There are 4 main ideas when thinking about number sense: spatial relationships, part-part-whole, one/two more, one/two less, and benchmarks of 5 & 10. This page was created to provide a quick overview for each idea and some games to help build understanding.
What Is It:
-spatial relationships is the foundation of number sense -having conversations about how visual number sets are the same and different Why It's Important: -helps students notice patterns so relational thinking can happen -helps give students something to visualize when solving problems instead of just thinking of the numeral -helps kids get beyond counting one by one -helps move them into the 'counting on' part of the number sense continuum Assessments: -on ESGI, we created one assessment where we show students dot patterns that have 1-7 dots and ask students to quickly subitize the amount Tools/Helpful Tips: -remember to use more than just dot patterns ex. math rack, dominoes, number paths or open number lines -use purposeful color organizing to help students see the intended pattern and get beyond counting one by one -along with asking "how many" also ask, "how does what you see compare/contrast to another set?" Games to Build Understanding: 1. Spatial Relationship Memory-pick 10 pairs of dot pattern cards, each pair having the same number but different arrangements of dots, students place them face down and play memory 2. Cover It: (need 1-6 cover it strips for each child, counters, regular dot die for each group) groups of 3-4 kids, each player takes a turn rolling the die and they cover the number on their strip with a counter, when everyone covers their strip they can clear and start over 3. Cover It Bump: (use only one strip for a group of 2), students roll the die and cover that number on their strip, if your opponent rolls the same number, you can bump them off of their spot, if the same player rolls the same number twice and covers that number with two counters, that spot is safe and cannot be bumped, player with the most counters wins 4. Finger Flash: teacher flashes fingers and the students say or write down the number you show (should be done almost daily), when you first start-only show numbers 0-5 until they show an understanding of those numbers
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What is it?
-looking at one number and realizing all the ways to make that number -understanding that even though you move pieces around or change the color, the total number stays the same -solidifies the concept that parts of a number make up the whole, and that the whole can be broken up into parts Why it’s important: -all other relationships between numbers depend on it!!! -all derived facts depend on students understanding this skill -helps students understand that numbers can be broken up into lots of different ways -helps students when they begin to work on multi-digit numbers and fractions as they get into the older grades -helps students learn their facts and derived facts Assessment: -on ESGI, we created two different assessments -first: teacher counts out 7 cubes on the table and then asks student how many cubes are there, then the teacher divides the cubes into two groups and asks the student how many are there now? -second: teacher counts out 8 cubes and says, "Now I am going to put some of them in this cup." teacher puts 3 in the cup so the child can't see how many were taken and asks "How many cubes are in the cup?" Tools/Helpful Tips: -10 frames should be shown in many different ways (pair-wise, five-wise, random) -can use any numbers when working on this skill (not just 5 and 10) -when working on this skill, don’t forget to teach the kiddos WHEN it is useful for them to use part part whole (like when solving a problem like 7+9-have conversations about how to break apart 7 in a useful way Games to Build Understanding: Part-Part-Whole: Chunk It! Materials Needed: Connecting Cubes Give each child 7 connecting cubes. When you say, “Chunk It” the students will break their stack of cubes into two “chunks”. The students should notice how many are in each chunk and share the combination they made with the class. Model using a sentence frame: “7 can be chunked into ______ and ______. As each student shares write the number sentence on the board. Practice activity using different numbers and have students share their combinations. You can also use in partners once students have an understanding of the game. Part-Part-Whole: In the Hand Materials Needed: Number Cards, Counters The student will work in pairs. One child will flip a number card and count out that many counters. The child will then close their eyes and their partner will grab some of the counters in his/her hand. When the other child opens his/her eyes, that child will think back to the whole amount to try to figure out how many counters are in their partner’s hand. The kids will then switch roles and continue playing the activity. Part-Part-Whole: Salute Materials Needed: Deck of cards (for each group of 3 students) The players sit forming a triangle with their deck of cards face down in the center. Two of the players are ‘Saluters’ and the third is the ‘Caller’. The two Saluters will grab a card off the deck and without looking at it, place it on their forehead facing out. The Caller will then call out the sum of the cards. The first Saluter who can figure out the number on their own head gets both cards. Continue playing until all the cards in the deck are gone. Whoever has the most cards gets to continue being a Saluter and the Caller switches roles with the other Saluter. What is it?
-One/Two More & Less is about noticing relationships in numbers. Why It's Important: -Understanding one/two more or less will help students be more flexible in their thinking about numbers. -Understanding one/two more/less will help students when they are ready to do mental math. -One/two more/less is about noticing relationships in numbers. Having students rote count does not guarantee they are noticing relationships because it is not concrete enough for young learners. It is important to start with visuals so they can see how one number contains one/two more/less than another. When kids first start counting they do not understand that with each number you are adding one more. -An understanding of one/two more/less will help students when they get to doubles. If students have good number sense and develop an understanding of relationships they will figure out the strategy without someone telling them. -When students are able to notice connections in numbers it will be easier to pull them from memory. -Hierarchical Inclusion. It is important that students understand that if you have a certain amount you also have less than that amount (ie. 8 is included in 9). This will allow them to use what they know about numbers and relationships to solve problems in a more efficient way. Tools: -Ways to match abstract number to concrete visual representation of that number -Use spatial relationship patterns to show one/two more/less and help students see the relationship. -Show abstract number sentences and symbols alongside visual representation. -Addition Fact Chart Assessment: -on ESGI, we created two different assessments -first: teacher asks student to count out 5 cubes, then teacher adds one cube to the pile and says, "I added one cube to your pile. How many do you have now?" (teacher should note if the child had to recount entire pile) -second: teacher asks student to please count out 6 cubes, them teacher takes away one cube from the pile and says, "I took away one cube from your pile. How many do you have now?" (teacher should note if the child had to recount entire pile) Games to Build Understanding: -One/Two More and Less: Scoop it-Make it-Students scoop a spoonful of counters onto their mat in an area labeled "My Scoop". Have student make the number that is one more than their amount and one less. Have students practice saying the relationships. "_______ is one more than ______. Repeat activity with two more/less. -One/Two More and Less: Stacking Cups-Supplies: 10 foam cups with dot patterns for numbers 1-10 drawn on that cups, die. Give each pair the foam cups out of order. Have them stack them in order from 1-10. Have them practice so they can stack more quickly. After they have practiced going from 1-10 have them roll the die. Whatever the die lands on the student will start stacking from there. Have them mix the cups up and repeat. This activity will let you know which kids are able to subitize. You can also see which kids are able to count on without having to go back and recount to see which number comes next. To challenge students you can extend into the teens or write numerals on the cups rather than dots. -One/Two More and Less: Slap it-Materials: Number Cards, Fly Swatter. Within a group of three children, two are slappers and one is the speaker. Lay out the number cards from 0-20 in order. The speaker will say a number out loud and the slappers have to race to slap the cards that is one more than that number. The first slapper to slap the card gets to keep it. In the next round they will slap the card that is one less than. You can also continue on to two more/two less with students. What is it?
-relationship between a number and the benchmark of 5 or 10 Why it’s important: -when a student understands all three friendly number benchmarks (0. 5, 10), then any number is only 2 away from an important benchmark and can be easily added to or subtracted from -if students do not have an understanding of this concept, the only strategy they are left with is counting and it will be hard to move beyond counting each object one by one -helps students move along the number sense continuum-they will go from counting on to derived facts/facts Tools/Helpful Tips: -when developing this skill, remember that placement of objects is VERY important Ex. if you place your counters in a straight line, it will not be obvious to students that they should try to make a quick group of 5-they will only try to count each individual counter -when working on benchmarks of 5 & 10-arrange your tools in a five-wise set up (five is clearly visible and then the extras under or on top (random placement and paired placement are okay too, just not ideal for this skill) -develop “five-ness: the ability to quickly find five” before “ten-ness: the ability to quickly find ten” -helps students subitize easier if they understand how to find 5 first -make sure students know that the top or bottom row on a 10 frame is 5 -use 5 frames before you use 10 frames when developing this skill Assessments: -on ESGI, we created four different assessments -first: give child a math rack and say, "Please slide over 7 beads on one side of the rows." (teacher should note how they slid the beads ex. 1 by 1, grab 5 and then 2, counts how many to leave and slides the rest) -second: count out 6 cubes in front of the child and say, "I have six cubes here. How many more do I need to put here so that I have 10 cubes?" (teacher should note how they figure it out (ex. child adds cubes by ones until 10, child adds groups, just knows) -third: teacher says, "I have a bunch of cubes here. Will you count out just twelve cubes for me?" "Great. Now can you write the number?" teacher points to the 2 "Show me with cubes what this number means." Then for part two of this assessment, point to the 1 and ask student, "Show me with cubes what this number means." Games to Build Understanding: 1. Bump: students roll a die (has 0-5 printed on it), and then they cover up the number they need to add to it to make 5 on the game board Ex. The student rolls a 3, the student will cover up 2 on the game board. If the student rolls a 3 in the future, they will cover up the 2 twice. This means they are safe and cannot be bumped. If their opponent rolls a 3 before they have made that space safe, their opponent can bump them off and steal the space. 2. Capture 4: students roll a die (has 0-5 printed on it), and then they cover up a space on the game board that has the number to add to it to make 5, then the next player rolls and does the same -the first player to get four in a row on the game board wins 3. I have, Who Has: each student gets a card that has an amount shown on it that is more or less than 5 (shown in a five-wise pattern on a 5 frame) on the top-it will read “I have 7”, then a different amount on the bottom-it will read “Who has one more than 5?” -the player that has 6 listed on the top will read their card -play continues until you find the end 4. Make 5 Memory -students will lay out cards in a square shape and turn over two-if they make 5 together (3 and 2) then they match and the student keeps the cards, if the cards do not make five, they flip them back over and the next player goes To create this blog, I used books, videos, and other resources from Christina Tondevold's website https://buildmathminds.com/. This website has many wonderful FREE resources as well that you can use to help build your student's number sense in all four areas.
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AuthorHi! My name is Brooke Praska. I am a kindergarten teacher, and I wanted to share my journey in striving to be better every day! Contact |