## At-Home Activities from *Investigations 3*

#### Below you’ll find a set of activities that focus on important mathematics, involve little in the way of materials, and provide experiences that can be tweaked and repeated and extended over time. While these activities are from *Investigations 3*, they will engage and interest all students. A new activity, with suggestions for each grade (K-5), will be posted regularly.

**Today’s Number: Part 2**

Today’s Number develops number sense and computational fluency across the grades. In this activity students find and record ways to make a given number, sometimes using specific constraints. These additional variations focus on different mathematics.

**Kindergarten: Tile Arrangements**

Use 6 tiles to make an arrangement. (You can color and cut tiles from grid paper, or color tile arrangements on the sheet. Or, use digital square tiles.) Rule: Tiles must share whole sides. For example:

Look at your arrangement. Use numbers to describe it. For example:

**Try More**

- Find many different ways to arrange and describe 6 tiles.
- Repeat the activity with a different number of tiles.

MWI: Arranging 5 Tiles

(CCSS: K.CC.A.3, K.CC.B.4a, K.CC.B.4b, K.CC.B.4c, K.CC.B.5, K.OA.A.3, K.G.A.1, K.G.B.6)

**Grade 2: Today’s Number with Coins**

Today’s Number is 56. Find ways to make 56 using pennies, nickels, dimes and quarters. Record the ways you find. For example:

*How do you know this equals 56? **What do you know about 56 that helped you decide which coins to use?*

**Try More **

- Ask: “Did/can you use one solution to find another?” For example, “I see you have 2 quarters and 6 pennies. Could you trade in those quarters for other coins to come up with another way to make 56?”
- Repeat the activity with another number between 30-100.

**Resources **

MWI: Money

(CCSS: 2.NBT.B.5, 2.MD.C.8)

**Grade 4: Today’s Number: Broken Calculator**

Today’s Number is 2,400. Imagine using a calculator, but the 2 and 4 keys are broken. Find at least 5 ways to make the calculator display 2,400 using either addition or subtraction. Remember you can’t use 2 or 4 in your expressions! For example:

*How do you know these expressions equal 2,400? What do you know about 2,400 or what do you know about addition or subtraction that helped you decide what numbers to use?*

**Try More**

- Create five expressions that equal 124. Use multiplication and addition in each expression. The 1 and 2 keys are broken. E.g., (3 x 40) + 4 and (4 x 6) + (4 x 5 x 5).
- Create five expressions that equal 998. Use only subtraction in each expression. The 1 and 9 keys are broken. E.g., 3,000 – 2,002 and 2,000 – 700 – 250 – 52).
- Choose a number between 200 and 5,000. Choose which operation(s) need to be used. Choose which keys are broken. Try to make it challenging!

(CCSS: 4.NBT.B.4 and 4.NBT.B.5)

**Grade 1: Dot Addition**

Today’s Number is 12. Use Dot Addition Cards to find ways to make 12. Record the ways you find. For example:

*How do you know this equals 12? **What do you know about 12 that helped you decide what numbers to use?*

**Try More**

- Try to use one solution to find another. (
*I see you have 5+5+2. Can you use what you know about 5 to make another way?*) - How many different ways can you find to make 12 with Dot Addition Cards? (
*Do you think you found all the ways? How do you know? … Is 5+5+2 and 5+2+5 the same or different? Why do you think so?*) - Find ways to make 12 that use any numbers. You can use addition and/or subtraction.

**Resources**

Online Games: Dot Addition (U3), Dot Addition (U5)

MWI: Today’s Number

(CCSS: 1.OA.B.3, 1.OA.C.6)

**Grade 3: Today’s Number**

Today’s Number is 276. Find ways to make 276 using multiplication and addition. For example:

*How do you know this one equals 276? *

*What do you know about 276 that helped you decide what numbers to use?*

**Try More**

- Repeat but use multiples of 100 and subtraction. E.g., for 276: 300 – 20– 4 = 276
- Repeat but use a combination of 100 in each expression. E.g. for 276: 60 + 40 + 70 + 30 + 76 = 276
- Repeat but use addition, subtraction, or both. E.g., for 276: 150 + 150 – 50 + 26 = 276
- Repeat the activity with another number between 100-1,000.

(CCSS: 3.OA.C.7, 3.NBT.A.2)

**Grade 5: Today’s Number: Fractions**

** **Today’s Number is 1. Find 5 ways to make 1 using fractions and only using addition. Do not use a denominator more than once in an equation. For example:

*How do you know these expressions equal 1? How did you decide which fractions to use?*

**Try More**

- Use the same constraints but with a different whole number (e.g. 5), a fraction (e.g. 1/2) or a mixed number (e.g. 2 1/2) as Today’s Number.
- Instead of using only addition, use only subtraction. Or, use both addition and subtraction. For example: Create 5 expressions that equal 2 1/2 using only subtraction in each expression. Do not use a denominator more than once. E.g.: 2 3/4 – 2/8 = 2 1/2 and 3 10/12 – 1/2 – 2/3 – 1/6 = 2 1/2.

(CCSS: 5.NF.A.1)

*Compare* Games

*Compare*Games

The *Compare* games all involve comparing two quantities. The quantities might be single-digit numbers (e.g., which is more, 6 or 9?) or the answer when you add, subtract, multiply, or divide two (or more) numbers (e.g., which has the larger product, 6x8 or 7×7?). Some variations involve figuring out *how much more* one quantity is, compared to the other.

**Kindergarten****: The Game of Compare**

Each player turns over one Primary Number Card. (You can also use playing cards without the face cards.) Players decide who has more. Full directions and variations here; you can also play online.

Players explain how they know which is more or how someone could figure it out. For example:

*“Six is bigger becomes it comes after 4 when you count.”**“Count the pictures.”**“Build a tower for each number and see which is taller.”*

**Try More**

- Play
*Double Compare*. Players flip two cards on each turn. See directions and variations here. Play online with the 0-6 cards or the 0-10 cards. - Occasionally ask, “Can you tell who has more without finding the total? … If I have 6 and 4 and Lionel has 5 and 6, how could we tell who has more?”

*“You have 6 and Lionel has 6. Lionel has more because his other card Is 5 and yours is 4 and 5 is more than 4.”*

**Resources **MWI: More, Fewer, Equal

(CCSS: K.CC.A.1, K.CC.B.4.a, K.CC.B.4.b, K.CC.B.5, K.CC.C.6, K.CC.C.7)

**Grade 2: Sticker Compare**

Each player turns over a sticker card. The players decide who has more and how many more that player has. Full directions here.

Encourage the players to explain how they know who has more and how many more. For example:

*“46 is 11 more than 35. I can see it in the stickers. In 46, there’s 1 more strip of 10 and 1 more single. That’s 11.”**“It’s 11. I know that 35 + 10 is 45 and 46 is one more.”**“46 is 11 more because 35 + 5 = 40 and then 6 more is 46 and I know that 5 + 6 = 11.”*

**Try More**

Use Digit Cards or playing cards (with the 10s and face cards removed). Players turn over two cards. Each card can stand for a number of tens or a number of ones. So, for example, a player that turns over a 2 and a 5 could make 25 or 52. Compare the numbers. Who has more? How many more?

(CCSS: 2.NBT.A.3 2.NBT.B.5)

**Grade 4**

**:**

*Decimal Compare*Each player turns over one Decimal Card. The players decide who has the greater number. There are full directions here. This game can also be played online.

Encourage the players to explain how they know which number is greater. For example:

*“I always look at the tenths first. I saw that 0.45 has 4 tenths and 0.5 has 5 tenths, so I knew that 0.5 is a larger number.”**“I got confused because 45 is a bigger number than 5. But then I remembered that the 4 in 0.45 and the 5 in 0.5 are tenths and the 5 in 0.45 is 5 hundredths, which is really small compared to a tenth.”*

**Try More**

- Play
*Capture Fractions*using Fraction Cards or online. The directions are the same as above except fraction cards are used. - Use Compare Cards or the online game to play
*Multiplication Compare*. See directions here.

(CCSS: 4.NF.C.7, 4.NF.A.2, 4.NBT.B.5)

**Grade 1****: Double Compare**

Each player turns over 2 Primary Number Cards (without Wild Cards, or 2 playing cards without the face cards). Players decide who has more. Full directions and variations here; you can also play online.

Players explain how they know who has more. (Some will count or add to find and compare the totals. Others may not find the total but reason about the numbers.) For example:

*“They both have a 4, but Player 2 has an 8, and 8 is more than 7, so Player 2 has more.”**“Player 1 has 11 and Player 2 has 12. Player 2 has more.”*

**Try More**

- Play
*Double Compare Dots*with Dot Cards Set A or online or with Dot Cards Set B. (Print 4 copies and cut apart to make a deck.)

(CCSS: 1.OA.B.3, 1.OA.C.5, 1.OA.C.6)

**Grade 3:**

*Multiplication Compare*Each player turns over 2 Digit Cards. The players decide who has the greater product. There are full directions here. This game can also be played online.

Encourage the players to explain how they know which product is greater. Some will multiply to find and compare the products. Others may *not* find the product but reason about the numbers. For example:

*“I know 7 x 5 is 35. 6 x 8 is a hard one for me! But I know 5 x 8 is 40 and 6 x 8 is one more 8. So, 6 x 8 is 48 and 48 is bigger than 35.”**“8 is bigger than 7 and we’re multiplying 8 by a bigger number than we are multiplying 7 by. So, 7 x 5 must be smaller than 6 x 8.”*

*(CCSS: 3.OA.C.7)*

**Grade 5: ***Addition Compare with Fractions*

Each player turns over 2 Fraction Cards. The players decide who has the greater total. There are full directions here. This game can also be played online.

Encourage the players to explain how they know who has the greater total. Some will add to find and compare the totals. Others may *not* find the total but reason about the numbers. For example:

*“I thought about the 6/8 compared to 9/8 + 1/8. 9/8 + 1/8 is 4/8 bigger than 6/8. So, in order for 5/6 + 6/8 to be bigger, 5/6 has to be bigger than 4/8. And it is!”**“9/8 + 1/8 is easy to add. It’s 10/8. 5/6 + 6/8 is harder. I know that 6/8 is 3/4 and both sixths and fourths are related to twelfths. 5/6 is equivalent to 10/12, and 3/4 is equivalent to 9/12. So added together, they are 19/12. Hmm, it’s hard to compare twelfths and eighths, but maybe I can compare them to landmark numbers. 10/8 is 1 2/8. 19/12 is 1 7/12. 1 2/8 is less than 1 1/2, and 1 7/12 is more than 1 1/2. Player 2’s sum is bigger than Player 1’s.”*

**Try More**

- Play
*Decimal Double Compare*using Decimal Cards or online. The directions are the same as above except with decimal cards. - Play
*Division Compare*using Compare Cards or online. See directions here.

(CCSS: 5.NF.A.1, 5.NBT.A.3.B, 5.NBT.B.6)

**Quick Images**

Quick Images develops students’ ability to visualize quantities and to use numbers and notation to describe them. In this activity, students briefly see an arrangement of dots or stickers, several times. They work to determine the number of dots or stickers, and to explain how they saw and remembered it.

**Kindergarten**

You’re going to see dots in a Ten Frame, for a short time. As you look at it, think about how you would make a copy. You will have a chance to look again! Follow these steps:

- Look at the image for about 5 seconds.
- Use counters and a blank Ten Frame to make a copy.
- Look at the image for another 5 seconds.
- Check your work. Do you want to change anything?
- Leave the image showing. Describe how you saw and remembered it. … Is there another way to see it?

For example, here are three different ways students saw one image:

**Try More**

- Here are videos you can use to do two Quick Images: Image 1, Image 2.
- If you’d rather work offline, print or sketch these images on cards and shuffle them. Flip a card and then follow the directions above, turning the card face down after the 5 seconds is up each time.

**Resources**

MWI: Ten Frames

(CCSS: K.CC.A.1, K.CC.b.4a, K.CC.B.4b, K.CC.B.5)

**Grade 2**

You’re going to see some stickers, for a short time. As you look, think about how many stickers you see and how you know. You will have a chance to look again! Follow these steps:

- Look at the image for about 5 seconds.
- Think about how many stickers you see and how you know.
- Look at the image for another 5 seconds.
- Check your work. Do you want to change your thinking?
- Leave the image showing. Discuss how you saw and remembered the image. … Is there another way to see it?

For example, here are three different ways students saw one image:

**Try More**

- Here are videos you can use to do two Quick Images: Image 1, Image 2.
- If you’d rather work offline, print or sketch these images on cards and shuffle them. Flip a card and then follow the directions above, turning the card face down after the 5 seconds is up each time.

**Resources**

MWI: Sticker Station: Tens and Ones

(CCSS: 2.NBT.A.3)

**Grade 4**

You’re going to see an image of dots for about 3 seconds. As you look it, think about how many dots and how you know. You will have a chance to look again! Follow these steps:

- Look at the image for 3 seconds.
- How many dots did you see? You may want to write down some numbers or equations.
- Look at the image for 3 more seconds.
- Write an equation that includes multiplication that shows how you saw the image.
- Leave the image showing. Check your equation. Does it match the image? Can you write a different equation that
*also*matches the image?

For example, here are some equations students wrote for one image:

**Try More**

- Here are videos you can use to do two Quick Images: Image 1, Image 2.
- Or, if you want to do the activity offline, print out these images and cut them into cards. Then, follow the directions above, turning the card face down after the 3 seconds is up each time.

(CCSS:4.NBT.B.5)

**Grade 1 **

You’re going to see some Ten Frames with dots, for a short time. As you look, think about how many dots you see and how you know. You will have a chance to look again! Follow these steps:

- Look at the image for about 5 seconds.
- Think about how many dots you see and how you know.
- Look at the image for another 5 seconds.
- Check your work. Do you want to change your thinking?
- Leave the image showing. Discuss how you saw and remembered the image. … Is there another way to see it?

For example, here are three different ways students saw one image:

**Try More**

- Here are videos you can use to do two Quick Images: Image 1, Image 2.
- If you’d rather work offline, print or sketch these images on cards and shuffle them. Flip a card and then follow the directions above, turning the card face down after the 5 seconds is up each time.

**Resources**

MWI: Combinations of 10

(CCSS: 1.OA.B.3, 1.OA.C.6)

**Grade 3**

You’re going to see an image of dots for about 3 seconds. As you look it, think about how many dots and how you know. You will have a chance to look again! Follow these steps:

- Look at the image for 3 seconds.
- How many dots did you see? You may want to write down some numbers or equations.
- Look at the image for 3 more seconds.
- Write an equation that includes multiplication that shows how you saw the image.
- Leave the image showing. Check your equation. Does it match the image? Can you write a different equation that
*also*matches the image?

For example, here are some equations students wrote for one image:

**Try More**

- Here are videos you can use to do two Quick Images: Image 1, Image 2.
- Or, if you want to do the activity offline, print out these images and cut them into cards. Then, follow the directions above, turning the card face down after the 3 seconds is up each time.

(CCSS: 3.OA.C.7)

**Grade 5**

You’re going to see an image of dots for about 3 seconds. As you look it, think about how many dots and how you know. You will have a chance to look again! Follow these steps:

- Look at the image for 3 seconds.
- How many dots did you see? You may want to write down some numbers or equations.
- Look at the image for 3 more seconds.
- Write an equation that includes multiplication that shows how you saw the image.
- Leave the image showing. Check your equation. Does it match the image? Can you write a different equation that
*also*matches the image?

For example, here are some equations students wrote for one image:

**Try More**

- Here are videos you can use to do two Quick Images: Image 1, Image 2.
- Or, if you want to do the activity offline, print out these images and cut them into cards. Then, follow the directions above, turning the card face down after the 3 seconds is up each time.

(CCSS: 5.NBT.B.5)

**Today’s Number**

Today’s Number develops number sense and computational fluency across the grades. In this activity students find and record ways to make a given number, sometimes using specific constraints.

**Kindergarten**

Provide a set of 8 [buttons] and ask, “How many are there?”

Provide some [pennies] and ask, “Can you make a set that has the same amount as the [buttons]?”

Ask, “You said there were 8. How could you show on paper that there were 8?”

**Try More**

- “Can you find another way to show 8?” (Some students write the number or the word. Others draw 8 pictures, hashmarks, or fingers. Many use a combination.)
- Repeat the activity with a different number, up to 20.
- Repeat the activity but use 2 or 3 subsets of related objects (e.g. red buttons and blue buttons).

**Resources **Math Words and Ideas: The Counting Jar

(CCSS-M: K.CC.A.1, K.CC.A.3, K.CC.B.4, K.CC.B.4.A, K.CC.B.4.B, K.CC.B.5)

**Grade 2**

Today’s Number is 29. Find some ways to make 29 using addition and subtraction. Record the ways you find. For example:

*How did you know this one equals 29? What do you know about 29 that helped you decide what numbers to use?*

**Try More**

- Repeat the activity with another number between 10-100.
- Find all of the ways to make 29 with 2 addends.

(CCSS-M: 2.NBT.B.5)

**Grade 4**

Today’s Number is 348. Find ways to make 348 using at least one multiple of 10 or 100, and only subtraction in each expression. For example:

*How do you know these expressions equal 348? What do you know about 348 or what do you know about subtraction that helped you decide what numbers to use?*

**Try More**

- Choose a different number between 200 and 1,000, and use the same constraint.
- Use a different constraint, such as:
- Use a combination of 100 in each expression. E.g., for 425: 15 + 85 + 300 + 25 and 39 + 61 + 250 + 75.
- Use addition and multiples of 10. E.g., for 562: 500 + 50 + 10 + 2 and 80 + 20 + 450 + 12.
- Use addition, subtraction, or both. E.g., for 471: 600 – 200 + 50 + 30 – 9 and 300 + 150 + 21.

(CCSS-M: 4.NBT.B.4)

**Grade 1 **

Today’s Number is 9. Find some ways to make 9. Show the ways you found. For example:

*How do you know this one equals 9?*

*What do you know about 9 that helped you decide what numbers to use?*

**Try More**

- Find ways with more than 2 addends or ways that use subtraction.
- “You found lots of ways with 2 addends. Do you think you found all of the ways that use 2 addends? How do you know?”
- Repeat the activity with another number between 0-20.

**Resources**

Math Words and Ideas: Today’s Number

(CCSS-M: 1.OA.B.3, 1.OA.C.6)

**Grade 3**

Today’s Number is 198. Find some ways to make 198 using at least 3 numbers and both addition and subtraction. Record the ways you find. For example:

*How did you know this one equals 198? What do you know about 198 that helped you decide what numbers to use?*

**Try More**

- Repeat the activity with another number between 100-1,000.
- Repeat the activity using at least one combination that adds to 100. For example: 60 + 40 + 100 – 2 = 198.

(CCSS-M: 3.NBT.A.2)

**Grade 5**

Today’s Number is 648. Find 10 ways to make 648 using only multiplication and addition. For example:

*How do you know these expressions equal 648? What do you know about 648 or what do you know about multiplication and addition that helped you decide what numbers to use?*

**Try More**

- Use the same constraint with a different number between 500 and 5,000.
- Use a different constraint, for example:
- Create 10 expressions that equal 3,300, using multiplication and no more than 2 factors. E.g., 1650 x 2 and 50 x 66. (Some other numbers to use: 800, 5,600, and 4,824. Can you find more?)
- Create 10 expressions that equal 1,800, using multiplication. Each expression must have 3 factors, and none of the factors can be 1. E.g., 3 x 20 x 30 and 6 x 20 x15. (Some other numbers to use: 720, 3,300, and 900. Can you find more?)

(CCSS-M: 5.NBT.B.5)