Alpha School · Math · built 2 October 2026
This guide covers the eight skills that the Grade 3 math test leans on hardest. Each one starts with something you can already do, adds one new move, and then gives you practice that climbs.
Every question here is new. None of them is from a test. The numbers and stories are different on purpose, so what you are practicing is the method, not the answer.
How to use it: answer a question, press Check, then read the answer even when you were right. The answer tells you where the wrong choices come from, and that is the part worth knowing on test day. Your work saves in this browser, so you can stop and come back.
In this guide
What is 300 + 40 + 2?
300 is 3 hundreds. 40 is 4 tens. 2 is 2 ones.
300 + 40 + 2 = 342.
Each number in that sum fills one place. That is all expanded form is: the number taken apart, one place at a time.
Now a bigger one, with a hole in it.
50,000 + 2,000 + 60 + 7
Ten thousands: 5. Thousands: 2. Hundreds: nothing is listed. Tens: 6. Ones: 7.
The hundreds place still exists. It needs a digit, so it gets a 0.
50,000 + 2,000 + 60 + 7 = 52,067.
The same number can be described in words more than one way. 52,067 is "fifty-two thousand, sixty-seven". It is also "5 ten thousands, 2 thousands, 6 tens, and 7 ones", and "52 thousands and 67 ones". A description is wrong only if one of its pieces lands in the wrong place.
To put numbers in order, count the digits first. More digits means a bigger number. If two numbers have the same number of digits, compare from the left, one place at a time, and stop at the first place that differs.
Every place gets a digit. If a place has nothing in it, write 0 to hold it.
To order: more digits wins; same digits, compare from the left.
Skipping the empty place. 50,000 + 2,000 + 60 + 7 looks like four pieces, so it is tempting to write four digits: 5,267. But the hundreds place is still there, empty. Writing a 0 in it is what keeps the 5 in the ten thousands place.
Reading a description too fast. "3 ten thousands, 6 thousands, 4 tens, 8 ones" and "30,000 + 6,000 + 400 + 8" look alike. One of them has moved the 4 into the hundreds. Check each piece against its place.
Practice
What is 600 + 50 + 3?
653
6 hundreds, 5 tens, 3 ones. Each piece fills one place.
Which expanded form shows 40,315?
40,000 + 300 + 10 + 5
40,315 is 4 ten thousands, 0 thousands, 3 hundreds, 1 ten, 5 ones. The thousands place is empty, so nothing is written for it.
"40,000 + 3,000 + 10 + 5" puts the 3 in the thousands; that is 43,015. "4,000 + 300 + 10 + 5" is 4,315, one digit short. "40,000 + 300 + 15" has not finished taking the number apart: 15 is a ten and a five, two places.
The expanded form of a number is 70,000 + 800 + 9. What is the standard form?
70,809
Ten thousands 7. Thousands: empty, write 0. Hundreds 8. Tens: empty, write 0. Ones 9.
7,809 skipped the empty thousands place, so every digit slid down one place. 70,089 put the 8 in the tens. 78,009 put the 8 in the thousands.
Which answer choice does NOT describe the number 36,048?
30,000 + 6,000 + 400 + 8 does not describe 36,048.
Check each piece against its place. In 36,048 the 4 is in the tens place, so it is worth 40, not 400. That sum is 36,408.
The other three are all 36,048 said a different way: in words, place by place, and as 36 thousands plus 48.
What is 400 + 300?
4 hundreds plus 3 hundreds is 7 hundreds.
400 + 300 = 700.
So 425 + 300 is 725. Adding hundreds leaves the tens and ones alone.
Test stories usually have two steps. Here is one.
Maya had $348 in her account. She earned $125 more. Then she spent $160 on a skateboard. How much is in her account now?
Earned more: add. Spent: minus. Write the equation in the order the story happens.
348 + 125 − 160 = □
Now one step at a time.
348 + 125 = 473.
473 − 160 = 313.
Maya has $313.
When the test asks "which equation can be used", it wants that first line, before any arithmetic. When it asks for the amount, it wants the last line.
One story, one step at a time. "More", "earned", "put in" means add. "Spent", "took out", "gave away" means minus. Write the equation in story order, then work it down line by line.
Stopping after one step. 473 is a real number from the story, and it will be one of the choices. It is not the answer to the question asked.
Subtracting the small digit from the big digit in each column. In 612 − 478, the ones column is 2 minus 8. You cannot take 8 from 2, so you rename a ten. A student who writes 8 minus 2 = 6 in the ones gets an answer that is too big, every time.
Practice
Two quick ones.
a) 736 and b) 236
Only the hundreds change. 5 hundreds plus 2 hundreds is 7 hundreds. 5 hundreds minus 3 hundreds is 2 hundreds.
Jonah had 215 stickers. He got 140 more for his birthday. Then he gave 85 to his sister. Which equation can be used to find how many stickers Jonah has now?
215 + 140 − 85 = □
Got more: add 140. Gave away: minus 85. Story order.
"215 − 140 + 85" has the two operations backwards. "215 + 140 + 85" treats giving away as getting. "215 − 140 − 85" treats his birthday as a loss.
Now work Jonah's equation. How many stickers does he have?
270
215 + 140 = 355.
355 − 85 = 270.
If you got 355, you stopped after the first step.
Priya's class collected 612 cans in September and 478 cans in October. How many more cans did the class collect in September than in October?
134
"How many more" is a difference: 612 − 478.
Ones: 2 minus 8 cannot be done, so rename. 12 minus 8 = 4. Tens: now 0 minus 7, rename again. 10 minus 7 = 3. Hundreds: 5 minus 4 = 1.
612 − 478 = 134.
266 is what you get by taking the smaller digit from the bigger one in every column, without renaming. 234 renamed the ones but not the tens. 1,090 added the two months together.
Mixed check 1
These two questions do not say which skill they use. Decide the method first, then answer.
Which list shows these numbers in order from greatest to least? 9,870 · 10,089 · 9,978 · 10,809
Method: Place value
10,809; 10,089; 9,978; 9,870
Five-digit numbers beat four-digit numbers, so both 10-thousands come first. 10,809 beats 10,089 in the hundreds. Then 9,978 beats 9,870 in the tens.
The second choice is least to greatest. The third compared first digits only and put the 9s first. The fourth mixed the two groups.
Kai had $507. He spent $189 on a bike helmet. Then he earned $45 mowing a lawn. How much money does Kai have now?
Method: Add and subtract
$363
Spent: minus. Earned: add. 507 − 189 + 45 = □.
507 − 189 = 318.
318 + 45 = 363.
318 stopped after one step. 273 took the 45 away too. 741 added everything.
There are 3 boxes of crayons with 5 crayons in each box. How many crayons?
Count by fives, once for each box: 5, 10, 15.
3 × 5 = 15.
3 groups, 5 in each group, 15 in all. That is what the × sign says.
The test likes to hide equal groups inside a table.
| Boxes | Crayons |
|---|---|
| 1 | 5 |
| 2 | 10 |
| 3 | 15 |
| 4 | 20 |
Each row is boxes × 5. 1 × 5 = 5. 2 × 5 = 10. 4 × 5 = 20.
A table that says 1 → 6, 2 → 7, 3 → 8 is adding 5 to the box number. That is not groups of 5.
The other place multiplication hides is the phrase times as many.
There are 4 red pens. There are 3 times as many blue pens as red pens.
3 × 4 = 12. There are 12 blue pens.
"3 times as many" is three groups of 4. It is not "3 more than 4", which would be 7.
One more place: a strip diagram. Six equal parts in a bar, each labeled 9, with a question mark over the whole bar, means 6 × 9.
And odd or even is about the ones digit only. 3,721 is odd because it ends in 1, even though there is a 2 in it.
Equal groups means multiply: groups × in each group = total.
"Times as many" is multiplying. "More than" is adding. Even numbers end in 0, 2, 4, 6 or 8.
Reading 3 × 4 as "3 more". The statement "there are 3 more blue pens" sounds right and is one of the choices. The expression 3 × 4 says 3 groups of 4.
A table that adds. The wrong table goes up by the right amount but starts in the wrong place. Check the first row: 1 box should be 5 crayons, not 6.
Practice
Two quick ones.
a) 42 and b) 5,931
6 × 7 = 42.
5,931 ends in 1, so it is odd. The other three end in 8, 6 and 0, which are even.
There are 8 markers in each pack. Which table shows the relationship between the number of packs and the number of markers?
Packs 1, 2, 3 → Markers 8, 16, 24
Each row is packs × 8. 1 × 8 = 8. 2 × 8 = 16. 3 × 8 = 24.
"8, 9, 10" adds one marker per pack instead of eight. "8, 16, 32" doubles each time; 3 packs is 24, not 32. "9, 10, 11" adds 8 to the pack number.
Lena made 6 bracelets. She used 9 beads for each bracelet. Which strip diagram can be used to find the number of beads Lena used?
A bar of 6 equal parts, each labeled 9, with ? for the whole bar
6 bracelets are 6 equal groups. Each group is 9 beads. The whole bar is the total: 6 × 9 = 54.
Two parts labeled 6 and 9 is 6 + 9. A bar of 9 with 6 taken away is 9 − 6. Six parts labeled ? with 9 for the whole is 9 ÷ 6: it shares 9 beads among 6 bracelets, which is the story backwards.
There are 7 oak trees in a park. The expression 4 × 7 represents the number of pine trees in the park.
There are 4 times as many pine trees as oak trees, and there are 28 pine trees.
4 × 7 is 4 groups of 7. The 7 is the oak trees, so pine trees are 4 times the oak trees.
4 × 7 = 28.
"4 more pine trees" would be 7 + 4. "4 times as many oak trees" has the two kinds of tree swapped: that would make the oaks 28. "7 more" would be 7 + 7.
What number times 4 equals 24?
4 × 6 = 24, so the missing number is 6.
You already know the fact. Division is just asking for the factor you cannot see.
24 ÷ 4 = 6.
Two stories, same numbers, same equation, different meaning.
Sharing: 24 cookies are shared equally by 4 children. How many does each child get?
24 ÷ 4 = 6. Each child gets 6 cookies.
Grouping: 24 cookies are put in bags of 4. How many bags?
24 ÷ 4 = 6. There are 6 bags.
Either way, the total is split by the thing you know, and the answer is the thing you do not know.
The test's favorite trick is to hide the total. "3 teams of 8 players are split into 4 equal groups." Nobody said 24. You have to make it.
3 × 8 = 24 players in all.
24 ÷ 4 = 6 players in each group.
Total ÷ what you know = what you want. If the story gives you groups instead of a total, multiply to find the total first.
Dividing the first two numbers you see. In the teams story, 8 ÷ 4 = 2 uses two numbers from the story and ignores the third. Ask: is 8 the total? No, 8 is one team. The total has to be built.
Mixing up ÷ and ×. A story that ends "how many cups" when you know the total and the size of each cup is division, even though the numbers get smaller.
Practice
7 × □ = 56. What is the missing number?
8
7 × 8 = 56, so 56 ÷ 7 = 8. The missing factor is the division answer.
Deshawn poured 42 ounces of juice into cups. He put 6 ounces in each cup. Which equation can be used to find the number of cups Deshawn filled?
42 ÷ 6 = □
42 is the total. 6 is the size of each group. The number of groups is the total split into sixes.
42 × 6 would be 42 cups of 6 ounces. 42 − 6 is one cup poured, not all of them. 42 + 6 adds the cup to the juice.
Marisol has 45 trading cards. She shares them equally among 5 friends. How many cards does each friend get?
9
45 ÷ 5 = 9.
Check it: 5 × 9 = 45.
There are 2 vans going to a museum. Each van carries 9 students. At the museum, all the students are split into 3 equal groups. How many students are in each group?
6
The total is hidden. 2 × 9 = 18 students in all.
18 ÷ 3 = 6 students in each group.
3 is 9 ÷ 3: one van split into groups, the other van forgotten. 27 is 9 × 3. 54 multiplied all three numbers.
Mixed check 2
These three questions do not say which skill they use. Decide the method first, then answer.
A bakery puts 6 muffins in each box. It fills 9 boxes. How many muffins is that?
Method: Equal groups
54
9 boxes × 6 muffins = 54.
There are 48 chairs set up in 6 equal rows. How many chairs are in each row?
Method: Division
8
48 is the total, 6 is the number of groups. 48 ÷ 6 = 8.
Elena had 356 beads. She used 128 of them for a necklace. Then she bought 200 more. How many beads does she have now?
Method: Add and subtract
428
356 − 128 = 228.
228 + 200 = 428.
A number line from 0 to 1 is cut into 4 equal parts. How big is each part?
Each part is one fourth: 1/4.
The marks from left to right are 1/4, 2/4, 3/4, and then 1, which is 4/4.
Now cut the same line into 8 equal parts as well. Quarters are marked above the line and eighths below it.
Point P is 2 quarter-marks from 0, so P is 2/4.
Count the eighth-marks below: P is 4 of them from 0, so P is also 4/8.
Same point, two names. 2/4 and 4/8 are equivalent. So is 1/2.
When a question says "ride 2/3 of a mile, which number line shows the point", look for two things: the line between 0 and 1 is cut into 3 equal parts, and the point sits on the second mark.
The bottom number is how many equal parts between 0 and 1. The top number is how many parts you count from 0. Two fractions sitting on the same point are equivalent.
Counting tick marks instead of parts. A line cut into 4 parts has 5 tick marks, counting the ends. A point on the third mark after 0 is 3/4, not 3/5. Count the spaces, not the lines.
A line that goes past 1. If the line runs from 0 to 2, the parts between 0 and 1 are what the bottom number counts, not all the parts you can see.
Practice
Point A is shown on the number line.
What fraction does point A represent?
4/6 (which is also 2/3)
The line from 0 to 1 is cut into 6 equal parts, so each part is 1/6. Point A is 4 parts from 0.
You want to show 5/6 on a number line from 0 to 1.
6 equal parts, and the point is 5 parts from 0.
Bottom number: how the line is cut. Top number: how far you count.
Point K is shown. Fourths are marked above the line and eighths below it.
Point K represents two equivalent fractions. Which two?
3/4 and 6/8
Above the line, K is 3 fourths from 0. Below the line, K is 6 eighths from 0. Same point, two names.
3/8 keeps the 3 and changes the bottom number, which moves the point. 4/8 is the halfway mark, one eighth short of K. 7/8 is what you get by counting the tick marks including the one at 0.
A number line from 0 to 1 is cut into 6 equal parts. Omar says the point halfway along it represents 3/6. His friend says the same point represents 1/2.
Both are right: 3/6 and 1/2 name the same point
Halfway along a line cut into 6 parts is 3 parts from 0, so 3/6. Halfway is also one of two equal halves, so 1/2. They are equivalent fractions.
You can have 1/3 of a pizza or 1/8 of the same pizza. Which piece is bigger?
Cutting a pizza into 3 pieces makes big pieces. Cutting it into 8 makes small ones.
1/3 is greater than 1/8.
A bigger bottom number means more cuts, so smaller pieces.
There are two kinds of comparison on the test, and each has one thing to look at.
Same top number: 3/6 and 3/8. Three pieces each. Sixths are bigger pieces than eighths.
3/6 is greater than 3/8, because sixths are larger than eighths.
Same bottom number: 5/8 and 3/8. The pieces are the same size. Five of them is more than three.
5/8 is greater than 3/8, because 5 pieces is more than 3 pieces of the same size.
The test asks for the comparison and the reason. Your reason has to say which pieces are bigger, or which count is bigger.
Same bottom: more pieces is more. Same top: the smaller bottom number is bigger, because its pieces are bigger.
Comparing only works when both fractions are of the same-size whole.
"8 is bigger than 6, so eighths are bigger." It is the most natural thing to think, and it is backwards. More cuts, smaller pieces.
Different wholes. 3/8 of a small pizza and 3/8 of a large pizza are not the same amount of pizza. If the wholes are different sizes, the fractions cannot be compared.
Practice
Which is greater, 1/4 or 1/6?
1/4
Fourths are bigger pieces than sixths. Fewer cuts, bigger pieces.
You need to compare 2/3 and 2/5. What should you look at?
The tops match, so compare the pieces: thirds are bigger than fifths
Two pieces each. Thirds are bigger pieces. So 2/3 is greater than 2/5.
"5 is bigger than 3" is the backwards trap. Adding tops and bottoms is not a comparison. Matching tops do not make fractions equal; the pieces are different sizes.
Fraction strips are shown.
Which comparison and explanation are true?
4/6 is greater than 4/8, because sixths are larger than eighths
Four pieces each. Look at the strips: each sixth is wider than each eighth, so four sixths covers more.
The two "less than" choices both rest on the backwards idea that a bigger bottom number means bigger pieces. "Equal because both have 4 shaded parts" ignores that the parts are different sizes.
Tara ate 3/8 of a small pizza. Ben ate 3/8 of a large pizza. Tara says they ate the same amount of pizza.
No. The wholes are different sizes, so 3/8 of each is a different amount. And 7/8 is greater than 5/8.
Three eighths of a large pizza is more pizza than three eighths of a small one. Fractions only compare when the whole is the same.
5/8 and 7/8 have the same bottom number, so the pieces are the same size, and 7 pieces is more than 5.
Mixed check 3
These three questions do not say which skill they use. Decide the method first, then answer.
A number line from 0 to 1 is cut into 8 equal parts. Point R is 6 parts from 0. Which two fractions can point R represent?
Method: Fractions on a line
6/8 and 3/4
Six eighths from 0. Every second eighth-mark is a fourth-mark, so 6 eighths is 3 fourths. Same point.
Which comparison is true?
Method: Comparing fractions
2/6 is less than 2/4, because fourths are larger than sixths
Same top number, so compare the pieces. Fewer cuts means bigger pieces, so fourths are bigger.
A classroom has 4 tables. Each table has 7 chairs. All the chairs are moved into 2 equal rows for an assembly. How many chairs are in each row?
Method: Division
14
First the hidden total: 4 × 7 = 28 chairs.
28 ÷ 2 = 14.
28 stopped at the total. 2 is 4 ÷ 2, dividing before finding the total. 56 multiplied everything.
A rectangle is 5 cm long and 3 cm wide. If you walk all the way around it, how far do you walk?
Four sides: 5, 3, 5, 3.
5 + 3 + 5 + 3 = 16.
The perimeter is 16 cm. Perimeter is the distance around.
A square only shows you one side. The other three are the same length, even though they are not labeled.
7 + 7 + 7 + 7 = 28.
Or 4 × 7 = 28.
The perimeter is 28 cm.
Area is a different question: how many squares fit inside.
3 rows of 5 squares. 3 × 5 = 15.
The area is 15 square units. Perimeter is measured in cm; area is measured in square cm, because you are counting squares.
Two different shapes can have the same area. A 2 by 6 rectangle and a 3 by 4 rectangle both cover 12 squares.
Perimeter is the distance around: add every side, including the ones not labeled.
Area is the squares inside: rows × squares in each row.
Adding only the sides you can see. A square labeled 12 has four sides of 12. Adding 12 + 12 gives you half the fence.
Multiplying for perimeter. 12 × 12 = 144 is the area of that square, not its perimeter. If the question says "around", add.
Practice
A square has sides of 9 inches. What is 9 + 9 + 9 + 9?
36
Four sides of 9. 4 × 9 = 36. That is the perimeter of the square, in inches.
A rectangle is shown.
Perimeter: 8 + 3 + 8 + 3. Area: 8 × 3.
Perimeter adds all four sides, two of them 8 and two of them 3. Area is 3 rows of 8 squares.
"8 + 3" is only two sides. "8 + 8 + 8 + 8" treats the rectangle as a square.
The shaded figure on the grid is Noor's garden. Each square is 1 square meter.
Area 24 square meters. Perimeter 20 meters.
4 rows of 6 squares: 4 × 6 = 24.
Around the outside: 6 + 4 + 6 + 4 = 20.
A square garden has one side labeled 12 feet. Jules says the perimeter is 24 feet, because 12 + 12 = 24. What is the perimeter of the garden?
48 feet
A square has four equal sides. 12 + 12 + 12 + 12 = 48.
Jules added the two sides he could picture; 24 is half the fence. 144 is 12 × 12, the area. 36 is three sides.
A pictograph row for "Mystery books" shows ●●●●. The key says ● = 2 books. How many mystery books?
4 symbols, each worth 2.
4 × 2 = 8 mystery books.
Read the key before you count anything.
A dot plot puts one dot above a number for each thing counted. This table and dot plot show the same data.
| Pets at home | Number of students |
|---|---|
| 0 | 3 |
| 1 | 5 |
| 2 | 2 |
| 3 | 1 |
Five students have 1 pet, so there are 5 dots above the 1. Every dot is one student.
How many students have more than 1 pet? Count the dots above 2 and above 3: 2 + 1 = 3 students.
A bar graph has a scale on the side. If the lines go 0, 5, 10, 15, a bar that stops halfway between 10 and 15 is about 12 or 13, not 11.
When the test asks "which answer choice does NOT represent the table", check every row of every choice against the table. The wrong one usually has the right shape with one number off, or ignores its own key.
Read the key or the scale first. Then check every row, not just the first one.
Counting symbols as 1 each. If the key says ● = 4, then ●●● is 12, not 3. A pictograph that draws 12 symbols for 12 items when its key says 4 each is wrong, even though 12 is the right number.
Reading a scale of 2 as 1. Look at the gap between the numbers on the side before you read a bar.
Practice
A pictograph key says ● = 5 marbles. The row for "Red" shows ●●●. How many red marbles?
15
3 symbols × 5 = 15.
In another pictograph, each ★ stands for 4 shells. Nia found 20 shells. How many ★ should be in Nia's row?
5
20 ÷ 4 = 5 stars. Twenty stars would be a graph that ignored its own key.
The dot plot shows how many goals each player on a team scored this season.
4 players scored more than 1 goal, and there are 10 players.
More than 1 means the dots above 2, 3 and 4: 3 + 0 + 1 = 4.
All the dots: 2 + 4 + 3 + 0 + 1 = 10.
If you got 8 for the first question, you counted the dots above 1 as well. "More than 1" does not include 1.
The table shows the favorite fruit of the students in a class.
| Fruit | Students |
|---|---|
| Apple | 12 |
| Banana | 8 |
| Grape | 4 |
Which answer choice does NOT represent the information in the table?
A pictograph with a key of 4 students per symbol, showing 12, 8 and 4 symbols does not represent the table.
With a key of 4, twelve symbols means 48 students, not 12. That graph ignored its own key.
Key of 4 with 3, 2, 1 symbols: 12, 8, 4. Correct. Bars at 12, 8, 4: correct. Key of 2 with 6, 4, 2 symbols: 12, 8, 4. Correct.
Mixed run
Every skill in this guide, in no order, and nothing tells you which one to use. Name the method on your paper before you work it. That is exactly what the test asks.
The expanded form of a number is 90,000 + 4,000 + 30 + 1. What is the standard form?
Method: Place value
94,031
The hundreds place is empty, so it gets a 0. 9,431 dropped that place. 94,301 and 94,310 moved the 3 and the 1.
A rectangular rug is 9 feet long and 4 feet wide. What is the perimeter of the rug in feet?
Method: Perimeter and area
26 feet
9 + 4 + 9 + 4 = 26.
If you got 36, you found the area. The next question wants that.
The same rug is 9 feet long and 4 feet wide. What is the area of the rug in square feet?
Method: Perimeter and area
36 square feet
4 rows of 9 squares: 9 × 4 = 36.
Same rug as the last question, one word different. "Around" is perimeter; "square feet" is area.
Priya has 6 marbles. Theo has 4 times as many marbles as Priya. How many marbles does Theo have?
Method: Equal groups
24
"Times as many" is multiplying. 4 × 6 = 24.
Priya has 6 marbles. Theo has 4 more marbles than Priya. How many marbles does Theo have?
Method: Add and subtract
10
"More than" is adding. 6 + 4 = 10.
Same numbers as the last question, one phrase different. "Times as many" multiplies; "more than" adds.
A library has 5 shelves of picture books with 8 books on each shelf. All the picture books are shared equally among 4 classrooms. How many books does each classroom get?
Method: Division
10
Hidden total first: 5 × 8 = 40 books.
40 ÷ 4 = 10.
2 is 8 ÷ 4, one shelf only. 40 is the total, not the share. 13 is 5 + 8.
Which comparison is true?
Method: Comparing fractions
5/6 is greater than 5/8, because sixths are larger than eighths
Same number of pieces; sixths are the bigger pieces.
Point D is shown on the number line.
What fraction does point D represent?
Method: Fractions on a line
2/3
The line from 0 to 1 is cut into 3 equal parts. D is 2 parts from 0.
If you wrote 2/4, you counted the tick marks instead of the spaces.
The pictograph shows how many cars were washed at a fundraiser.
| Saturday | ♦♦♦♦ |
| Sunday | ♦♦ |
Key: ♦ = 3 cars
How many more cars were washed on Saturday than on Sunday?
Method: Reading data
6
Saturday: 4 × 3 = 12. Sunday: 2 × 3 = 6. 12 − 6 = 6.
If you got 2, you counted the symbols instead of reading the key.
Which answer choice does NOT describe the number 70,205?
Method: Place value
7 ten thousands, 2 tens, 5 ones does not describe 70,205.
In 70,205 the 2 is in the hundreds place. "2 tens" describes 70,025.
Read this once, cold. The first move of each skill, then a few habits.
| Skill | First move |
|---|---|
| Place value | Say each digit's place. An empty place gets a 0. To order, count digits first. |
| Add and subtract | Write the whole equation in story order before you add or subtract anything. |
| Equal groups | Ask: how many groups, how many in each? Groups × each = total. "Times as many" multiplies. |
| Division | Find the total first. Then total ÷ what you know = what you want. |
| Fractions on a line | Count the equal parts between 0 and 1 (bottom number). Count parts from 0 (top number). |
| Comparing fractions | Same bottom: more pieces wins. Same top: smaller bottom wins, because its pieces are bigger. |
| Perimeter and area | "Around" means add every side, even the unlabeled ones. "Square units" means rows × columns. |
| Reading data | Read the key or the scale before counting a single symbol or bar. |