DIRECTIONS AND ANSWERS
The activity cards in the book are designed to fit in a 5x8 inch file box. Cards with tabs for grouping the activity cards by topic are provided in the back of the book. The numeral inside a weight on an activity card indicates where students are to place a weight or weights on a math balance.
ADDITION, 1-8: Students may need to be shown that the addition problem is represented with weights on either side of the balance and the answer with weights on the other side the balance. For activity 4, students should represent 11 as one weight on 10 and one weight on 1.
MULTIPLICATION, 9-18: Multiplication on the math balance is repeated addition. For example, 3x4 on the math balance is interpreted as, “Three weights on 4 are balanced by what?” or “Four weights on 3 are balanced by what?” Students will need to be shown to place as many weights on the ten as possible. Thirty-two can be represented in many ways on the math balance, but when a student is solving 4x8, three weights on the 10 and a weight on the 2 making 32 is the easiest to read. Students can solve activities 17 and 18 without asking about the title—Square Numbers. Should they inquire, square numbers can be explained by having students cut different size squares out of graph paper. They will find that these large squares are made of 1, 4, 9, 16, 25, … little squares.
Answers:
1+3=2x2, 1+3+5=3x3, 1+3+5+7=4x4, 1+3+5+7+9=5x5, 1+3+5+7+9+11=6x6
OTHER NAMES, 19-22: Students are to represent the numbers 12, 16, 18 and 9 on one side of a math balance and record ten ways they balanced each number using as many weights as desired.
TENS, 23-30: These activities are designed to reinforce the concept of 10 in our decimal number system. The second problem on activity 26 is impossible. Students should be encouraged to work on this problem until they are positive that it is impossible.
DIVISION, 31-42: On a math balance, a division problem like 12 ÷ 3 is interpreted as “How many 3s does it take to balance 12?” Many of the problems on activities 41 and 42 have remainders. A child solving 19 ÷ 5 discovers that three 5s will not balance 19 and that four 5s are too heavy. However, three 5s and one 4 will balance 19. This can be expressed as 3 R4.
PLACE VALUE, 43-46: On all four place value activities, students are to balance the numbers at the right of the page using only the weights designated as shown in the table on the next page.
43 The numbers from 1 to 15 are to be balanced with weights on the 1, 2, 4, and 8.
44 The numbers from 1 to 15 are to be balanced with weights on the 1 and 5.
45 The odd numbers from 1 to 27 are to be balanced with weights on the 1, 3, and 9.
46 The multiples of 5 from 5 to 70 are to be balanced with weights on the 1 and 8.