MULTIPLICATION LOGIC, 59-66: Students who place the weights on a math balance in a logical, systematic manner will be able to solve these problems..
Answers:
59 1. 2x3=3x2 2. 2x6=3x4 3. 2x9=3x6
60 1. 2x6=4x3 2. 2x8=4x4
61 1. 3x4=4x3 2. 3x8=4x6
62 1. 4x5=5x4 2. 4x10=5x8
63 1. (4x2)+2=5x2 2. (4x7)+2=5x6
64 1. Many possible answers
65 1. 3x1=(2x1)+1 2. 3x3=(2x4)+1 3. 3x5=(2x7)+1 4. 3x7=(2x10)+1
66 1. (4x1)+2=6x1 2. (4x4)+2=6x3 3. (4x7)+2=6x5 4. (4x10)+2=6x7
BALANCE, 67-76: Ask students to record their estimates before checking them on a math balance.
Answers:
67—No, yes; 68—No, yes; 69—10, 1; 70—7, impossible; 71—4, 3; 72—3, 3; 73—4, 9;
74—12, 3; 75—4, 5; 76—9, 8.
AND/OR LOGIC, 77-86: Each of these activities consists of three questions. For example, activity 79 asks that 16 be balanced with weights on 3 and 4, then with weights on 3 or 4, but not both, then with no weights on the 3 or 4. Possible answers include:
77 2+3+3=8, 4x2=8, 4+4=8 82 (5x2)+(3x5)=25, 5x5=25, 7+8+10=25
78 2+2+2+3+3=12, 4x3=12, 7+5=12 83 3+3+3+3+4+5=21, 7x3=21, 6+7+8=21
79 3+3+3+3+4=16, 4x4=16, 9+5+2=16 84 3+4+5+5+5+5=27, 9x3=27, 10+10+7=27
80 (5x3)+5=20, 5x4=20, 10x2=20 85 6+5+5+4+4+4=28, 7x4=28, 9+9+2+8=28
81 9+9+6=24, 6x4=24, 3x8=24 86 4+4+5+5+6+6=30, 5x6=30, 9+9+9+3=30
FACTORS, 87-94: The factors of 12, 13, 14, 15, 16, and 18 are recorded individually before this information is listed on activity cards 93 and 94. For activities 87-92, the students are to check “yes” or “no” if the numeral at the top of the page can be balanced with weights only on 1, then with weights only on 2, etc. Activity 93 asks students to color all the yes answers on the chart. For activity 94, students are to list the common factors. For example, the common factor (divisor) for 11 and 12 is 1, and the common factors (divisors) for 12 and 14 are 1 and 2.
Answers:
12 and 13—1 15 and 12—1, 3 16 and 12—1, 2, 4 14 and 12—1, 2
12 and 14—1, 2 15 and 13—1 16 and 13—1 14 and 13—1
12 and 15—1, 3 15 and 14—1 16 and 14—1, 2 14 and 15—1
12 and 16—1, 2, 4 15 and 16—1 16 and 15—1 14 and 16—1, 2
12 and 18—1, 2, 3, 6 15 and 18—1, 3 16 and 18—1, 2 14 and 18—1, 2
STUDENT DESIGNED ACTIVITY CARDS: The last three pages are for student use in designing activity cards for fellow students or cross-age tutoring. To this end, make multiple copies of the pages and provide scissors and glue for cutting and pasting. A friend of the student designer is to sign the last page to indicate that he or she has done the activity on a math balance.