Order of operations, properties, and multi-step problems
Predict
Evaluate each expression. Which operation comes first in each? Pause the video and work them out.
Show me
10 and 38. Multiplication starts the first; the exponent starts the second.
Quick check
What comes after brackets in the order of operations?Show me
Exponents.
Use the distributive property: 7 × 12 = ?Show me
84 — 7 × 10 + 7 × 2 = 70 + 14.
Blue to white is 2 : 3. How much blue in 15 L?Show me
6 L — 5 parts of 3 L, and blue is 2 parts.
Recap. Brackets, exponents, multiply and divide left to right, then add and subtract left to right. Use operation properties and inverse operations to simplify and check multi-step work.
B2.2 Math facts: common equivalents
Percent, fraction and decimal equivalents
Predict
Give each as a percent, from recall. Pause the video and write your answers.
Show me
75%, 12.5% and 40%.
Quick check
1/5 as a percent?Show me
20% — five fifths make 100%.
1/8 as a decimal?Show me
0.125 — half of 0.25.
Is 1/3 equal to 33%?Show me
No — it is exactly 33 1/3%.
Recap. Learn a few anchors — halves, quarters, fifths, tenths, eighths — and build the rest from them. One third is exactly 33 1/3%.
B2.3 Mental math with percents
Increasing and decreasing by a percent, mentally
Predict
A jacket costs 60 dollars. Take 25% off, then add 10% tax on the sale price. What do you pay? Pause the video and work it out.
Show me
45 dollars, then 49.50 dollars.
Quick check
How do you find 5% of a number?Show me
Find 10%, then halve it.
Increase 80 by 25%.Show me
100 — 25% of 80 is 20.
What does increasing by 100% do?Show me
It doubles the number.
Recap. Find 10% by dividing by 10 and 1% by dividing by 100. Halve for 5%, 50% and 25%. Add the percent to increase; subtract to decrease.
B2.4 Adding and subtracting integers
Adding and subtracting integers
Predict
The tray shows −6. Subtract 9: nine positive counters must be removed. What must you do first, and what is left? Pause the video and decide.
Show me
Add nine zero pairs first. Removing the nine positives leaves −15, so −6 − 9 = −15.
Quick check
What is a zero pair worth?Show me
Zero — one positive and one negative cancel.
−3 + (−4) = ?Show me
−7 — same signs: add the sizes, keep the sign.
4 − (−3) = ?Show me
7 — subtracting −3 is adding 3.
Recap. Adding a positive moves right; adding a negative moves left. Zero pairs are worth zero, so add them when you need counters to remove. Subtracting a number is adding its opposite.
B2.5 Adding and subtracting fractions
Adding and subtracting fractions
Predict
Work out each. Where does the second one need regrouping? Pause the video and write your answers.
Show me
11/12 and 7/12. The second regroups 2 4/12 as 1 16/12.
Quick check
Why is 2/7 + 3/7 not 5/14?Show me
The unit stays sevenths — only numerators are added.
A common denominator for thirds and quarters?Show me
12 — the first multiple of both.
3 1/4 − 1 1/2 = ?Show me
1 3/4 — regroup 3 1/4 as 2 5/4.
Recap. Rewrite with a common denominator, then add or subtract numerators. Handle whole numbers separately, and regroup a whole when a fraction is too small to subtract from.
B2.6 Greatest common factor and lowest common multiple
Greatest common factor and lowest common multiple
Predict
Find each. Pause the video and work them out.
Show me
GCF 6 and LCM 30.
Quick check
Is 1 a prime number?Show me
No — a prime has exactly two factors.
GCF of 84 and 144?Show me
12 — shared primes 2 × 2 × 3.
LCM of 4, 6 and 10?Show me
60.
Recap. GCF: multiply the shared primes, or find the largest shared factor. LCM: use every prime the most times it appears, or list multiples.
B2.7 Exponential notation
Exponents
Predict
Write the first with an exponent. Evaluate the second. Pause the video and write your answers.
Show me
2⁴ and 27.
Quick check
What does the exponent count?Show me
How many times the base is a factor.
2⁵ = ?Show me
32.
Write 5 × 5 × 5 with an exponent.Show me
5³.
Recap. The base is the repeated factor; the exponent counts it. 3⁴ is not 3 × 4, and 2⁵ is not 5². Squared means exponent two; cubed means exponent three.
B2.8 Multiplying and dividing fractions
Multiplying and dividing fractions
Predict
Work out each. Which result is larger than the fraction you started with, and why? Pause the video and write your answers.
Show me
2/5 and 15/8 = 1 7/8. The division grew, because the divisor is less than one.
Quick check
1/2 × 2/3 = ?Show me
1/3 — the overlap is 2 of 6 pieces.
What is the reciprocal of 4/5?Show me
5/4.
2/5 ÷ 4/5 = ?Show me
1/2 — 2/5 × 5/4 = 10/20.
Recap. Multiply numerators and denominators. To divide, multiply by the reciprocal of the divisor, and check by multiplying back. For positive numbers, a fraction less than one shrinks a product and enlarges a quotient.
B2.9 Multiplying and dividing decimal numbers
Multiplying and dividing decimal numbers
Predict
Work out each. How many decimal places does the first product have before simplifying? Pause the video and write your answers.
Show me
0.3 (0.30 before dropping the final zero) and 3.
Quick check
1.2 × 0.4 = ?Show me
0.48 — tenths × tenths gives hundredths.
First step in dividing by a decimal?Show me
Scale both numbers until the divisor is whole.
0.36 ÷ 0.04 = ?Show me
9 — 36 ÷ 4.
Recap. Estimate first. To multiply, multiply as whole numbers and add the decimal places. To divide, scale both until the divisor is whole. Check against the estimate.
B2.10 Proportional and non-proportional situations
Proportional and non-proportional situations
Predict
Which situation is proportional? Explain using one of the two tests. Pause the video and decide.
Show me
The apples. The gym has a joining fee, so zero months still costs 20 dollars.
Quick check
Name one test for a direct proportional relationship.Show me
A constant oriented ratio for non-zero pairs, or zero input pairs with zero output.
5 kg cost 12 dollars. What is the unit rate?Show me
2.40 dollars per kg.
Why is a taxi fare with a start fee not proportional?Show me
Zero distance still costs the start fee.
Recap. A direct proportional relationship has a constant oriented ratio for non-zero pairs and pairs zero input with zero output. Solve with a unit rate or scale factor.