conversions.

42 Teacher Resource 13A Galaxy Biaculus Answer Key Today our spacecraft arrived in the Galaxy of Biaculus. The inhabitants of Biaculus use the Base 2 place value system. Since we just came from Galaxy Quintopia, you and your space crew need to translate Quintopian base 5 numbers into Biaculean base 2 numbers! Example: Convert to base x 125 = x 25 = 0 2 x 5 = 10 3 x 1 = First convert to base 10: 1 x x x x 1 = 3 = = Now convert to base x128=128 0x64=0 0x32=0 0 x 16 = 0 1 x 8 = 8 0 x 4 =0 1 x 2 = 2 0x 1 = Think There is one group of 128 in = 10. There are zero groups of 64, zero groups of 32, and zero groups of 16 in 10. There is one group of 8 in = 2. There are zero groups of 4 in 2, one group of 2 in 2, and zero groups of 1. Answer: Now you try, using the above charts to help you.

43 Teacher Resource 13B Galaxy Biaculus Answer Key Convert these numbers from base 5 to base = 4 x x x = = 1 x x x x x x x = = 2 x x x x = = 1 x x x x x x x x =

44 Teacher Resource 13C Galaxy Biaculus Answer Key Almost home! In order to get there, you and your space crew should practice converting Biaculean numbers back into Earth s base 10 numbers! Look at the following example: x 16 = 16 1 x 8 = 8 0 x 4 =0 1 x 2 = 2 1 x 1 = So, = = Now you try! Use the Base 2 Place Value Chart shown above to help you = (1 x 32) + (0 x 16) + (1 x 8) + (1 x 4) + (0 x 2)+ (1 x 1) = = 1 x x x x x x x 2+ 0 x = CHALLENGE: Can you convert to a base 5 number?

45 Teacher Resource 14 Quintopian Practice Answer Key Use the chart to convert 4321 in base 5 to base 10. Base 5 Places Step Step 2 4 x 125 = x 25 =75 2 x 5 = 10 1 x 1 = 1 Step Step Write the digits in the chart. 2. Multiply the digit by the place. 3. Add the values of each place. 4. The sum is the number in base 10. Now, use the chart to help convert from base 5 to base Base 5 Places Step Step 2 3 x x 25 4 x 5 4 x 1 Step Step Base 5 Places Step Step 2 1 x x 25 4 x 5 1 x 1 Step Step

46 Teacher Resource 15A A Ticket Home Day 3 Answer Key In order to train future space cadets in BASE-ic space travel, please complete the following to show all that you have learned. Good luck on your mission. 3. The following number is written in base 10. What does the digit 4 represent? A 4 B 40 C 400 D 4, In the base 10 number below, the 3 is in what place? 3, A ones B tens C hundreds D thousands 3. In the following number, the digit 3 is called the: 2 3 A base B exponent C square D cube 4. The number 100 can be represented by which expression? A 10 0 B 10 1 C 10 2

47 D 10 3

48 Teacher Resource 15B A Ticket Home Day 3 Answer Key Brief Constructed Response Complete this boarding pass in order to board your spacecraft and travel back to our home base, Planet Earth: Part A Convert the following base 5 number to base 10: = Part B Use what you know about place value to explain why your answer is correct. Use numbers and/or words in your explanation. To convert from Base 5 to Base 10, it is important to understand the place value of each digit. In Base 5, the digit farthest to the right has a value of one, so you multiply that digit by one. The next digit represents five, so you multiply that digit by five. The next place has a value of 25, so you multiply that digit by twenty-five. You continue in this manner, and each place in Base 5 is worth five times more than the previous place. After the value of each digit is determined, the values are added to calculate the Base 10 equivalent. See the chart below: Base 5 Places Step Step 2 0 x 125 = 0 1 x 25 =25 4 x 5 = 20 3 x 1 = 3 Step Step Let s go home!!

### Title: Place Value Made Simple

Title: Place Value Made Simple Brief Overview: This concept development unit will provide students with the knowledge and understanding of place value of whole numbers (0-1,000,000). s will be able to

### Place Value of Whole Numbers Through One Million

Place Value of Whole Numbers Through One Million Brief Overview: This learning unit develops and reviews place value concepts through millions. It involves the utilization of manipulatives. The lessons

### Warning! Construction Zone: Building Solids from Nets

Brief Overview: Warning! Construction Zone: Building Solids from Nets In this unit the students will be examining and defining attributes of solids and their nets. The students will be expected to have

### Plunge Into Place Value

Plunge Into Place Value Brief Overview: Understanding place value and expanded notation are critical components in understanding number sense. Through the lessons and activities in this unit, students

### Connect Four Math Games

Connect Four Math Games Connect Four Addition Game (A) place two paper clips on two numbers on the Addend Strip whose sum is that desired square. Once they have chosen the two numbers, they can capture

### This lesson introduces students to decimals.

NATIONAL MATH + SCIENCE INITIATIVE Elementary Math Introduction to Decimals LEVEL Grade Five OBJECTIVES Students will compare fractions to decimals. explore and build decimal models. MATERIALS AND RESOURCES

### Level ABE FLORIDA MATH RESOURCE GUIDE

Level 4.0-5.9 217 Benchmark: 17.01 LEVEL: 4.0 5.9 STANDARD: 17.0 Show awareness of the ways whole numbers are represented and used in the real world. BENCHMARK: 17.01 Identify whole numbers combining up

### Title: Measurement Conversion

Title: Measurement Conversion Brief Overview: Students will explore the relationship between various units of measurement including inches to feet, feet to yards, and inches to yards. They will develop

### Base-Ten and Place Value

1 Base-Ten and Place Value Jumping Jelly Beans Hundred Board-O Order Up! Number Neighborhood Stretching Numbers Place Value Pause Place Value Bingo 1 2 BRAIN-COMPATIBLE ACTIVITIES FOR MATHEMATICS, GRADES

### Title: Integers: Quick, Fun and Easy To Learn

Title: Integers: Quick, Fun and Easy To Learn Brief Overview Students will identify and understand positive and negative integers. Using this understanding, the students will use the number line, study

### Second Grade Math Standards and I Can Statements

Second Grade Math Standards and I Can Statements Standard CC.2.OA.1 Use addition and subtraction within 100 to solve one and two-step word problems involving situations of adding to, taking from, putting

### Polygon of the Day Discovering Area Formulas

Polygon of the Day Discovering Area Formulas Utilizing Technology and Manipulatives Cuisenaire pop-cubes Geometry tiles GSP triangles tool Trapezoid magnets Sixth Grade 6-day Unit Plan (40 minute classes)

### II. III Core Knowledge National Conference, Grade 2, Confucius Says = 2X3 1

Confucius Says 2+2+2 = 2X3 Introduction to Multiplication with a connection to the Study of Ancient China Grade level: Grade 2 Written by: Lottie Trudell, St. Mary s School, East Moline, Illinois Length

T276 Mathematics Success Grade 6 [OBJECTIVE] The student will add and subtract with decimals to the thousandths place in mathematical and real-world situations. [PREREQUISITE SKILLS] addition and subtraction

### Topic: 1 - Understanding Addition and Subtraction

8 days / September Topic: 1 - Understanding Addition and Subtraction Represent and solve problems involving addition and subtraction. 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step

### Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers. with Integers Divide Integers

Page1 Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers Lesson Topic I Can 1 Ordering & Adding Create a number line to order integers Integers Identify integers Add integers 2 Subtracting

NUMBER OPERATONS GRADE 4 Western and Northern Canadian Protocol (WNCP) Edition hands-on mathematics Grade 4 Project Editor Jennifer E. Lawson Mathematics Consultants Meagan Mutchmor Dianne Soltess Writer

### Reading and Writing Large Numbers

Reading and Writing Large Numbers Objective To read and write large numbers in standard, expanded, and number-and-word notations. www.everydaymathonline.com epresentations etoolkit Algorithms Practice

### Grade 2. M4: and M:5 Addition and Subtraction of Numbers to 1000. M3: Place Value, Counting, and Comparison of Numbers to 1000

Grade 2 Key Areas of Focus for Grades K-2: Addition and subtraction-concepts, skills and problem solving Expected Fluency: Add and Subtract within 20 Add and Subtract within 100 Module M1: Mastery of Sums

### Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Equivalent Fractions and Comparing Fractions: Are You My Equal? Brief Overview: This four day lesson plan will explore the mathematical concept of identifying equivalent fractions and using this knowledge

### What Is Singapore Math?

What Is Singapore Math? You may be wondering what Singapore Math is all about, and with good reason. This is a totally new kind of math for you and your child. What you may not know is that Singapore has

### Lesson Description. Texas Essential Knowledge and Skills (Target standards) Texas Essential Knowledge and Skills (Prerequisite standards)

Lesson Description Students will learn how financial institutions are able to pay savers interest while understanding the difference between interest earned and interest paid. Students will participate

### Title: Fun with Football (Data Collecting Activities)

Title: Fun with Football (Data Collecting Activities) Brief Overview: These lessons will encompass collecting and displaying data with line plots and stem and leaf plots. Students will also understand

### TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers

TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime

### Common Core State Standards for Math Grades K - 7 2012

correlated to the Grades K - 7 The Common Core State Standards recommend more focused and coherent content that will provide the time for students to discuss, reason with, reflect upon, and practice more

Grade 1 and 2: Basic Addition and Subtraction Facts Series 2: First and Second Grade Texas Essential Knowledge and Skills (TEKS): (1.3) Number, operation and quantitative reasoning. The student recognizes

### Primes. Name Period Number Theory

Primes Name Period A Prime Number is a whole number whose only factors are 1 and itself. To find all of the prime numbers between 1 and 100, complete the following exercise: 1. Cross out 1 by Shading in

### OA3-10 Patterns in Addition Tables

OA3-10 Patterns in Addition Tables Pages 60 63 Standards: 3.OA.D.9 Goals: Students will identify and describe various patterns in addition tables. Prior Knowledge Required: Can add two numbers within 20

### FIRST GRADE Number and Number Sense

FIRST GRADE Number and Number Sense Hundred Chart Puzzle Reporting Category Number and Number Sense Topic Count and write numerals to 100 Primary SOL 1.1 The student will a) count from 0 to 100 and write

### Huntsville City Schools Second Grade Math Pacing Guide

Huntsville City Schools Second Grade Math Pacing Guide 2016-2017 Thoughtful and effective planning throughout the school year is crucial for student mastery of standards. Once a standard is introduced,

### BREATHITT COUNTY SCHOOLS KINDERGARTEN MATH CURRICULUM

Weeks 1-2 Instructional Emphasis: Counting and Cardinality Topic 1: One to Five K.CC.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count

### Associative Property The property that states that the way addends are grouped or factors are grouped does not change the sum or the product.

addend A number that is added to another in an addition problem. 2 + 3 = 5 The addends are 2 and 3. area The number of square units needed to cover a surface. area = 9 square units array An arrangement

### I 2 T 2 Project Kimberly Grimaldi

I 2 T 2 Project Kimberly Grimaldi GRADE LEVEL: 8 th Grade TIME SPAN: One day lesson plan TOOLS: Algebra Tiles LESSON TITLE: Using Algebra Tiles to Explore the Distributive Property MATERIALS: Overhead

### 1) Make Sense and Persevere in Solving Problems.

Standards for Mathematical Practice in Second Grade The Common Core State Standards for Mathematical Practice are practices expected to be integrated into every mathematics lesson for all students Grades

### Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. Add and subtract within 20. MP.

Performance Assessment Task Incredible Equations Grade 2 The task challenges a student to demonstrate understanding of concepts involved in addition and subtraction. A student must be able to understand

### 1 Mathematics Curriculum

New York State Common Core 1 Mathematics Curriculum G R A D E GRADE 1 MODULE 1 Topic F Development of Addition Fluency Within 10 1.OA.3, 1.OA.6 Focus Standard: 1.OA.3 Apply properties of operations as

### Area and Circumference of Circles

Teacher Created Materials 21208 Focused Mathematics Student Guided Practice Book of Circles Learning Objectives Geometry Know the formulas for the area and circumference of a circle and use them to solve

### Math Journal HMH Mega Math. itools Number

Lesson 1.1 Algebra Number Patterns CC.3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Identify and

### Gap Closing. Decimal Computation. Junior / Intermediate Facilitator's Guide

Gap Closing Decimal Computation Junior / Intermediate Facilitator's Guide Module 8 Decimal Computation Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions...5

CCSSM: Grade 7 DOMAIN: The Number System Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Standard: 7.NS.1: Apply

### 7 th Grade Integer Arithmetic 7-Day Unit Plan by Brian M. Fischer Lackawanna Middle/High School

7 th Grade Integer Arithmetic 7-Day Unit Plan by Brian M. Fischer Lackawanna Middle/High School Page 1 of 20 Table of Contents Unit Objectives........ 3 NCTM Standards.... 3 NYS Standards....3 Resources

### Grade Level Objective: 1.A.2.1: Count, represent, read, compare, order & conserve whole numbers

Benchmark A: Understand and apply number properties and operations. 1.A.2.1: Count, represent, read, compare, order & conserve whole numbers Give classroom objects to partners. Each partner sorts objects

### Lesson Description. Texas Essential Knowledge and Skills (Target standards) Skills (Prerequisite standards) National Standards (Supporting standards)

Lesson Description This lesson focuses on comparing simple interest and compound interest. Students discover the differences between simple and compound interest by creating a year chart using both methods.

### Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

### Number Talks. 1. Write an expression horizontally on the board (e.g., 16 x 25).

Number Talks Purposes: To develop computational fluency (accuracy, efficiency, flexibility) in order to focus students attention so they will move from: figuring out the answers any way they can to...

### Counting Money and Making Change Grade Two

Ohio Standards Connection Number, Number Sense and Operations Benchmark D Determine the value of a collection of coins and dollar bills. Indicator 4 Represent and write the value of money using the sign

### First Grade Exploring Two-Digit Numbers

First Grade Exploring Two-Digit Numbers http://focusonmath.files.wordpress.com/2011/02/screen-shot-2011-02-17-at-3-10-19-pm.png North Carolina Department of Public Instruction www.ncdpi.wikispaces.net

### Understanding Place Value of Whole Numbers and Decimals Including Rounding

Grade 5 Mathematics, Quarter 1, Unit 1.1 Understanding Place Value of Whole Numbers and Decimals Including Rounding Overview Number of instructional days: 14 (1 day = 45 60 minutes) Content to be learned

### Change of Number Bases

What are Number Bases? Change of Number Bases When converting to different number bases, one is expressing numbers in different numeration systems. These numeration systems, or bases, use different digits

T92 Mathematics Success Grade 8 [OBJECTIVE] The student will create rational approximations of irrational numbers in order to compare and order them on a number line. [PREREQUISITE SKILLS] rational numbers,

### Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c

Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics

Grade 2 Vocabulary Cards (Draft) Missouri Mathematics Core Academic Standards The Missouri Mathematics Core Academic Standards Grade 2 Vocabulary Cards (Draft) are aligned to explicit mathematical terms

### Modeling Planet Sizes

activity 14 Modeling Planet Sizes BROWARD COUNTY ELEMENTARY SCIENCE BENCHMARK PLAN Grade 4 Quarter 2 Activity 14 SC.E.1.2.4 The student knows that the planets differ in size, characteristics, and composition

### Every Day Counts: Partner Games. and Math in Focus Alignment Guide. Grades K 5

Every Day Counts: s and Math in Focus Alignment Guide Grades K 5 7171_Prtnrs_AlgnmtChrt.indd 1 9/22/10 6:04:49 PM Every Day Counts : s s offers 20 simple yet effective games to help students learn, review,

### Unit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction

Unit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction Introduction In this unit, students will review place value to 1,000,000 and understand the relative sizes of numbers in

### Danville District No. 118 Mathematics Fifth Grade Curriculum and Scope and Sequence First Quarter

Danville District No. 118 Mathematics Fifth Grade Curriculum and Scope and Sequence First Quarter Common Core Operations and Algebraic Thinking (5.OA) Common Core Number and Operations in Base Ten (5.NBT)

Ohio Standards Connection Patterns, Functions and Algebra Benchmark E Solve open sentences and explain strategies. Indicator 4 Solve open sentences by representing an expression in more than one way using

### Place Value in Whole Numbers

Place Value in Whole Numbers Objectives To provide practice identifying values of digits in numbers up to one billion; and to provide practice reading and writing numbers up to one billion. www.everydaymathonline.com

### Such As Statements, Kindergarten Grade 8

Such As Statements, Kindergarten Grade 8 This document contains the such as statements that were included in the review committees final recommendations for revisions to the mathematics Texas Essential

### Whole Numbers. hundred ten one

Whole Numbers WHOLE NUMBERS: WRITING, ROUNDING The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The natural numbers (counting numbers) are 1, 2, 3, 4, 5, and so on. The whole numbers are 0, 1, 2, 3, 4,

### Pocantico Hills School District Grade 1 Math Curriculum Draft

Pocantico Hills School District Grade 1 Math Curriculum Draft Patterns /Number Sense/Statistics Content Strands: Performance Indicators 1.A.1 Determine and discuss patterns in arithmetic (what comes next

### Comparing and Ordering Fractions

Comparing and Ordering Fractions Objectives To review equivalent fractions; and to provide experience with comparing and ordering fractions. www.everydaymathonline.com epresentations etoolkit Algorithms

### Unit 1: Place value and operations with whole numbers and decimals

Unit 1: Place value and operations with whole numbers and decimals Content Area: Mathematics Course(s): Generic Course Time Period: 1st Marking Period Length: 10 Weeks Status: Published Unit Overview Students

### Unit Plan Components. Appropriate Length of Time. Unit Name: Addition and Subtraction to 20. Common Core Standards

Unit Plan Components Big Goal Standards Big Ideas Unpacked Standards Scaffolded Learning Resources Appropriate Length of Time Aligned Assessment Comments This unit plan identifies a big goal for the overall

### Integer Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions

Grade 7 Mathematics, Quarter 1, Unit 1.1 Integer Operations Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Describe situations in which opposites combine to make zero.

### Roselle Math Curriculum Unit Title: 7 Multiplying and Dividing Decimals Grade: _5_. Common Core Standards, 2010

Essential Question(s) How do decimal numbers impact multiplication and division? Enduring Understanding(s) Decimals can be multiplied and divided in the same way as whole numbers. What strategies can be

### Exploring Length, Area, and Attributes

Explorations Exploring Length, Area, and Attributes Objectives To guide children as they measure lengths and distances to the nearest inch and centimeter, explore area by tiling surfaces, and sort attribute

### Investigate Investigate

Name Place Value and Patterns Essential Question How can you describe the relationship between two place-value positions? Lesson 1.1 COMMON CORE STANDARD CC.5.NBT.1 Understand the place value system. Investigate

### Accuplacer Elementary Algebra Study Guide for Screen Readers

Accuplacer Elementary Algebra Study Guide for Screen Readers The following sample questions are similar to the format and content of questions on the Accuplacer Elementary Algebra test. Reviewing these

### Year Five Maths Notes

Year Five Maths Notes NUMBER AND PLACE VALUE I can count forwards in steps of powers of 10 for any given number up to 1,000,000. I can count backwards insteps of powers of 10 for any given number up to

### 2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Vertical Alignment Chart Kindergarten Algebra I 1

2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Vertical Alignment Chart Kindergarten Algebra I 1 The materials are copyrighted (c) and trademarked (tm)

### 2 Mathematics Curriculum

New York State Common Core 2 Mathematics Curriculum GRADE GRADE 2 MODULE 3 Topic E: Model Numbers Within 1000 with Place Value Disks 2.NBT.A Focus Standard: 2.NBT.A Understand place value. Instructional

### Lesson 1: The Location of California

Lesson 1: The Location of California Focus Question: Where in the world is California? California History-Social Science Standard 4.1 Students demonstrate an understanding of the physical and human geographic

### The gas can has a capacity of 4.17 gallons and weighs 3.4 pounds.

hundred million\$ ten------ million\$ million\$ 00,000,000 0,000,000,000,000 00,000 0,000,000 00 0 0 0 0 0 0 0 0 0 Session 26 Decimal Fractions Explain the meaning of the values stated in the following sentence.

### Mathematics as Reasoning Students will use reasoning skills to determine the best method for maximizing area.

Title: A Pen for Penny Brief Overview: This unit is a reinforcement of the concepts of area and perimeter of rectangles. Methods for maximizing area while perimeter remains the same are also included.

### Objective: Apply and explain alternate methods for subtracting from multiples of 100 and from numbers with zero in the tens place.

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 2 5 Lesson 18 Objective: Apply and explain alternate methods for subtracting from multiples of Suggested Lesson Structure Fluency Practice Application Problem

### Name Period Date MATHLINKS GRADE 8 STUDENT PACKET 1 INTEGERS REVIEW

Name Period Date 8-1 STUDENT PACKET MATHLINKS GRADE 8 STUDENT PACKET 1 INTEGERS REVIEW 1.1 Integer Operations: Patterns Explore the meaning of integer addition, subtraction, multiplication, and division.

### INTRODUCTION CONTENTS

INTRODUCTION Algebra for All and No Child Left Behind are phrases in the education community that suggest, and in many cases require, action. They give impetus for mathematics teachers at all levels to

### Correlation to the Common Core State Standards. Math in Focus

Correlation to the Common Core State Standards Math in Focus Correlation to the Common Core State Standards Table of Contents Explanation of Correlation.......................... 1 Grade 1...........................................

### A Concrete Introduction. to the Abstract Concepts. of Integers and Algebra using Algebra Tiles

A Concrete Introduction to the Abstract Concepts of Integers and Algebra using Algebra Tiles Table of Contents Introduction... 1 page Integers 1: Introduction to Integers... 3 2: Working with Algebra Tiles...

### Unit 6 Number and Operations in Base Ten: Decimals

Unit 6 Number and Operations in Base Ten: Decimals Introduction Students will extend the place value system to decimals. They will apply their understanding of models for decimals and decimal notation,

### Common Core State Standards DECONSTRUCTED. Booklet I: Kindergarten to Second Grade, Math FOR INTERNAL USE ONLY

Common Core State Standards DECONSTRUCTED Booklet I: Kindergarten to Second Grade, Math How to use this booklet You cannot teach a Common Core Standard you must teach the skills inside of each standard.

### Exploring Decimals By: Amy Benjamin Math- Grade 4/5 6 day unit plan Technologies Used: *Computers *Class set of calculators(ti80)

Exploring Decimals By: Amy Benjamin Math- Grade 4/5 6 day unit plan Technologies Used: *Computers *Class set of calculators(ti80) * TI-84+ graphing calculator *Overhead unit for calculator *Overhead projector

### ALIGNMENT OF MATH PERSPECTIVES RESOURCES WITH COMMON CORE STATE STANDARDS IN MATHEMATICS

ALIGNMENT OF MATH PERSPECTIVES RESOURCES WITH COMMON CORE STATE STANDARDS IN MATHEMATICS KINDERGARTEN COUNTING AND CARDINALITY Count to tell the number of objects Understand the relationship between numbers

### Kindergarten Common Core Standards & Learning Targets

Kindergarten Common Core Standards & Learning Targets CCS Standards: Counting and Cardinality K.CC.1. Count to 100 by ones and by tens. K.CC.2. Count forward beginning from a given number within the known

### Pythagorean Theorem Differentiated Instruction for Use in an Inclusion Classroom

Pythagorean Theorem Differentiated Instruction for Use in an Inclusion Classroom Grade Level: Seven Time Span: Four Days Tools: Calculators, The Proofs of Pythagoras, GSP, Internet Colleen Parker Objectives

### Vocabulary, Signs, & Symbols product dividend divisor quotient fact family inverse. Assessment. Envision Math Topic 1

1st 9 Weeks Pacing Guide Fourth Grade Math Common Core State Standards Objective/Skill (DOK) I Can Statements (Knowledge & Skills) Curriculum Materials & Resources/Comments 4.OA.1 4.1i Interpret a multiplication

### a b Grade 6 Math Circles Fall 2010 Exponents and Binary Numbers Powers What is the product of three 2s? =

1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Powers What is the product of three 2s? 2 2 2 = What is the product of five 2s? 2 2 2 2 2 = Grade 6 Math

### Objectives To review and provide practice with the lattice method for multiplication.

Objectives To review and provide practice with the lattice method for multiplication. Teaching the Lesson materials Key Activities Students review the lattice method for multiplication with - and -digit

### Sue. Rubric for the Critical Area of Mathematics Grades K - 2

Rubric for the Critical Area of Mathematics Grades K - 2 The intent of this document is to provide support as teachers transition to Common Core s. It draws attention to the most critical skills for their

### Topic 1: Understanding Addition and Subtraction

Topic 1: Understanding Addition and Subtraction 1-1: Writing Addition Number Sentences Essential Understanding: Parts of a whole is one representation of addition. Addition number sentences can be used

### Year 1 Maths Expectations

Times Tables I can count in 2 s, 5 s and 10 s from zero. Year 1 Maths Expectations Addition I know my number facts to 20. I can add in tens and ones using a structured number line. Subtraction I know all

### Math Content by Strand 1

Math Content by Strand 1 Number and Operations: Whole Numbers Addition and Subtraction and the Number System Kindergarten Young students develop their understanding of the operations of addition and subtraction

### Overview. Essential Questions. Grade 7 Mathematics, Quarter 4, Unit 4.2 Probability of Compound Events. Number of instruction days: 8 10

Probability of Compound Events Number of instruction days: 8 10 Overview Content to Be Learned Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand

### Measure the Lakes SOURCES CONSULTED

K. Kelly Mottl kamottl@gbaps.org Washington Middle School, Green Bay, WI Measure the Lakes LESSON OVERVIEW Measuring the Lakes by K. Kelly Mottl has been designed to help students use mathematics, the

### Review: Addition and Subtraction of Positive and Negative Numbers

Review: Addition and Subtraction of Positive and Negative Numbers Objective To practice adding and subtracting positive and negative numbers. www.everydaymathonline.com epresentations etoolkit Algorithms

Fourth Grade Fractions http://upload.wikimedia.org/wikibooks/en/9/92/fractions_of_a_square.jpg North Carolina Department of Public Instruction www.ncdpi.wikispaces.net Overview The implementation of the