Eureka Math² · New York Next Gen · Grade 4

Module 1 study guide

Lessons 1, 2, 6, 7, 8, and 9 · multiplicative comparison and place value to 1,000,000

Quiz score –

What these lessons are doing

Module 1 starts with “times as many” so the place-value rule makes sense: each place is 10 times the place to its right. Then the same idea is used to write and compare big numbers.

Topic A · comparison

Lesson 1. Read a multiplication equation as “times as many.” Draw a tape diagram.

Lesson 2. Find the missing number, whether it is the total, the number of groups, or the size of a group.

Topic B · place value

Lesson 6. 10 times as much shifts one place left. Dividing by 10 shifts one place right.

Lesson 7. Unit form and expanded form. Lesson 8. Standard form and word form. Lesson 9. Compare with >, =, and <.

From the pages already turned in

  • The three-box tape for “15 is 3 times as many as 5” is the right model. The equation the page wants is 15 = 3 × 5 (or 15 = 5 × 3). 15 ÷ 5 = 3 is related, but it is not the equation they asked to complete.
  • Lesson 2 blanks are in good shape: 32 is 4 times 8, 30 is 5 times 6, 63 is 9 times 7. Side work that says 5 = 9 ÷ 63 is backwards. Use 63 ÷ 9 = 7.
  • The basketball and apple problems are reasoned correctly. Mom’s 54 apples are 6 times Adam’s 9, not 7 times, because 9 × 6 = 54 and 9 × 7 = 63.
  • Lesson 6 numbers are mostly right. The missing words are the place names: ten, hundred, thousand, ten thousand, hundred thousand, million.
  • Lesson 7 expanded form is the right idea. Keep the zero places in the number even when that unit is 0, like the 0 thousands in 270,364.

Lessons 8 and 9 were not in the photo set. They are the next two lessons in this module: word form, then comparing. The practice below follows that sequence, so the guide can be used before those pages come home.

4 · M1 · TA · Lesson 1

Times as many

Interpret multiplication as a comparison. A statement like “15 is 3 times as many as 5” is the equation 15 = 3 × 5.

Draw one small tape for the unit. Then draw that many copies for the total.

5
5
5
5
15 is 3 times as many as 5  ·  15 = 3 × 5

Count the boxes to get the “how many times.” Each box is the unit. Do not add 3 and 5. That would be an additive comparison (“3 more”), which is a different idea.

4 · M1 · TA · Lesson 2

The unknown can sit in three places

Solve “times as many” problems when the total, the number of copies, or the unit is missing.

Total missing. ___ is 4 times as many as 8.

4 × 8 = 32

Copies missing. 30 is ___ times as many as 6.

30 ÷ 6 = 5

Unit missing. 63 is 9 times as many as ___.

63 ÷ 9 = 7

Check a claim. 9 × 7 = 63, not 54. So 54 is 6 times 9, not 7 times.

4 · M1 · TB · Lesson 6

10 times as much

A digit in one place is 10 times what it would be in the place to its right. Multiplying by 10 moves one place left. Dividing by 10 moves one place right.
millionshundred thousandsten thousandsthousandshundredstensones
×10 →×10 →×10 →×10 →×10 →×10 →start
  • 10 times as much as 1 one is 1 ten. 10 × 1 = 10
  • 10 times as much as 1 ten is 1 hundred. 10 × 10 = 100
  • 10 times as much as 1 hundred is 1 thousand. 10 × 100 = 1,000
  • 10 times as much as 1 thousand is 1 ten thousand. 10 × 1,000 = 10,000
  • 10 times as much as 1 ten thousand is 1 hundred thousand. 10 × 10,000 = 100,000
  • 10 times as much as 1 hundred thousand is 1 million. 10 × 100,000 = 1,000,000

Same rule for a digit that is not 1. The 4 in 40,000 is 10 times the 4 in 4,000, because 4,000 × 10 = 40,000.

4 · M1 · TB · Lesson 7

Unit form and expanded form

Say how many of each unit, then write the number as a sum. Zeros still hold a place.

270,364

hundred thousandsten thousandsthousandshundredstensones
270364

Unit form: 2 hundred thousands, 7 ten thousands, 0 thousands, 3 hundreds, 6 tens, 4 ones.

Expanded form: 200,000 + 70,000 + 300 + 60 + 4

With multiplication: (2 × 100,000) + (7 × 10,000) + (3 × 100) + (6 × 10) + (4 × 1)

Skip a 0 in the sum, but do not skip the place when you are labeling the chart. 270,364 has 0 thousands.

4 · M1 · TB · Lesson 8

Standard form and word form

Standard form is the digits. Word form is the number said in words, with a comma between the thousands period and the ones period.

405,218

four hundred five thousand, two hundred eighteen

  • Read each group of three digits as hundreds, tens, and ones, then name the period: thousand or million.
  • 405,218 is “four hundred five thousand,” not “four hundred and five thousand.” Save “and” for decimals later.
  • A zero inside the number is silent in word form, but it has to be written in standard form. “six hundred twenty thousand, forty-five” is 620,045, not 6245.
4 · M1 · TB · Lesson 9

Compare with >, =, and <

Line the places up. Start at the greatest place. The first place that differs decides the comparison.

308,450  <  380,450

Both have 3 hundred thousands. The ten-thousands digits are 0 and 8. 0 < 8, so the first number is smaller. Digits after that do not matter.

72,450  =  72,450

Same digits in every place means equal. 499,999 is still less than 500,000, because 4 hundred thousands is less than 5 hundred thousands.

Mixed check · 30 questions · 5 from each lesson

Module 1 quiz

One question at a time. Answers are checked when you submit. You can retry the set.