Directions: Using the digits 0 to 9, no more than one time each, to fill in the boxes to decompose 1 1/10.

Where do you think you could use the 0?

2/10 + 3/10 + 5/10 + 10/100

1/10 + 3/10 + 5/10 + 20/100

1/10 + 2/10 + 5/10 + 30/100

1/10 + 2/10 + 3/10 + 50/100

1/10 + 3/10 + 5/10 + 20/100

1/10 + 2/10 + 5/10 + 30/100

1/10 + 2/10 + 3/10 + 50/100

Source: Christine Jenkins

]]>Directions: Use the digits, 0 through 9, without repeats, to complete the equation below:

How do you add numbers that are in decimal form?

Source: Shaun Errichiello

]]>Directions: Use the digits 0 through 9, without repeats, to solve the problem below.

How do you divide by a fraction?

Source: Shaun Errichiello

]]>Directions: Using the numbers 1 through 9 (without repeating), fill in the boxes to create a function such that at x = 2, the derivative (at that point) is closest to the value of 449.

Which blank has the LARGEST effect on the output?

How does the POWER RULE help you to get a possible solution?

In order left to right: {1,7}

Source: Gregory L. Taylor, Ed.D.

]]>Directions: Using the numbers 1 through 9 (without repeating), fill in the boxes to create a function such that at x = 2, the derivative (at that point) would fall in the interval of {0, 48}

One might consider solving the equation at the extremes and means of the interval of solutions

Sometimes small numbers are easier to start with

Reading left to right in image one (near largest I believe) solution is: {4, 3}

Source: Gregory L. Taylor, Ed.D.

]]>Directions: Using each of the digits 0-6 only once, make two equivalent ratios (also known as a proportion).

Can multiples help us find equivalent fractions?

5/10 = 23/46 or

5/23 = 10/46

5/23 = 10/46

Source: AnneMarie Untalan

]]>Directions: Find values for a and b that will make the expressions equivalent, assuming that a does not equal b.

How does each base’s factors affect the equivalence?

When a and b are 2 and 4 (does not matter which is which), then 2^4 = 4^2

Source: Owen Kaplinsky

]]>Directions: Using the digits 1 to 9, at most one time each, make two compound inequalities that are equivalent to 2 ≤ x < 4.

How does changing the coefficient affect the resulting value?

How does changing the constant next to x affect the resulting value?

How does changing the constant next to x affect the resulting value?

There are many answers including:

4 ≤ 1x + 2< 6 and 5 ≤ 2x + 1< 9.

Source: Robert Kaplinsky

]]>Directions: Using the digits 1 to 9, at most one time each, make a compound inequality that has the largest interval.

How does changing the coefficient affect the resulting value?

How does changing the constant next to x affect the resulting value?

How does changing the constant next to x affect the resulting value?

The largest possible interval is just less than 7 units long. You can get that from inequalities like:

2 ≤ 1x + # < 9

# can be any of the remaining numbers as it acts like a translation and doesn’t affect the size of the interval.

Source: Robert Kaplinsky

]]>Directions: Make the largest (or smallest) absolute difference by filling in the boxes using the whole numbers 1 through 9 no more than one time each.

What are the biggest and smallest numbers you can make with these digits in scientific notation?

Try thinking of the numbers you create on a number line.

Try thinking of the numbers you create on a number line.

Largest: 8×10^9 – 2×10^1

Smallest 3×10^2 – 9×10^1

Smallest 3×10^2 – 9×10^1

Source: Marie Isaac

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