Addition with renaming using MENTAL MATH!

Addition with Renaming ... what is it?

Renaming is the process used to solve math problems when there are too many ones, tens, or hundreds. This process is also known as "regrouping" or "borrow and carrying."  Example: 14 + 7 =  When you add the numbers in the ones place you get 11 ones.  The 11 ones have to be "renamed" for 1 ten and 1 one.  Solving the problem continues by adding the tens place value etc.

Below are some suggestions to help your child use mental math to add with renaming.  Your child WILL learn the vertical algorithm, which is often easier to use (and typically the preferred method for solving this type of math problem).

TIPS (using example problem of 54 + 7 = )

- Count up by starting at 54 and counting 7 higher (55, 56, 57, 58, 59, 60, 61)

- Place value chart - use items such as pennies for 1s, dimes for 10s, and $1 for hundreds (make the number 54 with 5 dimes and 5 pennies.  Have your child add 7 pennies to the board to make 61.

 11 ones = 1 ten 1 one

- Solve using "jump roping" (adding the ones, then adding the tens).  They will start by adding the numbers in the ones place (4 + 7).  Your child should recognize that equals a double digit number and cannot go into the ones place.  They will write the answer (11) below the problem and add the tens in 57 (5 tens = 50).  The new problem would look something like this: 50 + 11 =.  Now it is a problem that can be solved by "jump roping" (adding the ones, then adding the tens).

Number Bonds

Even if your school district has not adapted the Singapore Math curriculum, I'm sure you've heard the term "number bond" before.  The purposes of "number bonds" are to focus on the bonds between three numbers and to reduce the amount of math facts needed to be memorized.  A student can visualize one number bond and know the four related facts (Growing up I learned this as "fact families).

3 + 4 = 7

4 + 3 = 7

7 - 3 = 4

7 - 4 = 3

Curious how to help your child practice these math facts?  Press play:

Ideas for additional practice:
Number Bond Worksheets
Number Bond Machines
Save the Whale: Bonds of 10
Number Bonds: Make 10

Branching (And no, I'm not talking about trees!)

Ah yes, branching!  At first this sounded complicated but it ended up making complete sense.  First of all, what is branching?  Branching is a mental math strategy of breaking individual numbers into their hundreds, tens, and ones.  You can complete the problem by adding or subtracting once the number is broken (branched) apart:

To Add:
1.  Add the 10s
2.  Add the 1s
3.  Add 10s and 1s together

To subtract:
1.  Subtract the 10s
2.  Subtract the 1s
3.  Add 10s and 1s together

Branching is typically taught drawing everything out.  But then moves to students being able to do it using mental math.  The progression of Singapore Math is concrete --> pictorial --> abstract.  Of course, students will also learn the standard algorithm (vertical format) for solving these problems.  But it is nice to teach them how to solve these types of problems when they don't have a piece of paper and pencil handy.

If you take time to stop and think about how you would solve the problem 54 + 32, most of you would use a form of branching to solve.  Now you know the Singapore Math name for this mental math strategy!

Make a 10!

Understanding bonds of ten is a vital component of mental math.  Students are encouraged to use a "10-frame" to add and subtract (eventually this is all done through mental images).  Here is a sample 10 frame:

The 10-frame can be filled with counters, coins, erasers, small toys, and the list goes on.  

Steps to solving a problem using a 10-frame: (8 + 5)

1.  Fill the 10-frame with counters matching the largest number

2.  Use the second addend to fill the ten frame ("make a ten").  The filled 10-frame is the ten.  The left over counters will be the number in the ones place.  

I use 10-frames as part of my math stations.  However, I use egg cartons (with 2 spots cut out) as the 10-frame.  It adds a little more interest :-)

From there, the students roll two dice to get the two addends and fill the 10-frame as mentioned above. Last, they have to use "math talk" to describe the problem.  An example is written on an index card with the station: ____ + ____ = ___ ten and ___ ones.  This makes _____.

I don't know about you, but it is pretty cool to think about how people think! "Making a ten" is totally how my brain operates... didn't realize that until I started teaching mental math!