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At Home Math

One of the best things you can do for your child’s development of a mathematical mind is to ask them to talk about it! Encourage them to explain their math work to you, even if you’re unfamiliar with some of the Montessori terminology. Always feel free to ask your child’s teacher about the math works and how you can support learning at home.


First Grade

First Grade
  • First graders need lots of concrete experience with objects to solidify math operations. Count objects in day to day life (bananas, dogs, freckles, stoplights, etc) to reinforce one-to-one correspondence. Encourage your child to use objects and not their fingers.
  • Practice adding with objects and use real-world events to support learning.  Some examples could be:
    • There are 5 people in our family.  If Grandma and Grandpa came to stay with us, how many would we have at our house?
    • How many stuffed animals do you have? How many does your brother have? How many do you have all together? 
  • Begin memorization of addition facts by having your child offer their best guess of the answer before they do the problem. If they respond quickly and with confidence, move on to another problem without having them check their work with objects.

Second Grade

Second Grade
  • Second graders should solidify their knowledge of addition facts. Emphasize doing addition facts mentally or making a good guess and then using objects (not fingers) to check their work. Some ways to practice facts are:
    • Quiz your child on a couple of facts at the grocery store or any other place where they could check their work with objects (fruit, cans, etc).
    • Practice facts in the car or at meals. Work to remove the stigma of getting an answer wrong. If they say that they don’t know, tell them to make a good guess of a number that is close to the answer, and then help them check their work. Encourage all thier efforts.
  • Children in second grade should gain familiarity with subtraction and move towards mastery of subtraction facts as well as addition facts.
    • Practice subtraction with objects. Encourage them to make a guess and then check.
    • Food is fun for subtraction--count out pieces of pasta, apple slices, chicken pieces, etc.. This is your minuend. Eat the subtrahend, and count how many are left.
  • Quiz your child on a couple of facts at the grocery store or any other place where they could check their work with objects (fruit, cans, etc).
  • Practice facts in the car or at meals. Work to remove the stigma of getting an answer wrong. If they say that they don’t know, tell them to make a good guess of a number that is close to the answer, and then help them check their work. Encourage all thier efforts.

Third Grade

Third Grade
  • Third graders should finish solidifying their memorization of addition and subtraction facts.
    • Quiz your child in the car or while doing chores. If they don’t know the answer, encourage them to figure it out themselves.
  • Third graders should become very familiar with multiplication.
    • Talk through real-life examples of multiplication problems with your child. Help them understand the process, even if their answers are not always correct.
    • Quiz them on multiplication facts frequently, and encourage them to use different strategies (skip-counting, repeated addition) to find the answers. Encourage all their efforts.
    • Once your child is very familiar with the concept of multiplication, introduce the inverse relationship between division and multiplication (i.e. 2 x 4 = 8, and 8 ÷ 4 = 2) to provide support for further math work.
Get Creative at home

Montessori Math Curriculum

The Montessori math curriculum bridges the gap between concrete and abstract thinking with remarkable math materials.  Adults are easily able to understand the link between abstract ideas and concrete examples, but this skill can be all but impossible for elementary-aged children.  Thus, the Montessori math sequences provide the support and framework for children to internalize mathematical concepts and procedures successfully.  After the teacher has presented a new concept, material, or activity, children are able to explore the different mathematical implications of this presentation as they work. Once a child has mastered the concept from the previous lesson, a new concept is introduced. In this way, children are able to move at their own pace, and teachers are very aware of the strengths and weaknesses of each individual.


Numeration

  • Spindle Box

    • Age: 2-4.5
    • Objective: Understanding the uniform growth in quantity while counting.
    • Method: Count one object into your dominant hand and name the quantity. Place the amount in a container labeled “1”. Repeat with integers up to 9. If the child has been introduced to the concept of 0 already, emphasize how the 0 jar is “empty.” To put the work away repeat the counting process (from one hand to the other) from 1 to 9.
    • Materials: 45 cylindrical objects of the same size (pens, pencils, sticks, markers, etc.) 10 jars or small boxes labeled 0-9.
    • Link: https://www.youtube.com/watch?v=M42zdOzww_8

  • Sandpaper Numbers

    • Age: 3-6
    • Objective: Practice the correct formation of numerals 0-9.
    • Method: Trace the number correctly with your first two fingers while saying the name of the number. Emphasize the starting point of each new line, and pause at the end of the number, or ending point of each line. (For example, the number 2 has one continuous line, with a starting point at the top left. In contrast, the number 4 has two lines, with starting points at the top left and then the top right.)
    • Materials: These numbers can be made on card stock with strong glue and sand, or on card stock with bubble paint. It must be a sensory guide as well as a visual guide.
    • Link: https://www.youtube.com/watch?v=TcH8WzuWwKw (only need to go to 9)

  • Cards & Counters

    • Age: 4-5
    • Objective: Solidify the link between number quantity and number symbol.
    • Method: Lay out numbers from 0-9 in a line. Count out one object and place it under the symbol card for 1. Repeat with the counters and cards for the other quantities. Lay quantities in pairs. At a later date (after the child can do this work well) introduce the odd-even pattern that is especially visible when the counters are laid out in pairs.
    • Materials: Cards with numerals 0-9, small objects of the same size (buttons are ideal).
    • Link: https://www.youtube.com/watch?v=zXuJpv5hoac

  • Hundred Board

    • Age: 4-7
    • Objective: Understand the sequence of numbers from 1 to 100, and start to notice the patterns therein.
    • Method: Begin by dumping out all the numbers (or just from 1-50 at first) and sorting them into groups of tens. Lay out the row of numbers from 1-10, followed by 11-20, etc.
    • Options for follow-up work: Record (write) the work. Only lay out odd or even numbers. Lay out only multiples of 10. Fill it in backwards. Make a pattern and explain it. See how far you can count without checking on the board. Any other game you can think of.
    • Materials: Small square cards with numbers 1 to 100 on them. A 10x10 grid of squares of the same size (or slightly larger) on which to place the cards.
    • Link: https://www.youtube.com/watch?v=BzJpPM7iAJ0

  • Cards

    • Age: 5-6
    • Objective: Understand and practice forming the symbols of numbers into the 1000s.
    • Method: Introduce the terminology for units, tens, hundreds, and thousands. Use the cards to show how numbers can be stacked: 4721 can be made with the cards 4000, 700, 20, and 1. Practice saying the names of the numbers (eg. “four thousand seven hundred twenty-one,” remember not to use the word “and” in the middle of your number!)
    • Materials: Card stock cards of 4 different sizes with numbers written on them. Units and thousands should be in green ink, tens in blue ink, and hundreds in red ink.
    • Link: http://nebula.wsimg.com/4542a3e7639eca30877386b14c2b79af?AccessKeyId=6B2040F94691418F042F&disposition=0&alloworigin=1  

Addition

  • Bead Stair (operational)

    • Age: 5-7
    • Objective: Gain familiarity with the concept of addition and practice adding numbers from 1-9.
    • Method: Set up both pyramids next to each other with 1 at the top and 9 at the bottom. Take the first addend from the first pyramid and place it in your workspace. Take the second addend from the second pyramid and place it next to the first addend. Count up from left to right through both bars to find the answer. Record your work.
    • Options for follow-up: the child can build their own problems. Can be done with worksheets of addition problems. The child can make a guess and then check their work with the bars.
    • Materials: Two sets of bars for each number from 1-9. These can be made with beads on wire, or strips of cardstock with squares drawn on for each unit. When stacked they should make a pyramid shape. The colors must be as follows:
    • Link: https://www.youtube.com/watch?v=JvIp6KRBTJU

  • Stamp Game (Operational)

    • Age: 6-8 (*Must be familiar with Golden Bead addition)
    • Objective: Further abstraction of the concept of addition by adding large numbers.
    • Method: Build two numbers in the thousands with the stamp game. Combine the units from both numbers, and count the quantity. Repeat for the 10s, the 100s, and the 1000s. Be sure that the first problems are static, or that they have no regrouping (no place value exceeds 10). When moving on to dynamic problems, be sure to do the regrouping (“exchanging” or “trading in”) before moving on the the next place value.
    • Materials: A quantity of small squares in green, blue, and red. If helpful, label the green ones with “1,” the blue with “10,” the red with “100,” and more green ones with “1000.”
    • Link: https://www.youtube.com/watch?v=7-o2m1Wfv0A

  • Strip Board (operational)

    • Age: 6-8
    • Objective: Further abstraction of addition math facts.
    • Method: The two addend staircases are laid out on either side of the board. The first addend is taken from the red stair and placed on the board starting at 1, and the second addend is taken from the blue stair and placed next to the red addend. The answer is found above the end of the blue strip. Many problems are done, including exploration of a number plus itself (doubles) or different addition problems that make 10.
    • Materials: Strips of card stock from 1 cm to 9 cm, one set in red and another in blue. An 18 cm chart with each cm labeled (1 to 18).
    • Link: https://www.youtube.com/watch?v=iLR6FA1xA00

  • Charts (memorizing)

    • Age: 6-8
    • Objective: Movement towards memorization of basic addition math facts.
    • Method: For an example problem of 4 + 5 =, the left index finger is placed on “4” in the left column. The right index finger is placed on the number “5” in the top row. The fingers are then slid together, following the rows and columns until they meet on the answer, “9.”
    • Materials: Paper chart of all addends and answer combinations from 1-9. Can be printed from http://www.montessorialbum.com/montessori/images/9/96/Addition_Chart_3.pdf
    • Link: https://www.youtube.com/watch?v=vSAjAAJfbPQ

Multiplication

  • Stamp Game (Operational)

    • Age: 7-9
    • Objective: Further abstraction of the concept of multiplication by using large numbers.
    • Method: For an example problem of 3145 x 3 =, the multiplicand is made with the stamp game 3 times. The numbers are then added together, counting up the units first, followed by the 10s, 100s, and 1000s. Any regrouping is completed before counting the next place value.
    • Materials: A quantity of small squares in green, blue, and red. If helpful, label the green ones with “1,” the blue with “10,” the red with “100,” and more green ones with “1000.”
    • Link: https://www.youtube.com/watch?v=DCcZMQrgZlM

  • Bead Bars (memorization)

    • Age: 7-9
    • Objective: Further abstraction of multiplication math facts.
    • Method: Multiplication facts are built with the bead bars (or strips of cardstock) to create a visual representation of the multiplication problem array. For example, the problem of 6 x 3 = would be made with three bars of six, in a rectangle. The product can then be found by counting each bead/box, counting by sixes, counting by threes, or remembered mentally.
    • Materials: Nine sets of bars for each number from 1-9. These can be made with beads on wire, or strips of cardstock with squares drawn on for each unit. The colors must be as follows:
    • Link: https://www.youtube.com/watch?v=WCfomP9Su88 (2:00 through 3:30)

  • Charts (memorization)

Subtraction

  • Stamp Game (operational)

    • Age:6-8 (*Must be familiar with Golden Bead subtraction)
    • Objective: Further abstraction of the concept of subtraction by subtracting large numbers.
    • Method: A number in the thousands is formed with the stamp game. The subtrahend is then taken away and put back, starting at the 1s, then the 10s, 100s, and 1000s. If the minuend has insufficient 10s to take away those required by the subtrahend, break one of the 100s into ten 10s, etc.
    • Materials: A quantity of small squares in green, blue, and red. If helpful, label the green ones with “1,” the blue with “10,” the red with “100,” and more green ones with “1000.”
    • Link: https://www.youtube.com/watch?v=YB9RI4_H7O0

  • Strip Board (memorization)

    • Age: 6-8
    • Objective: Further abstraction of subtraction math facts.
    • Method: The two staircases are laid out on either side of the board. A blank strip is placed on the board to establish the minuend. The minuend is taken from the blue stair and placed on the board starting at the end of the blank strip, and the answer is taken from the red stair and placed in the remaining strip. The answer is the red strip. Many problems are done.
    • Materials: Strips of cardstock from 1 cm to 9 cm, one set in red and another in blue. An 18 cm chart with each cm labeled (1 to 18). A 17 cm blank strip (not red or blue).
    • Link: https://www.youtube.com/watch?v=3pLWxgiJpR4

  • Charts (memorization)

Division

  • Stamp Game (operational)

    • Age: 8-9
    • Objective: Further abstraction of the concept of division through the use of large numbers.
    • Method: For an example problem of 9123 ÷ 3, the quantity 9123 is made with stamps. Starting with the thousands, the stamps are distributed into 3 different groups. If there are any stamps left over in any place value, they are each exchanged for 10 of the next smallest place value. Note: Be sure to create problems without remainders for a control of error.
    • Materials: A quantity of small squares in green, blue, and red. If helpful, label the green ones with “1,” the blue with “10,” the red with “100,” and more green ones with “1000.”
    • Link: https://www.youtube.com/watch?v=fCDNoyBMHnk

  • Charts (memorization)