Test #2 Review

Bases

100

Discuss the meaning of the following numbers in their place value systems:

a) 312 (four)

b) 183 (seven)

a) 3 groups of sixteen, 1 group of four, and 2 groups of one. 

b) This number does not exist in base seven. 

200

What two numbers come before these numbers:

a) 343 (six)

b) 186 (nine)

a) 341 (six), 342 (six)

b) 184 (nine), 185 (nine)

300

What two numbers come after these numbers:

a) 123 (four)

b) 64 (seven)

a) 130 (four), 131 (four)

b) 65 (seven), 66 (seven)

400

Determine which solution represents 1312 (five):

_{a) 3 (five) cubes, 1 (five) flat, 5 (five) rods, 2 (five) small squares}

_{b) 1 (five) cube, 3 (five) flats, 1 (five) rod, 2 (five) small squares}

*Not supposed to change bases!*

a) This number does not exist in base five.

b) This number represents 1312 (five) because take 1 x 1000, 3 x 100, 1 x 10, and 2 x 1 and add those products together. 

500

Two children were given different amounts of skittles in their goodie bags. The first child counted 43 (five) and the second child counted 52 (six). Whose goodie bag contained more skittles? 

The second child had more skittles in their goodie bag. 

Bases

100

Use <, >, = to compare these numbers in their place value systems: 

a) 153 (six) and 127 (eight)

b) 42 (five) and 22 (three)

a) 153 (six) < 127 (eight)

b) 42 (five) > 22 (three)

200

What is wrong with the numeral 828 (eight)?

This number does not exist in base eight. 

300

How many exact and whole sixteens are in the number 231321 (four)? 

Exact: 2313.21 exact sixteens

Whole: 2313 whole sixteens 

400

Represent 21 (four) in two different ways. Keep your answers in base four. 

Various Answers!

Some Include:

-2 rods and 1 small square

- 21 small squares

500

Two students were each given different bags of pencils to count. The first student counted 156 (seven) and the second student counted 454 (six). Whose bag contained more pencils?

The second student had more pencils. 

Addition

100

Write a word problem for: 

x + 22 = 42

Various Answers!

Sample Answer:

Kristina has some jolly ranchers. She gets 22 more jolly ranchers and now she has 42 jolly ranchers in total. How many jolly ranchers did she start with?

200

Kristina has 16 skittles and Hannah gives her 53 more skittles. How many skittles does Kristina now have?

Solve using base ten pieces.

Provide a symbolic representation. 

Show visual. Kristina has 69 skittles. 

^{Base ten pieces would look like: 1 rod and 6 small squares plus 5 rods} 

^{and 3 small squares.} 

^{Symbolic Representation: 6 + 3 = 9}

                                    ^{10 + 50 = 60}

                                    ^{9 + 60 = 69 skittles}

300

Show two different ways (neither must be traditional algorithm) to add 75 + 67. 

Various Answers!

An example could be 70 + 60 = 130, 5 + 7 + 12, 130 + 12 = 142. 

Another example could be through a picture.

400

Will this student's method produce the correct result of 92 + 134? Why or why not?

^{100 + 130 = 230}

^{230 - 8 = 222}

^{222 + 4 = 226}

Yes! The student added 8 to 92, and subtracted 4 from 134 to make those numbers easier to add together. Then, the student subtracted 8 because they added 8 earlier in the problem. Finally, the student added 4 because they subtracted 4 earlier in the problem. 

500

In adding 135 and 935, will the strategy of adding 1000, 60, and 10 give the right answer? If so, why? 

Yes! This is the adding by place value method. 100 + 900 = 1000, 30 + 30 = 60, and 5 + 5 = 10, then add all of those sums together. The answer is 1070. 

Subtraction

100

Write a word problem for:

42 - x = 10 

Various Answers!

An example:

Sabrina has 42 skittles and gives some to her friend. Now, Sabrina has 10 skittles left. How many pieces of skittles did Sabrina give to her friend?

200

How many more skittles does Hannah have than Kristina? Given that Hannah has 53 more skittles than Kristina's 16 skittles. 

Solve using base ten pieces.

Provide a symbolic representation. 

Hannah has 37 more skittles than Kristina. 

_{Base ten pieces would look like: 5 rods and 3 small squares minus 1 rod} 

_{and 6 small squares.}

_{Symbolic Representation:}

_{13 small squares - 6 small squares = 7 small squares}

_{4 rods - 1 rod = 3 rods}

_{3 rods + 7 small squares = 37 skittles}

_{Therefore, 3 rods and 7 small squares is the answer. Otherwise, known} 

_{as 37 skittles Hannah has more than Kristina.} 

300

Find two different ways to find the difference of 143 - 79. Do not use the traditional algorithm. 

Various Answers!

Some examples: Visual

143 - 79 = Difference from 9 to 3 is -6, Difference from 70 to 40  is -30, Difference from 000 to 100 is +100. The overall difference is 64. 

400

What did the student do correctly or incorrectly when solving 126 - 34? 

^{126-34 = 100} 

^{100 - 10 = 90}

^{90 + 2 = 92}

^{So, the answer is 92.} 

The student is correct. They started subtracting by the difference of the bottom to top. 

500

Is this student's method correct or incorrect when solving for 532 - 136? Why or why not? What is the name of the method?

500 - 100 = 400, 30 - 30 = 0, and 2 - 6 = 4 Therefore, the answer is 404. 

The student is incorrect. This method is called partial differences. The student started finding the difference of each place value from top to bottom, except when they got to the ones place they took the difference from bottom to top. 

Multiplication

100

Solve for 45 x 12 at least 2 different ways. Do not use a calculator or the traditional paper and pencil algorithm. 

Answers vary! The overall answer should be 540.

Some Sample Answers:

Visual

Distributive Property

Four Boxes

200

Without using a calculator or traditional paper and pencil algorithm, compute the product in at least two different ways: 35 x 36

Answers vary! The overall answer should be 1260.

Some Sample Answers:

_Visual

_{Distributive Property}

_{Four Boxes}

300

Is a base ten visual picture of 16 x 4 the same as 4 x 16? Why or why not?

No. 16 x 4 means 16 groups of 4. 4 x 16 means 4 groups of 16.