Hundreds Grid. MathShop: Hundreds Grid


 Edgar McLaughlin
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1 Hundreds Grid MathShop: Hundreds Grid
2 Kindergarten Suggested Activities: Kindergarten Representing Children create representations of mathematical ideas (e.g., use concrete materials; physical actions, such as hopping or clapping; pictures; numbers; diagrams; dramatization; invented symbols), make connections among them, and apply them to solve problems. Pg. 81 The Kindergarten Program Overall Expectations demonstrate an understanding of numbers, using concrete materials to explore and investigate counting, quantity, and number relationships pg recognize, explore, describe, and compare patterns, and extend, translate,and create them, using the core of a pattern and predicting what comes next pg. 184 OE 15 As children progress through the Kindergarten program, they demonstrate an understanding of numbers, using concrete materials to explore and investigate counting, quantity, and number relationships there are many ways to count. Each way to count has a proper sequence We are learning that as we move up or down the counting sequence, the quantity increases or decreases by the number we are counting by (concept of magnitude) 15.1 investigate (e.g., using a number line, a hundreds carpet, a board game with numbered squares) the idea that a number s position in the counting sequence determines its magnitude (e.g., the quantity is greater when counting forward and less when counting backward) 15.3 make use of onetoone correspondence in counting objects and matching groups of objects 15.4 demonstrate an understanding of the counting sequence is always the same 1 is followed by 2, 2 by 3, and so on) and of order irrelevance (i.e. the concept that the number of objects in a set will be the same regardless of which object is used to begin the counting) 18. Recognize, explore, describe, and compare patterns, and extend, translate, and create them, using the core of a pattern and predicting what comes next. Kindergarten Suggested Activities Warm up: Ask each child What s your favourite number between 1 and 100? The child tells you their favorite number and then stands on it. They may need help finding the number.
3 How many? one bag/bucket with cubes Each child takes a turn to put one hand in the bag and remove some cubes. They place them down on the floor and everyone counts them out loud together. Once the number is counted, the child places their cubes on the corresponding number on the hundreds chart (e.g., six cubes, count 1,2,3,4,5,6 and then put the cubes on the number 6 on the chart) Repeat. If the number is already taken, a friend removes the previous cubes so that the new cubes can be placed on the number. Number train Procedure: Ask the students to stand on the beginning numbers i.e., if there are 6 students they stand on the numbers 1,2,3,4,5, and 6. Next, the child on number 1 moves to number 7, 2 moves to number 8, 3 moves to number 9 and so on. The last person moves the the front of the line and says the next number. All students count together as each a child moves on the the next space. Race to 100! Procedure: How high can we go before the timer rings? or Beat the Clock One die One timer (set at 5 minutes) In turn, each child rolls a die. Child #1 rolls a number (e.g., 6) and beginning at 0 they count 6 spaces and stand there. Child # 2 rolls a number (e.g., 5 )and begins counting 5 spots and stops. Child # 1 returns
4 to the end of the line. Child # 3 rolls a number and moves that many spaces ahead of child # 2. Child # 2 returns to the end of the line. Continue until the timer rings. Repeat and try to beat the previous score. Gr. 1 Curriculum expectations: Number Sense and Numeration: Overall Expectations By the end of Grade 1, students will: read, represent, compare, and order whole numbers to 50, demonstrate an understanding of magnitude by counting forward to 100 and backwards from 20; solve problems involving the addition and subtraction of singledigit whole numbers, using a variety of strategies Specific Expectations Counting count forward by 1 s, 2 s, 5 s, and 10 s to 100, using a variety of tools and strategies (e.g., move with steps; skip count on a number line; place counters on a hundreds chart; connect cubes to show equal groups; count groups of pennies, nickels, or dimes); count backwards by 1 s from 20 and any number less than 20 (e.g., count backwards from 18 to 11), with and without the use of concrete materials and number lines; count backwards from 20 by 2 s and 5 s, using a variety of tools (e.g., number lines, hundreds charts); use ordinal numbers to thirtyfirst in meaningful contexts (e.g., identify the days of the month on a calendar Patterning and Algebra : Overall Expectations By the end of Grade 1, students will: identify, describe, extend, and create repeating patterns; demonstrate an understanding of the concept of equality, using concrete materials and addition and subtraction to 10.
5 Grade 1 Suggested Activities: Guess my Number Bean bag Procedure: Students should sit on the row beginning with 51, facing forward. Choose a number and cover it with a bean bag. Students take turns guessing the hidden number. The winner can hide the next Number. Cooperative Skip Counting by 2s Have the students line up on the purple side facing the numbers (1,11,21,31,41,51) Child # 1 hops along the first line counting by 2s (2,4,6,8,10). Invite the group to help count. Remind them to count together when the person hops. Ask the child not to hop too fast. Child #2 continues hopping while everyone says their numbers (12, 14, 16, 18, 20). Continue until the last child has had a chance to hop along their line. Repeat. Face consecutive numbers on the hundreds chart (e.g., 41,51,61,71,81) and repeat the process Child # 1 hops counting 42,44,46,48,50 Child # 2 continues hopping 52,54,56 etc.
6 Race to 100! How high can we go before the timer rings? or Beat the Clock One die One timer (set at 5 minutes) In turn, each child rolls a die. Child #1 rolls a number (e.g., 6) and beginning at 0 they count 6 spaces and stand there. Child # 2 rolls a number (e.g., 5 )and begins counting 5 spots and stops. Child # 1 returns to the end of the line. Child # 3 rolls a number and moves that many spaces ahead of child # 2. Child # 2 returns to the end of the line. Continue until the timer rings. Repeat and try to beat the previous score. Three in a Row! Two dice. Note each die should only have dots to represent the number Bean bags or objects to cover the number Goal: to cover three numbers in a row (any direction) Note: Gr. 1 students use the numbers from Procedure: Form two teams, A and B. Team A takes a turn to roll the dice e.g., 2 and 3. They decide if they want to cover the number 23 or 32. A bean bag is placed on the number. Team B rolls the dice and decides on a number to cover.
7 Repeat until one team places a bean bag on a number that covers three in a row. Grade 2 Curriculum Expectations Number Sense and Numeration Overall Expectations By the end of Grade 2, students will: read, represent, compare, and order whole numbers to 100, and use concrete materials to represent fractions and money amounts to 100 ; demonstrate an understanding of magnitude by counting forward to 200 and backwards from 50, using multiples of various numbers as starting points; solve problems involving the addition and subtraction of one and twodigit whole numbers, using a variety of strategies, and investigate multiplication and division. determine, using concrete materials, the ten that is nearest to a given twodigit number, and justify the answer (e.g., use counters on ten frames to determine that 47 is closer to 50 than to 40); Patterning and Algebra Overall Expectations By the end of Grade 2, students will: identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns; demonstrate an understanding of the concept of equality between pairs of expressions, using concrete materials, symbols, and addition and subtraction to 18. Specific Expectations By the end of Grade 2, students will: identify and describe, through investigation, growing patterns and shrinking patterns generated by the repeated addition or subtraction of 1 s, 2 s, 5 s, 10 s, and 25 s on a number line and on a hundreds chart (e.g., the numbers 90, 80, 70, 60, 50, 40, 30, 20, 10 are in a straight line on a hundreds chart); Grade 2 Suggested Activities:
8 Warm Up Activity Guess my Number Use the following Clues My number has two digits. My number is greater than 2 and less than 19 My number is an even number. The digits in my number add up to 3. What s my number? Answer is 12. Second example: My number has two digits. My number is greater than 16 and less than 26. My number is an odd number. The digits in my number add up to 5. What's my number? Answer is 23. More or Less? Cards that say: What number is one more? What number is one less? What number is ten more? What number is ten less? Ask a student to choose a number that is not on the outside edge and stand on that number. Students take turns turning over a card and reading it out loud. The student on the number chart must respond to the question. Help as needed to ensure success.
9 Repeat choosing another child to choose a number. Race to 100! How high can we go before the timer rings? or Beat the Clock One die One timer (set at 5 minutes) In turn, each child rolls a die. Child #1 rolls a number (e.g., 6) and beginning at 0 they count 6 spaces and stand there. Child # 2 rolls a number (e.g., 5 ) and begins counting 5 spots and stops. Child # 1 returns to the end of the line. Child # 3 rolls a number and moves that many spaces ahead of child # 2. Child # 2 returns to the end of the line. Continue until the timer rings. Repeat and try to beat the previous score. Plus One! One large penny Procedure: Show kids how to add and subtract with a penny. Give an addition problem such as Have students identify the larger number and put a penny on that number. Then have a child move the penny up as many times as the second number shows. Practice with problems such as 6+14, and 9+63, to give kids practice identifying the larger number first, then adding the smaller number. This is an important addition skill. For Penny Subtraction, start on the larger number and move backwards. Adapted from
10 Rounding Up or Down Form two teams. Students will toss a bean bag and identify the number that it falls on. Round up or down to the nearest 10. For example: The bean bag lands on 33 and the student rounds it to 30. The other team has to count by 10s and do jumping jacks, jumps, claps etc. The number 30 would be 10, 20, 30 (three jumping jacks). Three in a Row! Two dice. Note each die should only have dots to represent the number Bean bags or objects to cover the number Goal: to cover three numbers in a row (any direction) Procedure: Form two teams, A and B. Team A takes a turn to roll the dice e.g., 2 and 3. They decide if they want to cover the number 23 or 32. A bean bag is placed on the number. Team B rolls the dice and decides on a number to cover. Repeat until one team places a bean bag on a number that covers three in a row. Grade 3 Curriculum Expectations: Number Sense and Numeration Overall Expectations By the end of Grade 3, students will:
11 read, represent, compare, and order whole numbers to 1000, and use concrete materials to represent fractions and money amounts to $10; demonstrate an understanding of magnitude by counting forward and backwards by various numbers and from various starting points; solve problems involving the addition and subtraction of single and multidigit whole numbers, using a variety of strategies, and demonstrate an understanding of multiplication and division. Patterning and Algebra Overall Expectations By the end of Grade 3, students will: describe, extend, and create a variety of numeric patterns and geometric patterns; Specific Expectation extend repeating, growing, and shrinking number patterns (Sample problem:write the next three terms in the pattern 4, 8, 12, 16,.); Grade 3 Suggested Activities: Who has my number? White board, marker, and eraser to demonstrate an answer if needed. Index cards: Card # 1 Who has the number ? I have 28. Who has ? I have 55. Who has 2 tens and 5 ones? I have 25. Who has 4 tens and 1 one? I have 41. Who has one less than 68? I have 67. Who has one more than 89? I have 90. Who has the number that extends this pattern 1,3,5,7,? I have 9. Who has the number that extends this pattern 22,24,26,? I have 28. Well done! Procedure: Hand out all of the cards randomly. Some students may have 2 cards. Begin with Card 1 and ask the question. Each student looks for the answer
12 on their card and then reads the answer and the next question. Keep track of the questions above in case a student needs help. Counting by 10s Looking at the hundreds chart count by 10s. Choose one student to stand on 10 and move forward on the chart counting by 10s to 100. Note: This is a growing pattern. Choose another student to stand on 100 and count by 10s backward to 10. Note: This is a shrinking pattern. Choose a student to select and stand a number on the number line (not on the outside lines). Ask them to move forward or backward counting by 10s e.g., The student stands on 34. Ask them to count forward by 10s (34,44,54,64,74,84,94). Is this a growing or shrinking pattern? A student stands on 76. Ask them to count backward by 10s (76,66,56,46,36,26,16,6). Is this a growing or shrinking pattern? Repeat. Ask them if they notice a pattern when they are counting by 10s on the hundreds chart. (They move in a straight line) Race to 0! How low can we go before the timer rings? or Beat the Clock One die One timer (set at 5 minutes) Begin at 50 and count backwards before the timer rings. In turn, each child rolls a die. Child #1 rolls a number (e.g., 6) and beginning at 50 they
13 count backwards 6 spaces and stand there. Child # 2 rolls a number (e.g., 5 ) and continues counting backwards 5 spots and stops. Child # 1 returns to the end of the line. Child # 3 rolls a number and c that continues counting backward from child # 2. Child # 2 returns to the end of the line. Continue until the timer rings or the reach 0. Repeat and try to beat the previous score. Grade 4 Curriculum Expectations: Number Sense and Numeration Patterning and Algebra Overall Expectations: By the end of Grade 4, students will: describe, extend, and create a variety of numeric and geometric patterns, make predictions related to the patterns, and investigate repeating patterns involving reflections; Specific Expectations: Patterns and Relationships By the end of Grade 4, students will: extend, describe, and create repeating, growing, and shrinking number patterns (e.g., I created the pattern 1, 3, 4, 6, 7, 9,. I started at 1, then added 2, then added 1, then added 2, then added 1, and I kept repeating this. ); connect each term in a growing or shrinking pattern with its term number (e.g., in the sequence 1, 4, 7, 10,, the first term is 1, the second term is 4, the third term is 7, and so on), and record the patterns in a table of values that shows the term number and the term; create a number pattern involving addition, subtraction, or multiplication, given a pattern rule expressed in words (e.g., the pattern rule start at 1 and multiply each term by 2 to get the next term generates the sequence 1, 2, 4, 8, 16, 32, 64, ); Grade 4 Suggested Activities: Who has my number? White board, marker, and eraser to demonstrate an answer if needed. Index cards: (one card for each statement) Card # 1 Who has the number ? (this is the only card identified #1) I have 28. Who has ? I have 55. Who has 2 tens and 5 ones? I have 25. Who has 4 tens and 1 one?
14 I have 41. Who has one less than 68? I have 67. Who has one more than 89? I have 90. Who has the number that extends this pattern 1,3,5,7,? I have 9. Who has the number that extends this pattern 22,24,26,? I have 28. Well done! Procedure: Hand out all of the cards randomly. Some students may have 2 cards. Begin with Card 1 and ask the question. Each student looks for the answer on their card and then reads the answer and the next question. Keep track of the questions above in case a student needs help. What s the Pattern? Rings to identify patterns. Procedure: Ask a student to put rings on the following pattern: 3, 6, 9,12. Have students tell you the next three numbers in the pattern. Ask them if it is a growing or shrinking pattern. (Growing) Can someone explain the pattern rule? Begin with 3 and add 2. Repeat for the next pattern: 36, 31,26,21,,. (Answer is 16, 11, 6 Pattern rule: Begin with 36 and subtract 5. This is a shrinking pattern.) 79, 68, 57, 46,,,. (Answer: 35, 24,13. Pattern rule: Begin with 79 and subtract 11. This is a shrinking pattern.)
15 Follow the Rule! The rule is Begin with 19 and add 6. Students organize themselves according to the rules. (Answer: 19, 25, 31, 37,43, 49, 55 ). The rule is Begin with 5 and add 9. Students organize themselves according to the rules. (Answer: 5,14, 23, 32, 41, 50, 59) Grade 5 Curriculum Expectations: Number Sense and Numeration Overall Expectations: By the end of Grade 5, students will: determine, through investigation using a table of values, relationships in growing and shrinking patterns, and investigate repeating patterns involving translations;  demonstrate and explain equivalent representations of a decimal number, using concrete materials and drawings (e.g., use base ten materials to show that three tenths [0.3] is equal to thirty hundredths [0.30]); Patterning and Algebra Specific Expectations Patterns and Relationships By the end of Grade 5, students will: create, identify, and extend numeric and geometric patterns, using a variety of tools (e.g., concrete materials, paper and pencil, calculators, spreadsheets); make a table of values for a pattern that is generated by adding or subtracting a number (i.e., a constant) to get the next term, or by multiplying or dividing by a constant to get the next term, given either the sequence (e.g., 12, 17, 22, 27, 32, ) or the pattern rule in words (e.g., start with 12 and add 5 to each term to get the next term); Grade 5 Suggested Activities Who has my number? (same activity as gr. 4) White board, marker, and eraser to demonstrate an answer if needed.
16 Index cards: (one card for each statement) Card # 1 Who has the number ? (this is the only card identified #1) I have 28. Who has ? I have 55. Who has 2 tens and 5 ones? I have 25. Who has 4 tens and 1 one? I have 41. Who has one less than 68? I have 67. Who has one more than 89? I have 90. Who has the number that extends this pattern 1,3,5,7,? I have 9. Who has the number that extends this pattern 22,24,26,? I have 28. Well done! Hand out all of the cards randomly. Some students may have 2 cards. Begin with Card 1 and ask the question. Each student looks for the answer on their card and then reads the answer and the next question. Keep track of the questions above in case a student needs help. 100 Percent! Review: Percent means out of % means 30 out of 100? Have a student show 30% of the chart (any three rows or columns) If the chart is one whole unit, then how much is each row (in decimal notation 10%)? What size is each box? (1%) Students form 2 teams and take turns rolling the dice to see who can reach 100% first. Continue rolling until 100% is reached. Begin at 0 and roll the dice e.g., number 8 means move forward 8 spaces or 8 %. Note: if doubles are rolled (1,1 or 5,5 etc. ), the team must move back 10% (10 spaces). What s the Pattern? (same activity as gr. 4)
17 Rings to identify patterns Procedure: Ask a student to put rings on the following pattern: 3, 6, 9,12. Have students tell you the next three numbers in the pattern. Ask them if it is a growing or shrinking pattern. (Growing) Can someone explain the pattern rule? Begin with 3 and add 2. Repeat for the next pattern: 36, 31,26,21,,. (Answer is 16, 11, 6 Pattern rule: Begin with 36 and subtract 5. This is a shrinking pattern.) 79, 68, 57, 46,,,. (Answer: 35, 24,13. Pattern rule: Begin with 79 and subtract 11. This is a shrinking pattern.) Follow the Rule! (same activity as gr. 4) The rule is Begin with 19 and add 6. Students organize themselves according to the rules. (Answer: 19, 25, 31, 37,43, 49, 55 ). The rule is Begin with 5 and add 9. Students organize themselves according to the rules. (Answer: 5,14, 23, 32, 41, 50, 59)
18 Grade 28 Game Jump2math plays during school program. Differentiated for grades 16 Two 12 numbered dice Bucket, suction cups Money manipulatives Procedure: Place all large money bills and coins in between all the numbers on the hundreds grid. Give all students a different colour suction cup when they arrive at your station. Each student rolls two 12number dice in the bucket. They can add, subtract, multiply or divide both numbers. Example: Student rolls a 5 and a 3. Is there money on the number 15? (5x3) OR is there more money on the 2? (53) Students need to strategize to figure out which order of operations will gain more money. Students pick up their money with their suction cup and keep it. They leave their suction cup behind on the number until their next turn. They move their suction cup with each roll forward or backward on the mat.
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21 Activity 1: Special Numbers This activity is designed to help familiarize the students to the number chart. Have students place five to ten counters on their very special numbers. Have students tell a partner why these numbers are important to them. Examples of special numbers may include: Your age The day you were born The number of people in your family Your favourite or lucky number Your shoe size The number of pets you have The number of relatives you have Your favourite sport s player s team jersey number Activity 2: Picture It This activity reinforces knowledge of the number chart and encourages children to visual patterns. Have students cover the following numbers as you call them out one at a time: 1, 71, 17, 53, 44, 35, 34, 8, 78, 12, 67, 23, 45, 62, 26, 56. Ask students to guess what the picture will be before you finish calling out the numbers. If students recognize the picture before the numbers have all been called, have students tell you the next number to cover up to complete the picture. Activity 3: Locating Number Neighbours This activity reinforces knowledge of the number chart. Have students use a blank number chart. Have a student select a number from 0 to 99. Everyone must find where the number belongs on the number chart. Students must then write the number neighbors. A number that is one more than, one less than, ten more than and ten less than the selected number. Continue until the chart is filled in. Activity 4: Name Patterns This activity introduces a variety of number patterns and relationships and lays the foundation for multiplication. Have students use a blank number chart. Have students begin writing their first name placing one letter in each box. They continue writing their first name until they reach the end of the chart. Next, have students shade in the first letter of their name. They must shade in all of the first letters of their name every time they wrote their name. Have students find other students who have the same shaded pattern. Have students examine the patterns together and discuss what they observe. The shaded patterns are the multiples of 3, 4, 5, 6, 7, 8, 9, 10, etc. depending on how many letters are in the students name.
22 Activity 5: Number Patterns This activity introduces a variety of number patterns and relationships and lays the foundation for multiplication. Have students begin by covering all numbers that have a 2 in either the ones or tens place. Have students discuss the patterns or number relationships they observe. For example, these numbers form a horizontal line and a vertical line. The lines meet at 22 and this number has a 2 in the ones and tens place. The vertical line increases by ten and the horizontal line increases by one. Ask if these relationships are the same for other numbers. Try covering numbers that have a six in either the ones or tens place and observe the patterns and number relationships. Have students cover the following numbers 11, 22, 33, 44, 55, 66, 77, 88, 99. Discuss the patterns and number relationships: One pattern students might notice is that the sums of the digits (11 is = 2; 22 is = 4) are 2, 4, 6, 8, 10, 12, 14, 16, 18. These are all even numbers. Have students cover 1, 12, 23, 34, 45, 56, 67, 78, 89. Ask what they notice about the sum of the digits with these numbers. They may notice that the sums of the digits are 1, 3, 5, 7, 9, 11, 13, 15, 17. These are all odd numbers. Ask students to try the numbers on the next diagonal and see what happens. Have students cover the following numbers and discuss their observation: 5, 14, 23, 32, 41, 50. Students may notice that the sum of the digits all equal 5 and that 5 was the first number covered. Have students cover 7, 16, 25, 34, 43, 52, 61, 70. Notice what the sum of the digits equal. (7) Check to see if this pattern holds for other diagonals. Provide students with an opportunity to discover additional patterns and number relationships that they observe. Activity 6: Counting On This activity lays the foundation for addition. Have students cover numbers as you give the directions. Start with: 22 and count on 3 more 37 and count on 6 more 63 and count on 2 more 54 and count on 1 more 42 and count on 2 more 30 and count on 5 more 43 and count on 2 more 36 and count on 10 more 41 and count on 6 more
23 Activity 7: More Than This activity reinforces the concept of more than and reinforces the concept of addition. Have students cover numbers as you give the directions. Start with: 3 more than 11 2 more than 50 2 more than 83 1 more than 57 5 more than more than 26 8 more than 86 3 more than 73 1 more than 54 6 more than more than 40 5 more than 20 3 more than 50 4 more than 47 9 more than 45 1 more than 55 4 more than 63 Activity 8: Counting Back This activity lays the foundation for subtraction. Have students cover numbers as you give the directions. Start with: 35 and count back 2 47 and count back 4 54 and count back 1 58 and count back 2 27 and count back 2 30 and count back 7 39 and count back 3 57 and count back 3 46 and count back 2 58 and count back 3 39 and count back 5 49 and count back 3 27 and count back 1 29 and count back 5 49 and count back 4 38 and count back 3 Activity 9: Less Than This activity reinforces the concept of less than and reinforces the concept of subtraction. Have students cover numbers as you read each clue. 3 less than 46 1 less than 4 5 less than 58 2 less than 79 6 less than 80 2 less than 65 1 less than 76 4 less than 27 3 less than 36 2 less than 78 3 less than 76 7 less than 20
24 Activity 10: Ten More or Less This activity reinforces an understanding of counting by tens. It also serves as a foundation in place value. Have students place a marker on the number that is 10 more than or 10 less than: 10 more than 2 10 more than more than more than more than 6 10 less than less than more than less than less than more than less than more than more than less than more than less than more than less than more than 57 Activity 11: BINGO This activity reinforces an understanding of place value with tens and ones. Place the numbers 099 in a container. Have a student take a number out and call out the number as ten and ones. For example the number 54 would be 5 tens and 4 ones. Have students cover the number on their number chart that was called out. Students take turns taking numbers out of the container, calling them out, and covering the numbers on their number chart. The game ends when students complete either a horizontal row or a vertical column.
25 Activity 12: Adding and Subtracting on the Number Chart This activity provides an opportunity for students to practice adding and subtracting using the number chart as a tool. Demonstrate how to add numbers using the number chart. ADD: Have students place a chip on 23. Next, ask them how many tens are in 38 (3 tens). Remind them that each of the horizontal rows on the number chart increase by ten so count down 3 rows from 23 (33, 43, 53). Ask what students what the 8 represents in the 38 (the ones units). Remind student s that the vertical columns count by ones so count to the right 8 spaces from the number 53 (54, 55, 65, 57, 58, 59, 60, 61). Students should land on = 61. Demonstrate several more examples and then let students practice adding using their charts. Demonstrate how to subtract using the number chart. SUBTRACT: Have students place a chip on 62. Ask students how many tens are in 34 (3 tens). Count up 3 horizontal rows from 62 (52, 42, 32). Ask students what the 4 in 34 represents (4 ones). Have students count to the left 4 spaces from 32 (31, 30, 29, 28). Students should land on = 28. Demonstrate several more examples and then let students practice subtracting using their charts. Activity 13: The Ultimate Addition Challenge This activity investigates different ways sets of numbers can be added. Following in the footsteps of a great mathematician name Gauss, have student add up all the numbers on the number chart. Before they begin, tell students the story of how one day a teacher asked the students to add together all of the numbers from The teacher hoped that this activity would keep the students busy for some time. However, one student, Carl Friedrich Gauss ( ), solved the problem in less than 2 minutes. How did he do it? Challenge students to figure out how Gauss added all of the numbers so quickly. Gauss summed the integers from 1 to 100 instantly by spotting that the sum was 50 pairs of numbers each pair summing to 101 which equals What would the total be if you added the numbers from 099?
26 Activity 14: Arrow Clues This activity provides reinforcement in counting by tens and ones. Choose a starting number and a secret number and a secret number. Using arrow clues, tell students how to find the secret number. Horizontal arrows move forward or backward one space as they count by ones. Vertical arrows move up or down by tens. For example have students start on 47. Show them the following arrow clues. Student move one space to the right, then another space to the right. Next, students Move down a row four times. They should land on 89. Have students write the equation to describe the moves to get from the starting number to the secret number. For example: = =89 Activity 15: Skip Counting or Naming Multiples This activity reinforces an understanding of skip counting, multiples and multiplication. Have students cover the numbers as they skip count by twos (0, 2, 4, 6, 8, 10 98). Have students identify the pattern. The numbers cover make five straight horizontal lines. These are the even numbers and are the multiples for 2. These numbers all end with 0, 2, 4, 6, 8. Have students cover the numbers as they skip count by threes. Have students identify the patterns. The multiples of 3 form diagonal lines. The sums of the digits are 3, 6, 9, 12, 15, 18. Have students cover the numbers as they skip count by 4, 5, 6, 7, 8, 9, and 10. Discuss the patterns and relationships. Activity 16: Finding Common Multiples This activity reinforces an understanding of skip counting and multiples. Have the students cover the multiples of 3. Next have students cover the multiples of 4. Have students record the numbers that have two chips on them (12, 24, 36, 48, 60, 72, 84, 96). Explain that these numbers are called common multiples. Have students identify the least common multiple (12). Have students identify the greatest common multiple for 3 and 4 shown on the number chart (96). Have students identify other common, least common and greatest common multiples. Activity 17: Prime Time This activity introduces the students to prime numbers. Have students predict how many prime numbers are between 0 and 99. Have students cover the numbers as you give the following directions. Cover all the multiples of 2 beginning with the number 4. Cover all of the multiples of 3 beginning with 6. Cover all the multiples of 4. Cover all the multiples of 5 beginning with 10. Cover all the multiples of 6. Cover all of the multiples of 7 beginning with 14. Identify the remaining numbers (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97) these are the prime numbers. Explain that prime numbers only have two factors, 1 and the number itself. Primes are only divisible by themselves and one.
27 Activity 18: Money Values This activity reinforces the values of coins. Have student cover numbers that have the same value as: 3 nickels 4 nickels and 4 pennies 1 dime, 2 nickels and 6 pennies 6 dimes, 2 nickels, and 3 pennies 2 dimes, 4 nickels and 4 pennies 1 quarter, 1 dime, and 2 pennies 2 quarters, 2 dimes, 1 nickel and 2 pennies 2 quarters, 1 dime, 1 nickel and 1 penny 2 quarters, 2 dimes, 2 nickels and 4 pennies 2 quarters and 1 nickel 1 quarter and 8 pennies 1 quarter 3 quarters, 2 nickels, and 1 penny 3 quarters and 1 dime 19 nickels Activity 19: The Answer Stacks Up! This activity reinforces mathematical thinking. Have children use their number chart to solve the riddle to guess the secret number. Example #1: Cover numbers whose ten s digit is one more than the one s digit. Of the numbers that have been covered, stack a second chip on top of all of the odd numbers. Place a third chip on the stack of numbers divisible by 5. Which number has the most chips stacked on it? That s the answer! Example #2: Cover numbers whose digits are both the same. Place a chip on the stack of numbers whose sum of their digits is even and the product is odd. Stack a chip on numbers whose sum of their digits is 3 less than their products. Which number has the most chips stacked on it? That s the answer!
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