## Jump in the River

In this lesson, children will explore addition of whole numbers.

### Lesson for:

Toddlers/Preschoolers
(See Step 5: Adapt lesson for toddlers or preschoolers.)

### Content Area:

Algebra
Numbers and Operations

### Learning Goals:

This lesson will help toddlers and preschoolers meet the following educational standards:

• Understand numbers, ways of representing numbers, relationships among numbers and number systems
• Understand meanings of operations and how they relate to one another
• Compute fluently and make reasonable estimates
• Use mathematical models to represent and understand quantitative relationships

### Learning Targets:

After this lesson, toddlers and preschoolers should be more proficient at:

• Developing and using strategies for whole-number computations, with a focus on addition and subtraction
• Developing fluency with basic number combinations for addition
• Using a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil and calculators
• Modeling situations that involve the addition and subtraction of whole numbers, using objects, pictures and symbols

## Jump in the River

### Lesson plan for toddlers/preschoolers

#### Step 1: Gather materials.

• Dice (two for each pair of students playing the game)
• Counters (Each player needs 12 different-colored counters to use as their game pieces. Together, the two players will have 24 counters total)
• Jump in the River board (To make this game board, use a regular 8×12 piece of paper. Make 1-inch spaces along the length of each side of the paper (the spaces should be 1-inch wide and 1½ inches long). Number the spaces on each side 1 through 12. In the middle of the paper, write the name of the game, Jump in the River, and draw some fish and waves.

Note: Small parts pose a choking hazard and are not appropriate for children age five or under. Be sure to choose lesson materials that meet safety requirements.

#### Step 2: Introduce activity.

1. Gather the children into a circle. You will need to be included in the circle with your materials in front of you and positioned where everyone can see you and what you are doing.
2. Explain that today the children will be playing an adding game called Jump in the River.
3. Ask the children what you mean when you say “adding. Say: “Who knows how to add numbers? Can you explain to everyone how to add?”
4. Paraphrase the possible definitions the children give as answers and tell them the working definition: “To add is to increase in amount or number. We have eight children sitting around the circle right now. If I were to add four more children to the circle, there would be 12 children in the circle. By adding four more children to the circle, that would increase the amount of children in the circle from eight to 12.”
5. Say: “We are going to play a game today that will help us learn about and practice adding numbers.”

#### Step 3: Engage children in lesson activities.

1. Explain and simultaneously model the rules of the game:
• Each player has 12 game pieces.
• Each player places one game piece on each of the numbers on his/her side of the board (12 in total).
• The first person rolls the dice. Model rolling the dice. Show the children exactly how to roll the dice calmly in their hands and gently toss them onto the game board. It is distracting when the children throw the dice around and spend the majority of their time fetching them. Say: “No crazy rolls. Only learning rolls” and model the different rolls.
• Roll the dice.
• Ask the children: “What numbers have I rolled?” (Pretend for now that you rolled a three and a four.) Say: “Yes, a three and a four.”  Count out the three dots on the first die and count out the four dots on the second die.
• Say: “Now I need to add both of these numbers to see what game piece I can throw into the river.”
• Ask for a volunteer. Ask: “Who can add the numbers three and four?”
• Assist the child in counting the total number of dots on the dice by counting all of the numbers out loud: “1, 2, 3, 4, 5, 6, 7.” Say: “That’s right. There are seven dots altogether. Three plus four equals seven.” Say: “Now this player can throw the marker that they have on the number seven into the river.” Take the game piece off of the number seven and place it in the middle of the game board (the river). Only the player rolling the dice, whose turn it is, throws his/her game piece in the river.
• The game continues until almost all of the game pieces are in the river. If the space is blank when a number is rolled, that player’s turn is skipped. NOTE: When playing this game for addition only, the game piece on the number one space will not go into the river. This can make for a great teaching moment.
• Stop the game as things are winding down and say: “I have noticed that all of you have been adding numbers and throwing the game pieces that are on those number spaces into the river. But I see that all of you still have a game piece on number one. Why do you think that is?” (No two numbers on the dice add up to one). Say: “That’s right. None of the numbers on the dice add up to one. So, will we be able to throw the number one game piece into the river?” (No). Say: “How do you think we can get that number one piece into the river?” Here you might have a child who suggests taking away or subtraction. If that is the case, then this is the perfect opportunity to segue into subtraction. If there are no ideas, just have the children throw their number one into the river as a “free jump.”

1. Introduce subtraction to the game. When the children place their 12 pieces on each of the 12 game spaces, they can either add or subtract the numbers rolled. So, if a three and a four are rolled, the player can either add the three and the four and throw the game piece on the number seven into the river or the player can subtract the three from the four and throw the game piece on the number one into the river. This way, the player has two options. They cannot do both. One or the other. In this complete version of the game, all of the pieces on the number spaces will eventually make it into the water.
2. Using their math journals, children can write the equation after they have a turn. For example, if the child rolls a three and a four and decides to remove the game piece on their number seven space, the child will write 3+4=7. If the child rolls that same three and four, but decides to remove the game piece on their number one space, then the child will write 4-3=1.
3. Once the children have played once or twice, allow them to put the 12 game pieces on any number they want. They can put several game pieces on one number. If they start noticing patterns, or the predictability that they will roll a combination of seven or six more times than they will roll a combination of 12, encourage them to think about this. Ask: “Why did you put several game pieces on eight and none on number 12?” (I roll that number more than the one.) Ask: “How many ways can you roll a seven?”  Say: “I see, you can roll a five and a two, you can roll a six and a one and you can roll a three and a four. Those are all of the ways that you can make seven.” Ask: How many ways can you roll a 12?” Say: “Only one way, a six and a six. It is more likely that you will roll one of these combinations of seven than roll the one combination of 12.”

#### Step 4: Vocabulary.

• Add: To increase the number (e.g.,”When I add three dots on one die to four dots on the other die, I get seven dots.”)
• Subtract: To remove something (e.g.,”When I have four dots on one die and I subtract three dots from the other die, I am left with only one dot.” You can also use take away. Reinforce that subtract means the same as take away.)
• Equals: Exactly the same amount or value (e.g.,”When I have four dots plus three dots, that equals seven dots.”)
• Altogether: In total (e.g.,”How many dots are there altogether?”)

#### Step 5: Adapt lesson for toddlers or preschoolers.

##### Adapt Lesson for Toddlers
###### Toddlers may:
• Not yet have one-to-one correspondence when counting the number on the dice
• Not yet grasp the operations of addition and subtraction
###### Child care providers may:
• Only use the numbers one through six on the game board and only use one die to reinforce one-to-one correspondence when counting, rather than focusing on addition
• Help the children count aloud while pointing to each dot on the die  (“Let’s count all of the dots that we see on the dice: 1-2-3 dots on the first die and 1-2-3-4 dots on the second die. Now let’s count them altogether. Seven dots on the dice: 3+4=7.”
• Help the children with the concept of addition by continually reinforcing that, when they combine the numbers on the dice, they are adding the two numbers together.
##### Adapt Lesson for Preschoolers
###### Preschoolers may:
• Be ready to add subtraction to the game (see additional extension #1 above)
• Use their math journals to extend their thinking by writing math equations (see additional extension #2 above)
• Be ready to extend the game by putting 12 game pieces on any number they want (see additional extension #3 above)
###### Child care providers may:
• Help reinforce the concept of subtraction. Using the pair of dice, help the children realize that the smaller number on one die needs to be taken away from the bigger number on the other die. “You’ve rolled a six and a three. Can we take six dots away from three dots?” (No)  Say: “No, there aren’t enough dots to take six away from three. But can we take three away from six?” (Yes)  Say: “So, six minus three equals?” (Three)  Say: “That is correct. So what number game piece are you going to throw in the river?”
• Help the children write the number sentences in their journals. Write the symbols for addition and subtraction at the top of the page for the children to reference.
• Ask questions that provoke thinking and reflecting on previous games. “Why did you put several game pieces on seven and none on number 12?” (I roll that number more than the 12.) “How many ways can you roll a seven? I see, you can roll a five and a two, you can roll a six and a one and you can roll a three and a four. Those are all of the ways that you can make seven. How many ways can you roll a 12? Only one way, a six and a six. It is more likely that you will roll one of these combinations of seven than roll the one combination of 12.”

### Suggested Books

• Let’s Throw the Dice (Let’s Move) by Heidi Linder (Meyer & Meyer Verlag, 2003)
• Richard Scarry’s Best Counting Book Ever by Richard Scarry (New York: Sterling, 2010)
• The Action of Subtraction (Math is Categorical) by Brian P. Cleary (New York: First Avenue Editions, 2008)

### Music and Movement

• Using two big, foam dice (you can get these at teacher stores), play Jump in the River in your classroom. Have the children form two lines with the space in between them representing the river. Toss the dice into the middle. Call out the two numbers rolled and then have the children figure out the total or the difference of the dice. The children on those numbers can “Jump in the River.” This is a great activity to help children who are struggling with addition and subtraction concepts. They will feel safe in a group activity and have the help of their classmates. Play until all of the children are in the river.

### Outdoor Connections

This game can be played outdoors just as easily as indoors!