I’m sure everyone would agree that learning the addition / subtraction facts associated with the number 10 are very important.  Or maybe you are thinking, aren’t they all important? Why single out 10? My feelings are that of all the basic facts, being fluent with 10 and the combinations that make 10 enable the user to apply more mental math strategies, especially when adding and subtracting larger numbers. Here are a few of my favorite activities to promote ten-ness! Check out the card trick videos below – great way to get kids attention, practice math, and give them something to practice at home. Continue reading

# Addition and Subtraction Part 2: Part-Part-Whole Models KG-2nd

In Part 1 I focused on a numerical fluency continuum, which defines the stages a child goes through to achieve number sense. After a child has a firm grasp of one-to-one correspondence, can count on, and understands concepts of more and less, he/she is ready to explore part-part-whole relationships which lead to the operations of addition and subtraction. That will be the focus of this post. Read on for free number bond activities and a free number bond assessment!

One way to explore part-part-whole relationships is through various number bonds experiences.  Number Bonds are pairs of numbers that combine to total the target or focus number. When students learn number bonds they are applying the commutative, identity, and zero properties. Do you notice from the chart below that there are 4 number bonds for the number 3; 5 number bonds for the number 4; 6 number bonds for the number 5, etc? And . . . half of the number bonds are actually just the commutative property in action, so there really aren’t as many combinations for each number to learn after all.

• KG students should master number bonds to 5.
• First graders should master number bonds to 10.
• Second graders should master number bonds to 20.Teaching Methods for Number Bonds
• Ideally, students should focus on the bonds for one number at a time, until mastery is achieved. In other words, if working on the number bond of 3, they would learn 0 and 3, 3 and 0, 1 and 2, 2 and 1 before trying to learn number bonds of 4. See the end of this post for assessment ideas.

• Ten Frame cards: Use counters to show different ways to make the focus number. (See above example of 2 ways to show 6.) Shake and Spill games are also great for this:  Using 2-color counters, shake and spill the number of counters matching your focus number.  See how many spilled out red and how many spilled out yellow.  Record results on a blank ten-frame template. Repeat 10 times.
• Number Bond Bracelets: Use beads and chenille stems to form bracelets for each number 2-10.  Slide beads apart to see different ways to make the focus number.
• Reckenreck: Slide beads on the frame to show different combinations.
• Part-Part-Whole Graphic Organizers:  Here are two templates I like. Start with objects matching the focus number in the “whole” section. Then move “part” of them to one section and the rest to the other section. Rearrange to find different bonds for the same focus number. Start students with manipulalatives before moving to numbers. Or use numbers as a way for students to record their findings.

Once students have a good concept of number bonds, these part-part-whole organizers are very helpful when doing addition and subtraction problems (including story problems) using these structures: Result Unknown, Change Unknown, and Start Unknown.  Children should use manipulatives at first to “figure out” the story.

• Here is an example of a change unknown story:  “I have 5 pennies in one pocket and some more in my other pocket. I have 7 pennies all together. How many pennies in my other pocket?” To do this, put 5 counters in one “part” section. Count on from 5 to 7 by placing more counters in the second “part” section (2). Then move them all to the whole section to check that there are 7 all together.  Students are determining “What goes with 5 to make 7?” 5 + ___ = 7
• Here is an example of a result unknown subtraction story:  “Mom put 7 cookies on a plate. I ate 2 of them. How many cookies are still on the plate?” To do this start with the whole amount (7) in the large section. Then move the 2 that were eaten to a “part” section. Count how many are remaining in the “whole section” to find out how many are still on the plate?  7 – 2 = ____.
• How are number bonds related to fact families?  A fact family is one number bond shown with 2 addition and 2 subtraction statements.  Ex:  With number bonds 3 and 4 for the number 7, you can make 4 problems: 3 + 4 = 7;  4 + 3 = 7;  7-3 = 4;  and 7-4=3.

# Daily Math Meeting Part 4: Number of the Day/Week and Fun Facts

This is part 3 of my “Daily Math Meeting” posts. I will share several different fun and motivational math activities that can be done in just a few minutes on a daily basis — all of them building number sense and reviewing concepts of subitizing, number bonds, addition, subtraction, less, greater, even, odd, etc.

Number of the Day / Week

You can look on Pinterest or TPT and see many good resources on this topic – from daily review sheets to bulletin board products. Here’s my take on it (depending on your grade level).  If you are KG, then I suggest a number of the week, building from 1-10 at first (for the first 10 weeks). Focus on #1 the first week, #2 the second and so on. Really go in depth with each number, revealing a little bit each day. Then after the 10th week, repeat. This will give students adequate time to focus on each number in depth. See the attached PDF for some of my slides regarding this topic. daily-practice-to-build-number-sense-pdf

Monday:  “Our number this week is one.” Here’s what it looks like (show the numeral 1).” Students say the number and make it in the air. Teacher shows how to write it. Then show a representation of the number (such as putting something in a jar or posting on the board).

Tuesday-Thursday: Review the above and then show another way to represent the number (maybe 1-2 more each day). Examples:  Five or Ten frame, dice, domino, fingers on a hand, place on the number line, word form, tally mark, random dot. Talk briefly about how the patterns help you remember the amount without counting them (which is subitizing). When showing the 4 on a dice, notice that “if you connect the corners, you make a square.” Then when showing 5, notice that, “it’s like 4, but with a dot in the middle.”

Friday: Quickly review previously posted information about your number. Share a problem involving the number.  “I had nothing in this jar, and then I put 1 marble in it. How many marbles are in there now?” Along with this type: “Look, I have a marble in my jar. That means I have how many? (Students answer with “one.”). “What if I take this 1 marble out? How many will there be in the jar?” Share other concepts of this number such as (uno, single for one; or double, twin, duet for two, etc.)

When working with numbers 2-10: You will also start focusing on number bonds. Using 2-color counters on a ten frame, show (and let students think of) different ways to make the number of the week. Example for #5: 1 red, 4 yellow; 2 red, 2 yellow; 3 red, 2 yellow; 4 red, 1 yellow; 5 red, 0 yellow; 0 red, 5 yellow. You don’t even need to make an equation yet. Just say “1 and 4 makes 5; 2 and 3 makes 5 . . .”

For first or second grade: I have two thoughts on this. You could do a number of the day utilizing the calendar date as your number. This means if it’s the 14th of the month, you are focusing on #14. This also means you would repeat these numbers each month – thus giving more exposure to the numbers students are most likely using on a regular basis. You could add the following concepts to your discussion: place value with tens/ones (in straw bundles, stick bundles, or posting sticky dots on ten frames); expanded notation (14 = 10 + 4); concepts of odd and even, and how to make the number using coins.

Second thought is this:  Keep track of the number of days of school (for those of you who like to celebrate the 50th and/or 100th day of school), but choose a number of the day or week to focus on so you can review those very important number concepts and number bonds with numbers from 0-20. Part of your board could have a whole/part/part section to show a way to break apart your number. Continue reading

# Number Talks Part 2: Strategies and decomposing with 1st-3rd grade

For 1st -3rd grade students: Refer to “Number Talks Part I” (posted Nov. 12, 2016) for ways to conduct a Number Talk with KG and early 1st grade students (focusing on subitizing and number bonds). For students in 1st – 3rd grade, place extra emphasis on number bonds of 10.

Write a problem on the board, easel, or chart tablet with students sitting nearby to allow for focused discussion. Have the following available for reference and support: ten frame, part-part-whole template, base ten manipulatives, and a 0-100 chart. Present addition and subtraction problems to assist with recall of the following strategies. If time allows, post another similar problem so students can relate previous strategy to new problem. Students show thumbs up when they have an answer in mind. The teacher checks with a few on their answer. Then he/she asks, “How did you solve this problem?” The teacher writes how each student solved the problem.

# Number Talks Part 1: Subitizing and Number Bonds KG-1st grade

A Number Talk is an opportunity to review number sense and operations by making it part of your daily math routine — so that what has previously been taught is not easily forgotten.

In this post I will expand on 2 methods for conducting a Number Talk session for KG-1st grade students (Subitizing and Number Bonds). Refer to a previous post (Sept. 10 – Daily Practice to Build Number Sense), in which I mentioned several other ways to review math concepts on a daily basis such as calendar topics, weather graphs, counting # of days of school, using a 100 chart, Choose 3 Ways, etc. Continue reading

Number Bonds are pairs of numbers that combine to total the target or focus number. When students learn number bonds they are applying the commutative, identity, and zero properties. PLUS, the information can be applied to both addition and subtraction problems. Number bonds of 10 are very critical to our place value system, and will enhance a student’s success with future addition and subtraction strategies such as use of an open number line.

• KG students should master number bonds to 5.
• First graders should master number bonds to 10.
• Second graders should master number bonds to 20.

# Subitizing – What does that mean?

by C. Elkins, OK Math and Reading Lady (updated post on 8-12-17)

The term “subitize” means to recognize quantity without counting. It is a concept recently added to the new OAS (Oklahoma Academic Standards). KG students should be able to “recognize without counting the quantity of a small group of objects in organized and random arrangements up to 10.” For first graders, the quantity is increased to 20 of “structured arrangements.” Subitizing is an important pre-requisite skill to learning addition and subtraction number combinations or number bonds.

Suggested items for the teacher to present this concept:

• Dot cards
• Ten frames and 2-color counters or tiles
• Dot dice
• Dominoes
• Tally marks