6NS1, 6NS2, 6NS3 Basic Number Sense - comparing and ordering, opposites
A scuba diver is swimming at -25 feet relative to sea level, while a seagull is flying at +15 feet relative to sea level.
Write an inequality to compare the two elevations.
What does 0 mean in this situation?
-25 < 15 or 15> -25
In this situation, 0 represents sea level (the surface of the water).
Four runners on a track team completed a relay race. Their individual times were 12.4 seconds, 11.85 seconds, 13.1 seconds, and 12.05 seconds. What was the team's total combined relay time?
Total Combined Time (Addition): 49.40 seconds or 49.4 seconds
Remember to line up the decimal points to add and subtract decimals!
Simplify and evaluate this long expression by looking for inverse properties and identity properties:
(5/6 x 6/5) x (9.43 x 1) + 0
9.43
Two lighthouse beacons begin flashing at the exact same time. The first beacon flashes every 8 seconds, and the second beacon flashes every 12 seconds. After how many seconds will both beacons flash at the same time again?
Find the LCM of 8 and 12: 24 seconds
A student completed 18/25 of her science project during class. What is this amount as a percent?
18/25 = 0.72= 72%
A submarine research platform uses an elevator that moves up and down relative to the ocean surface, which is labeled as 0. A scientist programs the elevator to go to the opposite of -15 meters.
1. Will the elevator go above the water or below the water?
2. If the scientist cancels the order and commands the elevator to go to the opposite of the opposite of -15 meters, what is the final destination number?
2. -15 meters The opposite of -15 is 15. The opposite of 15 is -15. The elevator ends up right back where it started at -15 meters.
Liam has a monthly data limit of 15.5 gigabytes (GB) on his phone. During the first two weeks of the month, he uses 0.6 GB of data each day.
1. How much data does Liam use in those 14 days?
2. How many gigabytes of data does he have left for the rest of the month?
1. Data Used (Multiplication): 8.4 GB
14 x 0.6 = 8.4
Liam uses 8.4 GB of data in the first two weeks.
2. Data Remaining (Subtraction): 7.1 GB
15.5 - 8.4 - 7.1
Liam has 7.1 GB of data left for the rest of the month.
Evaluate the expression below. State which math properties you used to make the addition easier to solve:
2.35+4.9+7.65
14.9
Properties used: commutative and associative
An auditorium Coordinator is setting up chairs for a concert. There are 40 red chairs and 100 blue chairs. Each row must have the same number of chairs, and each row can only contain one color of chair. What is the greatest number of chairs that can be put in a single row?
Find the GCF of 40 and 100: 20 chairs
A cell phone battery is at 35% power.
1. Write this percent as a fraction in simplest form.
2. Write this percent as a decimal.
1. 35% = 35/100 = 7/20
2. 35% = 0.35
A school store tracks its financial net income each week. A positive number indicates a profit, and a negative number indicates a net loss.
• Week 1: -$25.50
• Week 2: +$40.25
• Week 3: -$10.75
• Week 4: $0.00
• Week 5: -$25 3/4
1. Convert Week 5's income to a decimal.
2. Plot all 5 weeks on a number line. Then list the numbers from greatest to least.
1. -$25.75
2. $40.25 (week 2), 0 (week 4), -$10.75 (week 3), -$25.50 (week 1), -$25.75 (week 5)
Emma is cutting pieces of embroidery string to make friendship bracelets. Each bracelet requires a piece of string that is 3/8 of a yard long. If Emma buys a spool that has 3 yards of string, how many complete bracelets can she make?
Number of Bracelets (Division): 8 bracelets
Divide the total yards by the fraction needed per bracelet:
3 divided by 3/8 = 3/1 x 8/3 = 24/3 = 8
Emma can make exactly 8 complete bracelets.
Evaluate the numerical expression:
42 x (1.5 + 0.5) - 3.2
28.8
A school volunteer has 54 apple slices and 72 cheese sticks. She wants to pack them into identical snack bags for a field trip so that no food is left over.
1. What is the greatest number of snack bags she can make?
2. How many apple slices and cheese sticks will be in each bag?
1. Find the GCF of 54 and 72: 18 snack bags
2. Items per bag: 3 apple slices and 4 cheese sticks
The length of a small insect is 0.08 meters.
1. Write this decimal as a fraction in simplest form.
2. Write this decimal as a percent.
1. 0.08 = 8/100 = 2/25
2. 0.08 = 8%
Four runners are trying to beat their personal baseline times. A negative score means they ran faster than their baseline, and a positive score means they ran slower.
• Jaden: -0.45 seconds
• Amara: +0.12 seconds
• Leo: -1/2 second
• Maya: -0.08 seconds
1. Convert Leo's time change to a decimal.
2. List the runners in order from the most improved (fastest change) to the least improved (slowest change).
3. Write an inequality statement comparing Maya and Jaden. Who did better in the trials?
Sofia earns an allowance of $10.50 each week. She decides to save 2/3 of her allowance every week to buy a new video game that costs $42.00.
1. How much money does Sofia save each week?
2. How many weeks will she need to save before she can afford the game?
Evaluate the numerical expression:
(1/2)3 + (3 divided by 4/5)
3 7/8 or 3.875
Hot dogs come in packages of 10, but hot dog buns come in packages of 12.
1. Find the LCM of 10 and 12: 60 hot dogs and 60 buns
2. 60/10 = 6 packages of hot dogs and 60/12 = 5 packages of buns
A water pitcher is filled to 1 3/5 times its standard capacity. Convert this mixed number into a percent.
1 3/5 = 8/5 = 160/100 = 160%
A meteorologist records the low temperatures in five Canadian cities on the same morning:
1. Decimal Conversions:
• Calgary: -5.5
• Edmonton: -8.0
• Winnipeg: -12.3
• Vancouver: 4.1
• Toronto: -1.5
2. Ordering (Coldest to Warmest): -12.3 < -8 < -5.5 < -1.5 < 4.1
• Interpretation: Winnipeg was the coldest city because -12.3 is furthest to the left on a number line. Vancouver was the warmest because it is the only positive value.
3. Closest to 0: Toronto -1.5 is the closest to 0 because it has the smallest absolute value (|-1.5| = 1.5).
A baker needs 3 1/2 cups of flour for a batch of chocolate chip cookies and 2 3/4 cups of flour for a batch of sugar cookies.
1. How many total cups of flour does the baker need?
2. If the baker starts with a bag containing 8 cups of flour, how many cups will be left over after baking both batches?
1. Total Flour Needed (Addition): 6 1/4 cups
Find a common denominator (4) to add the fractions:
3 1/2 + 2 3/4 = 3 2/4 + 2 3/4 = 5 5/4
Convert the improper fraction: 5 5/4 = 6 1/4 cups
2. Flour Left Over (Subtraction): 1 3/4 cups
8 - 6 1/4 = 7 4/4 - 6 1/4 = 1 3/4 cups
The baker will have 1 3/4 cups of flour left.
Evaluate the numerical expression:
5 x [14.2 - (23 x 0.5)]
51
Express the sum of 45 + 60 as a multiple of a sum of two whole numbers with no common factor. Use the GCF as the outside multiplier.
GCF of 45 and 60 = 15
45 + 60 = (15 x 3) + (15 x 4) = 15(3 + 4)
A runner finished a race in 4 2/3 minutes.
1. Convert the fractional part of this number 2/3 into a decimal.
2. Write the entire time as a decimal using bar notation for any repeating digits.
1. 2/3 = 0.6666....
2. 4 2/3 = 4.6 (line over the 6)