Math Access for Teachers and Home Child Care Providers

Jump in the River

Children will explore addition of whole numbers.

Content Area Standard Target
• Number and Operations
• Algebra
• 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
• Develop and use strategies for whole-number computations, with a focus on addition and subtraction
• Develop fluency with basic number combinations for addition
• Use a variety of methods and tools to compute, including objects, mental computation,
estimation, paper & pencil, and calculators
• Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols
Obtain the 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 2 players will have 24 counters total.
• Jump in the River board. To make this game board:
• Take a regular 8 x 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 1 ½ inches in length).
• 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 create a choking hazard for children. Make sure that all materials you choose to use for an activity or lesson with children meet safety requirements. Small parts are not appropriate for children who are 5 years of age or younger.

Introduce the Activity

1. Gather the children into a circle. You will need to also 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 they will be playing an adding game called Jump in the River.
3. Ask the children what you mean when you say “adding”.
• “Who knows how to add numbers?”
• “Can you explain to everyone how to add?"
4. Paraphrase the possible definitions children give as answers and tell them the working definition:
• “To add, is to increase in amount or number."
• "We have 8 children sitting around the circle right now.  If I were to add 4 more children to the circle, there would be 12 children in the circle.  By adding 4 more children to the circle, that would increase the amount of children in the circle from 8 to 12.”
5. Say: “We are going to play a game today that will help us learn about and practice adding numbers.”

Engage the Children

1. Explain and simultaneously model the rules of the game:
• Each player has 12 games pieces.
• Each player places 1 game piece on each of the numbers on his or her side of the board (12 in total).
• The first person rolls the dice. (I always model rolling dice.  I show the kids exactly how to roll the dice calmly in their hand and gently toss it onto the game board.  It is distracting when the kids throw the dice around and spend the majority of their time fetching the die.  I say, “No Crazy rolls.  Only Learning rolls” and I model the different rolls).
• Roll the dice.
• Ask the children: "What numbers have I rolled? (pretend for now that you rolled a 3 & a 4)"  Say:“Yes, a three and a four.”  Count out the 3 dots of the first die and count out the four dots of 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 3 and 4?”
• Assist the child in counting the total number of dots on the two dice by counting aloud all of the numbers.  “1, 2, 3, 4, 5, 6, 7." Say:"That’s right.  There are 7 dots altogether.  3 plus 4 equals 7."  Say: "Now this player can throw the marker that they have on the number 7 into the river.”  Take the game piece off of the number 7 and place it into the middle of the game board (the river).  Only the player rolling the dice, whose turn it is, throws his or her game piece in the river.
• The game continues until almost all 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 havenoticed 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 1.  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 segway 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 3 and a 4 are rolled, the player can either add the 3 and the 4 and throw the game piece on the number 7 into the river or the player can subtract the 3 from the 4 and throw the game piece on the number 1 into the river.  This way, the player has 2 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 3 and a 4 and decides to remove the game piece on their number 7 space, the child will write 3 + 4 = 7.  If the child rolls that same 3 and 4 but decides to remove the game piece on their number 1 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 7 or 6 more times than they will roll a combination of 12, encourage their thinking around this.  Ask:“Why did you put several game pieces on 8 and none on number 12?”  (I roll that number more than the 1)  Ask: “How many ways can you roll a 7?”  Say:“I see, you can roll a 5 and a 2, you can roll a 6 and a 1 and you can roll a 3 and a 4.   Those are all the ways you can make 7." Ask: How many ways can you roll a twelve?”  Say:“Only one way, 6 and a 6.  It is more likely that you will roll one of these combinations of 7 than roll the one combination of 12.”

Encourage Vocabulary

• Add – To increase the number (e.g., "When I add 3 dots on the dice to 4 dots on the dice, I get 7 dots.")
• Subtract – To remove something (e.g., "When I have 4 dots on the dice and I subtract 3 dots on the dice, I am left with only 1 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 4 dots plus 3 dots, that equals 7 dots.")
• Altogether – In total (e.g., "How many dots are there altogether?")

Glossary of MATH vocabulary

Supporting Children at Different Levels

Toddlers   Pre-K

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.

Pre-K Children 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.

Home child care providers may:

• Only use the numbers 1 through 6 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 the dots we see on both die.  1 – 2 – 3- dots on the first die.  1 -2 -3- 4 dots of the second die. Now let’s count them altogether.  7 dots on both die.  3 + 4 = 7."
• Help the child with the concept of addition by continually reinforcing that when they combine the number of the 2 dice, they are adding the two numbers together.

Home child care providers may:

• Help reinforce the concept of subtraction.  Using the two dice, help the children realize that the smaller number on the dice needs to be taken away from the bigger number. “You’ve rolled a 6 and a 3.  Can we take 6 dots away from 3 dots?” (No) “No, there aren’t enough dots to take 6 away from 3.  But can we take 3 away from 6?” (Yes)  “So, 6 minus 3 equals?” (3)  “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 journal. 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 upon previous games.  “Why did you put several game pieces on 7 and none on number 12?”  (I roll that number more than the 12) “How many ways can you roll a 7?”  “I see, you can roll a 5 and a 2, you can roll a 6 and a 1and you can roll a 3 and a 4.  Those are all the ways you can make 7.  How many ways can you roll a twelve?”  “Only one way, 6 and a 6.  It is more likely that you will roll one of these combinations of 7 than roll the one combination of 12.”

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 between them acting as the river.  Toss the 2 dice into the middle.  Call out the two number rolled and then have the children figure out the total or the difference of the two dice.  The children on those numbers can “Jump in the River.”  This is a great activity to help children who are struggling with the addition & subtraction concepts.  They 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!

Web Resources

# Comment on this lesson

 To report a problem with the site, please email us. © 2011. M.A.T.H.