Planning GuideGrade 2
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Addition and Subtraction Facts to 18

Strand: Number
Outcome: 10

Step 3: Plan for Instruction

Guiding Questions

  • What learning opportunities and experiences should I provide to promote learning of the outcomes and permit students to demonstrate their learning?
  • What teaching strategies and resources should I use?
  • How will I meet the diverse learning needs of my students?

A. Assessing Prior Knowledge and Skills

Before introducing new material, consider ways to assess and build on students’ knowledge and skills related to counting.

Questions to Consider

  • Do students have instant recognition of spatial arrangements? Most will instantly recognize the number of dots on a standard die without counting.
  • Do they also recognize immediately the complete number of dots on various dominoes?
  • Do they have instant recognition of the number of dots in configurations in other settings?
  • Do they recognize them on ten frames?

Specific Outcome 8 from Grade 1 mentions in the indicators representation on a ten frame of numbers, so it is likely that the majority of Grade 2 students have some experience with ten frames.

  • Show the student dot plate flash cards for one to three seconds.
  • Students are asked to construct the pattern they viewed on their mats with counters.
  • Questioning follows about how many dots they saw and how they saw them.
    This is done for a few configurations each day until the students learn to recognize the number in the configurations without counting (Van de Walle and Lovin 2006, p. 44). The students' competency at recognizing spatial arrangements can be done individually with a minimal investment of time.

Have the students learned what 1 and 2 more or less than each number is without counting on or back (Specific Outcome 8 from Grade 1)?

  • A whole class assessment can be done by giving the students a sheet with random numbers written on it in the centre and columns on either side to write the numbers 1 or 2 less and 1 or 2 more, respectively.
  • Careful observation of the students while they complete this activity will give you an indication of which students are already proficient—those who do this very speedily and without using fingers or subvocalizing counting on or back.
  • Students who are not yet accomplished can use the calculator to give plus or minus 2 numbers by entering +2 = or 2 – 2 = and then entering numbers of their choice or from a deck of cards provided.
  • Students should enter a number, answering the question, then press the = key to confirm their answers.

If you have number machines (see directions for making these in Patterns and Relations Outcome 2)

  • Make a set of cards for plus 2 and another for minus 2.
  • Students try to "beat" the number machine at giving the correct number, which the machine will spit out for each card.
  • Students will hold the card with the beginning number in the top slot and not let go until they have the solution so that they can "beat" the machine.
  • Any hesitation the students have in dropping the card through the slot will indicate that students do not have automatic knowledge of these relationships yet.

It is also likely that students will be proficient first with the 2 more and the 2 less will follow, as is typical of students' mastery of addition facts first and then subtraction facts.

You also need to know if your students are using 5 and 10 as benchmarks.

  • Give each student a five frame printed in the centre of a page and some counters to check their knowledge of its use.
  • Any counters beyond 5 may be placed on the page, but not in the frame.
  • Tell them the rule that only one counter may be placed in a square.
  • Then ask them to show various numbers.
  • Ask them to describe their numbers on the frame.
  • Based on the rule given, no configuration is wrong.
  • The goal is to see if everyone in the class is trained to use frames in a consistent manner, filling them from top left to right.
  • Students may describe, for example, that 4 is 2 and 2 and place 2 counters on one side and 2 on the other.

Questioning should focus on how many more counters students would need to place on the frames to have 5 or how many more than 5 a number is.

Similarly, focus attention on the relation to ten with ten frames. If practice using ten frames is needed

  • Read numbers from a list of random numbers and have the students show each number on the ten frame.
  • When the next number is called, have the students determine what they need to do to alter the past number to create the new number.

Van de Walle and Lovin describe a ten-frame flash card game in which students quickly tell how many dots are on the ten frame or alternatively tell how many white spaces are left on it. Further variations such as having the students say the number 2 more or say the number 2 less provide practice for students who need work on those relationships.

Adapted from John A. Van de Walle, LouAnn H. Lovin, Teaching Student-Centered Mathematics: Grades K–3, 1e (pp. 46–47). Published by Allyn and Bacon, Boston, MA. Copyright © 2006 by Pearson Education. Reprinted by permission of the publisher.

Students also need to have part–part–whole relationships for numbers at least to 10 in place. This means that they know and understand that 5 can be represented as a set of 1 and a set of 4 or a set of 2 and a set of 3.

  • Students can be shown a number that you think they should be successful with and then hide part of it.
  • This can easily be done with Unifix trains.
  • The whole train of nine, for example, is shown to the students and it is confirmed that the students know it is a train of nine.
  • Then hide the nine train and take away some of the cars.
  • If the portion of the train that you bring forward then has only 5 cars, what number of cars were removed?

Repeat for other combinations of nine. If the student is able to tell you without counting the units, then the part–part–whole relationships are known for nine and they can move on to other numbers.

This activity can be done in a variety of ways if practice is needed.

  • Students can pretend that some counters are left in a cave by placing a margarine tub over a number of the counters on the mat.
  • They can do the "What's in the tent?" activity found on page 129 of the Alberta Diagnostic Mathematics Program, Division I, Operations and Properties).
  • Students enjoy making up all the combinations for each number with manipulatives. For example, with Unifix they use two colours to show the combinations.
  • A discussion could follow about whether 1 + 4 is different from 4 + 1.
  • Students may note that 1 yellow and 4 red is not the same group as 4 yellow and 1 red; there is an even more pronounced difference if the yellow represents dollars and the reds pennies.
  • To add challenge and mathematical interest for the more advanced students, ask them to record the number of possible combinations for each number from 1 to 10 and note the patterns.
  • After they have recorded the number of combinations for the first few numbers, can they predict how many combinations there will be for the next numbers? Have them build them and check their predictions.

Do the students have knowledge of the doubles from their work in Grade 1?

  • Inquire what they did or could visualize for doubles, such as: 3—a bug with three legs on each side
  • 4—a spider with four legs on each side
  • 5—the fingers on two hands
  • 6—an egg carton or two dice
  • 7—two weeks on the calendar
  • 8—a box of crayons with two rows of eight
  • 9—an 18‑wheeler with nine wheels on each side (Van de Walle and Lovin 2006, p. 56).

Students generally find doubles easy to learn and will likely be relatively proficient with these; however, you may still want them to draw some illustrations of their aids for recalling doubles or do some activities to review doubles, since many of the strategies used in Grade 2 to generate number facts are dependent upon doubles.

  • Students can use a calculator as a double maker by entering 2 X =.
  • Then when they enter any number it will be doubled. They can play "heads versus calculator," in which one student has a calculator that has been converted to a double maker and the other student responds using only brain power.
  • Number cards are turned up and the student relying on brain power may say the answer as soon as it is known.
  • The student using the calculator must see the answer on the display screen before saying it.
  • The person whose says the correct answer first wins a point.
  • Points can be tracked by taking a Unifix for each point earned, and then the students can compare the height of their towers at the game's end.
  • The game should eventually show that for basic facts, heads beat calculators and that is why we bother to learn them.

Making 10 was specified in the corresponding Grade 1 specific outcome. It can be tested by giving students a page of addition equations. Direct the students to answer or circle only those equations whose sums are ten. An observation of how quickly and accurately this is done will tell you if the student knows the combinations for 10 well and, if not, which ones need work. If the students' knowledge of combinations of 10 is weak, they can reinforce this skill through the following.

  • Pairs of students who each have two sets of shuffled cards 1 to 9 each lay down a card at the same time.
  • If a pair of cards are a combination of 10, the first student to say "makes 10" wins the pair of cards.
  • The student who has collected the most cards once they run out of cards is the winner of that round.

Adapted with permission from Trevor Calkins, Power of Ten: Brain Compatible Strategies for Learning to Add, Subtract and Regroup (revised ed.) (Victoria, BC: Power of Ten Educational Consulting, 2003), p. C‑7.

A game of fish can be played in which two to four students have 36 or 45 sets of shuffled cards labelled 1 to 9.

  • Each player is dealt five cards.
  • Players take turns asking the player to their left for a number that would go with one of the cards in their hand to make a combination of ten.
  • If the player is given the card with the number requested, those two cards are laid down and become points for that player.
  • The player should say the combination as it is laid down, for example, 6 + 4 = 10.
  • Now that player is able to ask for another number.
  • When the player to the left cannot supply the number requested, the player tells the asker, "Go fish."
  • That student then selects a card from the deck on the table.
  • The next person can now ask for a number needed to make a ten combination.
  • The game ends when one player is out of cards.

Grade 1 students were also expected to describe and use the "think addition for subtraction" strategy. The development of this can be checked by giving students a page of subtraction equations and asking them to write the addition fact that could help them with each one. In a structured interview or an activity for students who need practice, provide about 10 cards, of which five have a subtraction equation and the other five the corresponding addition equation. Spread these mixed up cards out on a table and ask the student to match the subtraction equations with the corresponding helpful addition equations.

Make sure that students can think of numbers from 11 to 20 as 10 and some more. Trevor Calkins (2003) notes that being able to visualize these numbers is a prerequisite of subtraction (p. 28). Van de Walle and Lovin (2006) point out that students are not ready to use the making 10 strategy until they have learned to think of these numbers as 10 and some more (p. 103). It is easy to assess the students' ability to visualize these numbers as 10 and some more. Ask the students how they see fifteen. If the students say 10 and 5, they are likely ready to move onto subtraction and use the make 10 strategy. If students state they see 1 and 5, you know they need more work on activities with numbers 10 to 20 and place value (Calkins 2003, p. 28). Thinking of the teen numbers as 10 and some more is the first step in understanding the base ten system.

If a student appears to have difficulty with these tasks, consider further individual assessment, such a structured interview, to determine the student’s level of skill and understanding.

Sample Structured Interview: Assessing Prior Knowledge and Skills  Word Document

B. Choosing Instructional Strategies

Consider the following instructional strategies for teaching addition and subtraction facts:

  • Introduce strategies with problems that relate to the students' lives. Allow the students time to create their personal strategies and then share them. Encourage critical thinking about relative strategy efficiency. Have the students critique their personal strategies as well as those of their classmates to decide which strategy works best for them and why.
  • Provide a variety of problems representing the different addition and subtraction situations with varying degrees of difficulty to differentiate instruction. Wording and using higher numbers impact the level of difficulty. Work with the whole group initially and help the students recognize which numbers in a problem refer to a part or to a whole. Insure they understand that there are comparison problems and part-part-whole problems that do not involve taking any away, but are still subtraction situations.
  • Demonstrate mental math strategies with manipulatives and in written formats so students can see how they work or could be communicated on paper. Model using mental math strategies by thinking aloud.
  • Guide discussions by asking questions to encourage thinking about number relationships, the connection between addition and subtraction, and the students' personal strategies.
  • There are many strategies for figuring out facts and students will have personal preferences. Generally students will select an efficient strategy if exposed to a variety. Students need only to understand the strategies that others elect to use.
  • Teaching mental math strategies needs to be explicit.
  • Drill comes after a strategy is in place, but is not automatic. Drill done too soon is ineffective. As Van de Walle and Lovin (2006) state, "If drill is undertaken when counting is the only strategy available, all you get is faster counting" (p. 95).
  • Time is not a factor in learning mental math strategies. Timed tests are often detrimental to student's learning strategies. The use of timed fact tests is not recommended.

C. Choosing Learning Activities

Learning Activities are examples of activities that could be used to develop student understanding of the concepts identified in Step 1.

Sample Learning Activities
Strategies Built on Doubles Download Activities  Word
Making Ten Download Activities  Word
Adding with Zeros Download Activities  Word
One or Two More or Less Download Activities  Word
Addition for Subtraction Download Activities  Word
Use and Describe a Personal Strategy for Determining a Sum to 18 and the Corresponding Subtraction Download Activities  Word
Refining Personal Strategies to Increase Their Efficiency Download Activities  Word