Day 1(8/24) - Problem Solving We were introduced to the use of sticks and cubes to problem solve. Students learn best in different and unique ways. When problem solving, we have to 1. understand the problem 2. devise a plan (strategize) 3. carry out the plan 4. reflect ( does it work?)
Problem Solving Strategies: 1. Look for a pattern 2. Examine a related Problem 3. Make a diagram 4. Work backwards 5. Use guess and Check 6. Write and equation
A student was making sandwiches 13 of the sandwiches had a slice of cheese. 14 had a slice of salami. 13 had a slice of tomato. 8 had a slice of cheese & a slice of tomato. Only 3 had a just a slice of salami. 5 had a slice of tomato, a slice of cheese, & a slice of salami. 8 had a slice of tomato & a slice of salami. How many sandwiches did the student make? In our groups we attempted to figure out the best way to solve this problem. Then we shared how we came up with the answer. After sharing, the instructor demonstrated how to solve the problem with a ven diagram. The total was : 21 sandwiches
Week 3
Day 1 (8/31)- intro to Base 10, 5, 3 -Base 10- Digits used: 0,1,2,3,4,5,6,7,8,9 numeral system: base- 10 system expanded notation = powers of ten
3. Associative Property of Addition (a+b) +c = a + (b+c)
Addition :
1. Standard American Algorithm 576 + 279 ---------- - Start from the one's place (R to L) - 6+ 9 =15 - write the 5 in the ones;add the 1 up of the 7
2. Partial Sums Algorithm - (R to L) -add starting at the ones - when the total of the row equals more than the place value, take it down to the total vs putting it above the next place value
3. Partial Sums - Emphasis on Place Value -(R to L) - add starting at the ones - when adding, place the total below the equal sign but put the actual total instead of putting it above the next place value
4. Left to Right Algorithm -(L to R) - add in an expanded form kind of way
5. Expanded Notation - (R to L) - add in expanded notation terms - Place value explicit
6. Lattice Algorithm - (R to L) - draw a lattice box and add
Day 2 (9/9) - Subtraction Subtraction - known as "take away", "missing addend" , - "I have four cookies, how many more do I need to get from the cookie jar so I have a total of 7?"
4 + 🍪 = 7 -4 -4 --------------- 🍪 = 3
- "I have 4 cookies, Skyler has 3 cookies, how many more cookies do I have?"
**number line example ** **Clock example** **array 3 x 8 ***
Commutative Property of Multiplication 3 x 8 = 8 x 3
Identity Property of Multiplication a x 1 = 1
Zero Property Of Multiplication a x 0 = 0
Associative Property of Multiplication (a x b ) x c = a x (b x c)
Distributive Property of Multiplication 3 x (5 + 2) = (3 x 5 ) + (3 x 2) ↓ ↓ partial product → When you multiply a number by a sum, the product remains the same
Multiplication Algorithms
1. Standard Algorithm of Multiplication → regular way of multiplying in the U.S
2. Place Value 23 4x 3 = 12 x 14 4 x 20 = 80 -------- 10 x 3 = 30 322 10 x 20 = 200
Head: 50+50 + 70 + 130 + 20 l l l l l l 100 200 = 320 4. Breaking Up & Bridging 67 + 36
Head: 67 + 36 l l _l_ l l 30 6
67 + 30 = 97 +6 ---------------- 103
Subtraction: 1. L -> R a) 47-32 = 15
Head: 40-30 = 10 7-2 = 5 ----------------- = 15
2. Breaking up and Bridging 67 - 36 = 31
Head: 67 - 36 l l l l l 30 6
67 - 30 = 37 -6 ---------------- 32
3. Compensation 47 - 29 = 18
Head: 47-30 = 17 +1 ——————————----- 18
4. Compatible Numbers:
170 - 50 - 30 - 50 =
Head: 170+ 30 = 140 50+50 = 100 140-100= 40
Multiplication: 1. Compatible numbers 2 x 9 x 5 x 20 x 5
Head: 5 x 2 = 10 20 x 5 = 100 9 x 1000 = 9,000
2. L -> R 3x 123
Head: 3x(100+20+3) 300+60+9 = 369
Division: 1. Compatible Numbers
105 ÷ 3
Head: 150 ÷ 3 = l__l _l__ l l 90 +15
90/3 = 30 > 35 15/3 = 5
TEST REVIEW***
Week 8
Day 1: 10/05 - Divisibility and Factors -
Divisibility: “a” is divisible by “b”, if there is a number “c” that meets the requirements EX: 10 is divisible by 5 b x a = c 5 x 2 = 10
Important Terminology: *10 is divisible by 5 or 5 divides 10 *5 is a divisor of 10 *5 is a factor of 10 *10 is. multiple of 5
Divisibility Rules: —————————- Ending By 2: 0,2,4,6,8
By 5: 0,5
By 10: 0
(a number is divisible by 2 if it ends in a 0,2,4,6,8; 5 is divisible if a number ends in 0,5; 10 is divisible by a number if it ends in 0)
Sum of Digits: By 3: *when the sum of the digits are divisible by 3* EX: 543 5+4+3 = 12/3 = 4
By 9: * when the sum of the digits are divisible by 9 ; just like #3*
Other: by 6: if it is divisible by both 2&3 EX: 3702
Last Digits: by 4: if the last two digits are divisible by 4 EX: 3,728 28/4
by 8: if the last three digits are divisible by 8
Special Numbers: by 7: EX: 826 step 1 - (double last digit) 6x2=12 step 2 - (take your first two digits from your given number and and subtract it from step 1) 82-12 = 70 *70 is divisible by * *if there is a bigger number repeat the first two steps*
Chop-Off: by 11: -Chop off last two digit numbers - add them to the remaining number(s) - repeat EX: 29,194 291 +94 = 385 ; 85+3 = 88/11=8
Prime numbers: *have two factors* when it has factors of 1 and itself
Prime #s 1-60: 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
0: not a prime - not composite 1: not prime- not composite
0: additive identity element 1: multiplicative identity element
Day 2: 10/07 - Prime Numbers -
Prime #s:2,3 5, 7, 11,13,17,19,23, 29,31 37, 41,43,47,53,59
GCF: greatest common factor LCM : least common multiple
List Method: 24: 1,2,3,4,6,8,12,24 36:1,2,3,4,6,9,18,36 GCF: 12
**you use common factors when you simplify EX: 25/100 ÷ 5/5 = 5/20 ÷ 5/5 = 1/4 vs. if you use your GCF 25/100 ÷ 25/25 = 1/4
24: 24, 48, 72, 96 36: 36,72 LCM: 72
**improper fraction 10/15 + 9/15 = 19/15
Prime Factorization : 20:1,2,4,5,10
20 20 / \ / \ 4 5 2 10 /\ /\ 2 2 2 5
2 x 2 x 5 = 22x 5
**If you take your found GCF and multiply by the remaining #s = LCM EX: 24: 2 x 2 x 2 x 3 36: 2 x 2 x 3 x 3 GCF: 12 after doing prime tree:
24: (23 x 3) 36: (22 x 32)
12 x 2 x 3 = 72
** list method is preferred for students due to the fact that if they mess up trying to find the GCF/LCM they will mess up their GCF/ LCM (both numbers)**
Week 9
10/11 NO SCHOOL
10/ 14 - FRACTIONS -
Fraction: is a part of a whole; it is a symbol that represents a part to a whole - quotient -part of a whole - division - ratio (to be a fraction - part to whole not part to part) EX: 3/10 3= part 10 = whole
30 balloons 3 red 27 blue
3/30 27/30
How you can demonstrate fractions to students: - surface area (region) -shading - length - folding a paper - number line - line segment
Mistakes made by students: 1/2 < 1/8
2/3 + 1/5 = 3/8
Practice: 4/7 or 5/7
4/5 or 4/9
3/7 or 5/ 8
9/10 or 3/4
Wholes: 8/8, 6/6, 4/4, 3/3, 1/2
what did you discover? When you use all the pieces you have 1 whole numerator = denominator = 1 whole
- Find the least common multiple by finding the multiple
** Yard example (look back at notes)
Day 2: 10/21 - In Class Fraction Problems -
1. Jim, Ken, Len, and Max have a bag of miniature candy bars from trick-or-treating together. Jim took ¼ of all the bars, and Ken and Len each took 1/3 of all the bars. Max got the remaining 4 bars. How many bars were in the bag originally? How many bars did Jim, Ken, and Len each get?
Jim= 12 Ken and Len = 16 each Max = 4 total: 48
2. Jim, Ken, Len, and Max have a bag of miniature candy bars from trick-or-treating together. Jim took ¼ of the bars. Then Ken took 1/3 of the remaining bars. Next, Len took 1/3 of the remaining bars, and Max took the remaining 8 bars. How many bars were in the bag originally? How many bars did Jim, Ken, and Len each get? How is this problem (with regards to fractions) different from Problem 1?
Jim= 6 Ken= 6 Len= 4 Max= 8
3. 3/4 of a pie in refrigerator John ate 2/3 left over How much did he eat?
John ate 1/2 of the pie
4. Three-fourths of the class are girls. Two-thirds of the girls have black hair. What fraction of the class is female and dark-haired?
half of the class have dark hair
**Look back at notes
Week 11
Day 1 : 10/26 - Fraction Problems in class -
1. 3/4 cups per serving 2 and 2/3 needs to prepare, how many cups of oil will she need?
2 cups
2. 3/4 pizza 1/2 ate How much did he eat? He ate 3/8 of the pizza
3. if 4 * = 2/7 of the whole ** ** ** ** ** ** ** 2**= 1/7 whole of 14 stars total
Day 2: 10/28 - HW & TEST Review/ Mind-map in Class
1. 1/3 cups of sugar needed to make 2 loaves How many cups of sugar are needed for 3 loaves?
- 1/2 a cup of oil to make 3 loaves
2. Sometimes you have to simplify when adding fractions with a least common denominator
