← 3-1 · Place big digits high to maximize a decimal · Build the Largest or Smallest Value from Digit Cards

Place big digits high to maximize a decimal · 10 practice problems

4.NF.C.74.NF.C.6

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 answer: 5.3, 5.9, 9.3, 9.5

Choose 2 of the given number cards and use each at most once to build a decimal of the form $\square.\square$ . Find every decimal you can build that is greater than $5$ .

$\boxed{3} \quad \boxed{5} \quad \boxed{9} \;\;\longrightarrow\;\; \square.\square$

The number cards are 3, 5, and 9, and each decimal you make has one digit in the ones place and one digit in the tenths place.

Show solution

Understand

Using the digit cards 3, 5, 9 (each at most once), build decimals of the form (ones).(tenths). List every such decimal that is greater than 5.

Givens

Digit cards available: 3, 5, 9
Each decimal uses two cards: one in the ones place, one in the tenths place
Each card is used at most once in a given decimal

Unknowns

All decimals of the form box.box greater than 5

Constraints

The decimal must be strictly greater than 5
The two chosen cards must be different (each used at most once)

Plan

#2 Make a Systematic List

There are only 6 two-card decimals, so listing them by the ones digit guarantees we find all that exceed 5 without missing any.

Execute

#2 Make a Systematic List 4.NF.C.7

A decimal box.box is greater than 5 mostly because of its ones digit. A ones digit below 5 gives a value under 5, so the ones digit must be at least 5.

\text{ones} \ge 5 \Rightarrow \text{decimal} > 5

Comparing decimals starts at the highest place, so the ones digit decides first.

#2 Make a Systematic List 4.NF.C.6

With 5 in the ones place, the tenths digit can be 3 or 9 (the remaining cards): 5.3, 5.9. All are greater than 5.

5.3 > 5,\quad 5.9 > 5

A ones digit of 5 keeps the number above 5 for any tenths digit.

#2 Make a Systematic List 4.NF.C.6

With 9 in the ones place, the tenths digit can be 3 or 5 (the remaining cards): 9.3, 9.5. All are greater than 5.

9.3 > 5,\quad 9.5 > 5

A ones digit of 9 keeps the number above 5 for any tenths digit.

#2 Make a Systematic List 4.NF.C.7

Listing every case with a qualifying ones digit gives 4 decimals greater than 5.

\{5.3,\; 5.9,\; 9.3,\; 9.5\}

A complete by-ones-digit list ensures none are missed and none repeat.

Answer: 5.3, 5.9, 9.3, 9.5

Review

Decimals with too-small ones digit (3) are at or below 5 and correctly excluded (3.5, 3.9); the 4 listed all exceed 5. There are 6 possible two-card decimals total and exactly 4 are greater than 5, which matches.

Eliminate possibilities (tool 3): of the 6 arrangements, cross out those at or below 5 (3.5, 3.9), leaving the same 4.

Standards · min grade 4

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Deciding which decimals are greater than 5 by their ones digit
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing each two-card arrangement in decimal form

💡 Read the ones place first, list each case in order, and you'll catch every decimal that beats the target!

Variant 2 answer: 5.2, 5.6, 6.2, 6.5

Choose 2 of the given number cards and use each at most once to build a decimal of the form $\square.\square$ . Find every decimal you can build that is greater than $5$ .

$\boxed{2} \quad \boxed{5} \quad \boxed{6} \;\;\longrightarrow\;\; \square.\square$

The number cards are 2, 5, and 6, and each decimal you make has one digit in the ones place and one digit in the tenths place.

Show solution

Understand

Using the digit cards 2, 5, 6 (each at most once), build decimals of the form (ones).(tenths). List every such decimal that is greater than 5.

Givens

Digit cards available: 2, 5, 6
Each decimal uses two cards: one in the ones place, one in the tenths place
Each card is used at most once in a given decimal

Unknowns

All decimals of the form box.box greater than 5

Constraints

The decimal must be strictly greater than 5
The two chosen cards must be different (each used at most once)

Plan

#2 Make a Systematic List

There are only 6 two-card decimals, so listing them by the ones digit guarantees we find all that exceed 5 without missing any.

Execute

#2 Make a Systematic List 4.NF.C.7

A decimal box.box is greater than 5 mostly because of its ones digit. A ones digit below 5 gives a value under 5, so the ones digit must be at least 5.

\text{ones} \ge 5 \Rightarrow \text{decimal} > 5

Comparing decimals starts at the highest place, so the ones digit decides first.

#2 Make a Systematic List 4.NF.C.6

With 5 in the ones place, the tenths digit can be 2 or 6 (the remaining cards): 5.2, 5.6. All are greater than 5.

5.2 > 5,\quad 5.6 > 5

A ones digit of 5 keeps the number above 5 for any tenths digit.

#2 Make a Systematic List 4.NF.C.6

With 6 in the ones place, the tenths digit can be 2 or 5 (the remaining cards): 6.2, 6.5. All are greater than 5.

6.2 > 5,\quad 6.5 > 5

A ones digit of 6 keeps the number above 5 for any tenths digit.

#2 Make a Systematic List 4.NF.C.7

Listing every case with a qualifying ones digit gives 4 decimals greater than 5.

\{5.2,\; 5.6,\; 6.2,\; 6.5\}

A complete by-ones-digit list ensures none are missed and none repeat.

Answer: 5.2, 5.6, 6.2, 6.5

Review

Decimals with too-small ones digit (2) are at or below 5 and correctly excluded (2.5, 2.6); the 4 listed all exceed 5. There are 6 possible two-card decimals total and exactly 4 are greater than 5, which matches.

Eliminate possibilities (tool 3): of the 6 arrangements, cross out those at or below 5 (2.5, 2.6), leaving the same 4.

Standards · min grade 4

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Deciding which decimals are greater than 5 by their ones digit
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing each two-card arrangement in decimal form

💡 Read the ones place first, list each case in order, and you'll catch every decimal that beats the target!

Variant 3 answer: 4.3, 4.9, 9.3, 9.4

Choose 2 of the given number cards and use each at most once to build a decimal of the form $\square.\square$ . Find every decimal you can build that is greater than $4$ .

$\boxed{3} \quad \boxed{4} \quad \boxed{9} \;\;\longrightarrow\;\; \square.\square$

The number cards are 3, 4, and 9, and each decimal you make has one digit in the ones place and one digit in the tenths place.

Show solution

Understand

Using the digit cards 3, 4, 9 (each at most once), build decimals of the form (ones).(tenths). List every such decimal that is greater than 4.

Givens

Digit cards available: 3, 4, 9
Each decimal uses two cards: one in the ones place, one in the tenths place
Each card is used at most once in a given decimal

Unknowns

All decimals of the form box.box greater than 4

Constraints

The decimal must be strictly greater than 4
The two chosen cards must be different (each used at most once)

Plan

#2 Make a Systematic List

There are only 6 two-card decimals, so listing them by the ones digit guarantees we find all that exceed 4 without missing any.

Execute

#2 Make a Systematic List 4.NF.C.7

A decimal box.box is greater than 4 mostly because of its ones digit. A ones digit below 4 gives a value under 4, so the ones digit must be at least 4.

\text{ones} \ge 4 \Rightarrow \text{decimal} > 4

Comparing decimals starts at the highest place, so the ones digit decides first.

#2 Make a Systematic List 4.NF.C.6

With 4 in the ones place, the tenths digit can be 3 or 9 (the remaining cards): 4.3, 4.9. All are greater than 4.

4.3 > 4,\quad 4.9 > 4

A ones digit of 4 keeps the number above 4 for any tenths digit.

#2 Make a Systematic List 4.NF.C.6

With 9 in the ones place, the tenths digit can be 3 or 4 (the remaining cards): 9.3, 9.4. All are greater than 4.

9.3 > 4,\quad 9.4 > 4

A ones digit of 9 keeps the number above 4 for any tenths digit.

#2 Make a Systematic List 4.NF.C.7

Listing every case with a qualifying ones digit gives 4 decimals greater than 4.

\{4.3,\; 4.9,\; 9.3,\; 9.4\}

A complete by-ones-digit list ensures none are missed and none repeat.

Answer: 4.3, 4.9, 9.3, 9.4

Review

Decimals with too-small ones digit (3) are at or below 4 and correctly excluded (3.4, 3.9); the 4 listed all exceed 4. There are 6 possible two-card decimals total and exactly 4 are greater than 4, which matches.

Eliminate possibilities (tool 3): of the 6 arrangements, cross out those at or below 4 (3.4, 3.9), leaving the same 4.

Standards · min grade 4

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Deciding which decimals are greater than 4 by their ones digit
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing each two-card arrangement in decimal form

💡 Read the ones place first, list each case in order, and you'll catch every decimal that beats the target!

Variant 4 answer: 4.1, 4.8, 8.1, 8.4

Choose 2 of the given number cards and use each at most once to build a decimal of the form $\square.\square$ . Find every decimal you can build that is greater than $4$ .

$\boxed{1} \quad \boxed{4} \quad \boxed{8} \;\;\longrightarrow\;\; \square.\square$

The number cards are 1, 4, and 8, and each decimal you make has one digit in the ones place and one digit in the tenths place.

Show solution

Understand

Using the digit cards 1, 4, 8 (each at most once), build decimals of the form (ones).(tenths). List every such decimal that is greater than 4.

Givens

Digit cards available: 1, 4, 8
Each decimal uses two cards: one in the ones place, one in the tenths place
Each card is used at most once in a given decimal

Unknowns

All decimals of the form box.box greater than 4

Constraints

The decimal must be strictly greater than 4
The two chosen cards must be different (each used at most once)

Plan

#2 Make a Systematic List

There are only 6 two-card decimals, so listing them by the ones digit guarantees we find all that exceed 4 without missing any.

Execute

#2 Make a Systematic List 4.NF.C.7

A decimal box.box is greater than 4 mostly because of its ones digit. A ones digit below 4 gives a value under 4, so the ones digit must be at least 4.

\text{ones} \ge 4 \Rightarrow \text{decimal} > 4

Comparing decimals starts at the highest place, so the ones digit decides first.

#2 Make a Systematic List 4.NF.C.6

With 4 in the ones place, the tenths digit can be 1 or 8 (the remaining cards): 4.1, 4.8. All are greater than 4.

4.1 > 4,\quad 4.8 > 4

A ones digit of 4 keeps the number above 4 for any tenths digit.

#2 Make a Systematic List 4.NF.C.6

With 8 in the ones place, the tenths digit can be 1 or 4 (the remaining cards): 8.1, 8.4. All are greater than 4.

8.1 > 4,\quad 8.4 > 4

A ones digit of 8 keeps the number above 4 for any tenths digit.

#2 Make a Systematic List 4.NF.C.7

Listing every case with a qualifying ones digit gives 4 decimals greater than 4.

\{4.1,\; 4.8,\; 8.1,\; 8.4\}

A complete by-ones-digit list ensures none are missed and none repeat.

Answer: 4.1, 4.8, 8.1, 8.4

Review

Decimals with too-small ones digit (1) are at or below 4 and correctly excluded (1.4, 1.8); the 4 listed all exceed 4. There are 6 possible two-card decimals total and exactly 4 are greater than 4, which matches.

Eliminate possibilities (tool 3): of the 6 arrangements, cross out those at or below 4 (1.4, 1.8), leaving the same 4.

Standards · min grade 4

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Deciding which decimals are greater than 4 by their ones digit
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing each two-card arrangement in decimal form

💡 Read the ones place first, list each case in order, and you'll catch every decimal that beats the target!

Variant 5 answer: 4.2, 4.8, 8.2, 8.4

Choose 2 of the given number cards and use each at most once to build a decimal of the form $\square.\square$ . Find every decimal you can build that is greater than $4$ .

$\boxed{2} \quad \boxed{4} \quad \boxed{8} \;\;\longrightarrow\;\; \square.\square$

The number cards are 2, 4, and 8, and each decimal you make has one digit in the ones place and one digit in the tenths place.

Show solution

Understand

Using the digit cards 2, 4, 8 (each at most once), build decimals of the form (ones).(tenths). List every such decimal that is greater than 4.

Givens

Digit cards available: 2, 4, 8
Each decimal uses two cards: one in the ones place, one in the tenths place
Each card is used at most once in a given decimal

Unknowns

All decimals of the form box.box greater than 4

Constraints

The decimal must be strictly greater than 4
The two chosen cards must be different (each used at most once)

Plan

#2 Make a Systematic List

There are only 6 two-card decimals, so listing them by the ones digit guarantees we find all that exceed 4 without missing any.

Execute

#2 Make a Systematic List 4.NF.C.7

A decimal box.box is greater than 4 mostly because of its ones digit. A ones digit below 4 gives a value under 4, so the ones digit must be at least 4.

\text{ones} \ge 4 \Rightarrow \text{decimal} > 4

Comparing decimals starts at the highest place, so the ones digit decides first.

#2 Make a Systematic List 4.NF.C.6

With 4 in the ones place, the tenths digit can be 2 or 8 (the remaining cards): 4.2, 4.8. All are greater than 4.

4.2 > 4,\quad 4.8 > 4

A ones digit of 4 keeps the number above 4 for any tenths digit.

#2 Make a Systematic List 4.NF.C.6

With 8 in the ones place, the tenths digit can be 2 or 4 (the remaining cards): 8.2, 8.4. All are greater than 4.

8.2 > 4,\quad 8.4 > 4

A ones digit of 8 keeps the number above 4 for any tenths digit.

#2 Make a Systematic List 4.NF.C.7

Listing every case with a qualifying ones digit gives 4 decimals greater than 4.

\{4.2,\; 4.8,\; 8.2,\; 8.4\}

A complete by-ones-digit list ensures none are missed and none repeat.

Answer: 4.2, 4.8, 8.2, 8.4

Review

Decimals with too-small ones digit (2) are at or below 4 and correctly excluded (2.4, 2.8); the 4 listed all exceed 4. There are 6 possible two-card decimals total and exactly 4 are greater than 4, which matches.

Eliminate possibilities (tool 3): of the 6 arrangements, cross out those at or below 4 (2.4, 2.8), leaving the same 4.

Standards · min grade 4

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Deciding which decimals are greater than 4 by their ones digit
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing each two-card arrangement in decimal form

💡 Read the ones place first, list each case in order, and you'll catch every decimal that beats the target!

Variant 6 answer: 7.4, 7.8, 8.4, 8.7

Choose 2 of the given number cards and use each at most once to build a decimal of the form $\square.\square$ . Find every decimal you can build that is greater than $7$ .

$\boxed{4} \quad \boxed{7} \quad \boxed{8} \;\;\longrightarrow\;\; \square.\square$

The number cards are 4, 7, and 8, and each decimal you make has one digit in the ones place and one digit in the tenths place.

Show solution

Understand

Using the digit cards 4, 7, 8 (each at most once), build decimals of the form (ones).(tenths). List every such decimal that is greater than 7.

Givens

Digit cards available: 4, 7, 8
Each decimal uses two cards: one in the ones place, one in the tenths place
Each card is used at most once in a given decimal

Unknowns

All decimals of the form box.box greater than 7

Constraints

The decimal must be strictly greater than 7
The two chosen cards must be different (each used at most once)

Plan

#2 Make a Systematic List

There are only 6 two-card decimals, so listing them by the ones digit guarantees we find all that exceed 7 without missing any.

Execute

#2 Make a Systematic List 4.NF.C.7

A decimal box.box is greater than 7 mostly because of its ones digit. A ones digit below 7 gives a value under 7, so the ones digit must be at least 7.

\text{ones} \ge 7 \Rightarrow \text{decimal} > 7

Comparing decimals starts at the highest place, so the ones digit decides first.

#2 Make a Systematic List 4.NF.C.6

With 7 in the ones place, the tenths digit can be 4 or 8 (the remaining cards): 7.4, 7.8. All are greater than 7.

7.4 > 7,\quad 7.8 > 7

A ones digit of 7 keeps the number above 7 for any tenths digit.

#2 Make a Systematic List 4.NF.C.6

With 8 in the ones place, the tenths digit can be 4 or 7 (the remaining cards): 8.4, 8.7. All are greater than 7.

8.4 > 7,\quad 8.7 > 7

A ones digit of 8 keeps the number above 7 for any tenths digit.

#2 Make a Systematic List 4.NF.C.7

Listing every case with a qualifying ones digit gives 4 decimals greater than 7.

\{7.4,\; 7.8,\; 8.4,\; 8.7\}

A complete by-ones-digit list ensures none are missed and none repeat.

Answer: 7.4, 7.8, 8.4, 8.7

Review

Decimals with too-small ones digit (4) are at or below 7 and correctly excluded (4.7, 4.8); the 4 listed all exceed 7. There are 6 possible two-card decimals total and exactly 4 are greater than 7, which matches.

Eliminate possibilities (tool 3): of the 6 arrangements, cross out those at or below 7 (4.7, 4.8), leaving the same 4.

Standards · min grade 4

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Deciding which decimals are greater than 7 by their ones digit
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing each two-card arrangement in decimal form

💡 Read the ones place first, list each case in order, and you'll catch every decimal that beats the target!

Variant 7 answer: 2.1, 2.6, 6.1, 6.2

Choose 2 of the given number cards and use each at most once to build a decimal of the form $\square.\square$ . Find every decimal you can build that is greater than $2$ .

$\boxed{1} \quad \boxed{2} \quad \boxed{6} \;\;\longrightarrow\;\; \square.\square$

The number cards are 1, 2, and 6, and each decimal you make has one digit in the ones place and one digit in the tenths place.

Show solution

Understand

Using the digit cards 1, 2, 6 (each at most once), build decimals of the form (ones).(tenths). List every such decimal that is greater than 2.

Givens

Digit cards available: 1, 2, 6
Each decimal uses two cards: one in the ones place, one in the tenths place
Each card is used at most once in a given decimal

Unknowns

All decimals of the form box.box greater than 2

Constraints

The decimal must be strictly greater than 2
The two chosen cards must be different (each used at most once)

Plan

#2 Make a Systematic List

There are only 6 two-card decimals, so listing them by the ones digit guarantees we find all that exceed 2 without missing any.

Execute

#2 Make a Systematic List 4.NF.C.7

A decimal box.box is greater than 2 mostly because of its ones digit. A ones digit below 2 gives a value under 2, so the ones digit must be at least 2.

\text{ones} \ge 2 \Rightarrow \text{decimal} > 2

Comparing decimals starts at the highest place, so the ones digit decides first.

#2 Make a Systematic List 4.NF.C.6

With 2 in the ones place, the tenths digit can be 1 or 6 (the remaining cards): 2.1, 2.6. All are greater than 2.

2.1 > 2,\quad 2.6 > 2

A ones digit of 2 keeps the number above 2 for any tenths digit.

#2 Make a Systematic List 4.NF.C.6

With 6 in the ones place, the tenths digit can be 1 or 2 (the remaining cards): 6.1, 6.2. All are greater than 2.

6.1 > 2,\quad 6.2 > 2

A ones digit of 6 keeps the number above 2 for any tenths digit.

#2 Make a Systematic List 4.NF.C.7

Listing every case with a qualifying ones digit gives 4 decimals greater than 2.

\{2.1,\; 2.6,\; 6.1,\; 6.2\}

A complete by-ones-digit list ensures none are missed and none repeat.

Answer: 2.1, 2.6, 6.1, 6.2

Review

Decimals with too-small ones digit (1) are at or below 2 and correctly excluded (1.2, 1.6); the 4 listed all exceed 2. There are 6 possible two-card decimals total and exactly 4 are greater than 2, which matches.

Eliminate possibilities (tool 3): of the 6 arrangements, cross out those at or below 2 (1.2, 1.6), leaving the same 4.

Standards · min grade 4

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Deciding which decimals are greater than 2 by their ones digit
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing each two-card arrangement in decimal form

💡 Read the ones place first, list each case in order, and you'll catch every decimal that beats the target!

Variant 8 answer: 3.2, 3.7, 7.2, 7.3

Choose 2 of the given number cards and use each at most once to build a decimal of the form $\square.\square$ . Find every decimal you can build that is greater than $3$ .

$\boxed{2} \quad \boxed{3} \quad \boxed{7} \;\;\longrightarrow\;\; \square.\square$

The number cards are 2, 3, and 7, and each decimal you make has one digit in the ones place and one digit in the tenths place.

Show solution

Understand

Using the digit cards 2, 3, 7 (each at most once), build decimals of the form (ones).(tenths). List every such decimal that is greater than 3.

Givens

Digit cards available: 2, 3, 7
Each decimal uses two cards: one in the ones place, one in the tenths place
Each card is used at most once in a given decimal

Unknowns

All decimals of the form box.box greater than 3

Constraints

The decimal must be strictly greater than 3
The two chosen cards must be different (each used at most once)

Plan

#2 Make a Systematic List

There are only 6 two-card decimals, so listing them by the ones digit guarantees we find all that exceed 3 without missing any.

Execute

#2 Make a Systematic List 4.NF.C.7

A decimal box.box is greater than 3 mostly because of its ones digit. A ones digit below 3 gives a value under 3, so the ones digit must be at least 3.

\text{ones} \ge 3 \Rightarrow \text{decimal} > 3

Comparing decimals starts at the highest place, so the ones digit decides first.

#2 Make a Systematic List 4.NF.C.6

With 3 in the ones place, the tenths digit can be 2 or 7 (the remaining cards): 3.2, 3.7. All are greater than 3.

3.2 > 3,\quad 3.7 > 3

A ones digit of 3 keeps the number above 3 for any tenths digit.

#2 Make a Systematic List 4.NF.C.6

With 7 in the ones place, the tenths digit can be 2 or 3 (the remaining cards): 7.2, 7.3. All are greater than 3.

7.2 > 3,\quad 7.3 > 3

A ones digit of 7 keeps the number above 3 for any tenths digit.

#2 Make a Systematic List 4.NF.C.7

Listing every case with a qualifying ones digit gives 4 decimals greater than 3.

\{3.2,\; 3.7,\; 7.2,\; 7.3\}

A complete by-ones-digit list ensures none are missed and none repeat.

Answer: 3.2, 3.7, 7.2, 7.3

Review

Decimals with too-small ones digit (2) are at or below 3 and correctly excluded (2.3, 2.7); the 4 listed all exceed 3. There are 6 possible two-card decimals total and exactly 4 are greater than 3, which matches.

Eliminate possibilities (tool 3): of the 6 arrangements, cross out those at or below 3 (2.3, 2.7), leaving the same 4.

Standards · min grade 4

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Deciding which decimals are greater than 3 by their ones digit
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing each two-card arrangement in decimal form

💡 Read the ones place first, list each case in order, and you'll catch every decimal that beats the target!

Variant 9 answer: 6.1, 6.7, 7.1, 7.6

Choose 2 of the given number cards and use each at most once to build a decimal of the form $\square.\square$ . Find every decimal you can build that is greater than $6$ .

$\boxed{1} \quad \boxed{6} \quad \boxed{7} \;\;\longrightarrow\;\; \square.\square$

The number cards are 1, 6, and 7, and each decimal you make has one digit in the ones place and one digit in the tenths place.

Show solution

Understand

Using the digit cards 1, 6, 7 (each at most once), build decimals of the form (ones).(tenths). List every such decimal that is greater than 6.

Givens

Digit cards available: 1, 6, 7
Each decimal uses two cards: one in the ones place, one in the tenths place
Each card is used at most once in a given decimal

Unknowns

All decimals of the form box.box greater than 6

Constraints

The decimal must be strictly greater than 6
The two chosen cards must be different (each used at most once)

Plan

#2 Make a Systematic List

There are only 6 two-card decimals, so listing them by the ones digit guarantees we find all that exceed 6 without missing any.

Execute

#2 Make a Systematic List 4.NF.C.7

A decimal box.box is greater than 6 mostly because of its ones digit. A ones digit below 6 gives a value under 6, so the ones digit must be at least 6.

\text{ones} \ge 6 \Rightarrow \text{decimal} > 6

Comparing decimals starts at the highest place, so the ones digit decides first.

#2 Make a Systematic List 4.NF.C.6

With 6 in the ones place, the tenths digit can be 1 or 7 (the remaining cards): 6.1, 6.7. All are greater than 6.

6.1 > 6,\quad 6.7 > 6

A ones digit of 6 keeps the number above 6 for any tenths digit.

#2 Make a Systematic List 4.NF.C.6

With 7 in the ones place, the tenths digit can be 1 or 6 (the remaining cards): 7.1, 7.6. All are greater than 6.

7.1 > 6,\quad 7.6 > 6

A ones digit of 7 keeps the number above 6 for any tenths digit.

#2 Make a Systematic List 4.NF.C.7

Listing every case with a qualifying ones digit gives 4 decimals greater than 6.

\{6.1,\; 6.7,\; 7.1,\; 7.6\}

A complete by-ones-digit list ensures none are missed and none repeat.

Answer: 6.1, 6.7, 7.1, 7.6

Review

Decimals with too-small ones digit (1) are at or below 6 and correctly excluded (1.6, 1.7); the 4 listed all exceed 6. There are 6 possible two-card decimals total and exactly 4 are greater than 6, which matches.

Eliminate possibilities (tool 3): of the 6 arrangements, cross out those at or below 6 (1.6, 1.7), leaving the same 4.

Standards · min grade 4

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Deciding which decimals are greater than 6 by their ones digit
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing each two-card arrangement in decimal form

💡 Read the ones place first, list each case in order, and you'll catch every decimal that beats the target!

Variant 10 answer: 3.2, 3.5, 5.2, 5.3

Choose 2 of the given number cards and use each at most once to build a decimal of the form $\square.\square$ . Find every decimal you can build that is greater than $3$ .

$\boxed{2} \quad \boxed{3} \quad \boxed{5} \;\;\longrightarrow\;\; \square.\square$

The number cards are 2, 3, and 5, and each decimal you make has one digit in the ones place and one digit in the tenths place.

Show solution

Understand

Using the digit cards 2, 3, 5 (each at most once), build decimals of the form (ones).(tenths). List every such decimal that is greater than 3.

Givens

Digit cards available: 2, 3, 5
Each decimal uses two cards: one in the ones place, one in the tenths place
Each card is used at most once in a given decimal

Unknowns

All decimals of the form box.box greater than 3

Constraints

The decimal must be strictly greater than 3
The two chosen cards must be different (each used at most once)

Plan

#2 Make a Systematic List

There are only 6 two-card decimals, so listing them by the ones digit guarantees we find all that exceed 3 without missing any.

Execute

#2 Make a Systematic List 4.NF.C.7

A decimal box.box is greater than 3 mostly because of its ones digit. A ones digit below 3 gives a value under 3, so the ones digit must be at least 3.

\text{ones} \ge 3 \Rightarrow \text{decimal} > 3

Comparing decimals starts at the highest place, so the ones digit decides first.

#2 Make a Systematic List 4.NF.C.6

With 3 in the ones place, the tenths digit can be 2 or 5 (the remaining cards): 3.2, 3.5. All are greater than 3.

3.2 > 3,\quad 3.5 > 3

A ones digit of 3 keeps the number above 3 for any tenths digit.

#2 Make a Systematic List 4.NF.C.6

With 5 in the ones place, the tenths digit can be 2 or 3 (the remaining cards): 5.2, 5.3. All are greater than 3.

5.2 > 3,\quad 5.3 > 3

A ones digit of 5 keeps the number above 3 for any tenths digit.

#2 Make a Systematic List 4.NF.C.7

Listing every case with a qualifying ones digit gives 4 decimals greater than 3.

\{3.2,\; 3.5,\; 5.2,\; 5.3\}

A complete by-ones-digit list ensures none are missed and none repeat.

Answer: 3.2, 3.5, 5.2, 5.3

Review

Decimals with too-small ones digit (2) are at or below 3 and correctly excluded (2.3, 2.5); the 4 listed all exceed 3. There are 6 possible two-card decimals total and exactly 4 are greater than 3, which matches.

Eliminate possibilities (tool 3): of the 6 arrangements, cross out those at or below 3 (2.3, 2.5), leaving the same 4.

Standards · min grade 4

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Deciding which decimals are greater than 3 by their ones digit
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing each two-card arrangement in decimal form

💡 Read the ones place first, list each case in order, and you'll catch every decimal that beats the target!