Solve addition and subtraction problems by going through tens.

Number Framework Stage 5.

Two blank Tens Frames (Material Master 4-6)

Bundled sticks or BeaNZ in canisters (tens and ones).

Or Magnetised Ten Frames board with mangets

Because this is a key concept at this stage, two different pieces of equipment can be used. A new piece of equipment can be used on a different day to broaden the concept. Some students may get the concept very quickly, while others may benefit from multiple representations. Use the equipment that works best for your students.

#### Using materials with bead strings

Use a 30-bead string set-up in groups of five, using only two colours (e.g., yellow and red). The bead string should be strung so that beads may be moved along it (in other words, not too tightly). Each student could have a bead string.

Problem: Pio has eight oranges and six apples. How much fruit has Pio got altogether?

Record 8 + 6 = ? on the board or in the modelling book.

Then say: “Show me the eight that Pio has on your bead strings.

Pinch the cord in the gap after eight. How do you know you have eight?”

Expect answers that link to the colour change shown as five and three.

Then say: “Pio gets six more apples. Hold your finger further along the string to show the six that are added on. Tell your partner what you notice about the colours in your six beads.” “What could we add first?” (two yellow beads). “So, 8 + 2 = 10. What do we have still to add?” (4). “What is 10 + 4 more? How could we record that?”

Record as 8 + 6 = (8 + 2) + 4 = 10 + 4 = 14.

Repeat activity using a number line and pegs.

#### Using imaging with bead strings

Problem: Andrea has seven polished stones, and she gets five more. How many polished stones does Andrea have now?

Say: “I am pinching the beads at seven.

What would you see if you could see the bead string?”

Expect answers such as “I would see five red beads and two yellow ones”. “I am now adding the five beads. How many beads will I add first? I want to make a ten. What will I add next? How will we record that?”

Invite students to do the recording.

Look for recording that shows working through a ten as illustrated above.

#### Using materials with tens frames

See Tens Frame: Bridging to Ten Strategy on the nzmaths website:

Problem: Peter has eight oranges and six apples. How many fruit has Peter got altogether?

Record 8 + 6 = ? on the board or in the modelling book.

Model eight on a tens frame and six on another tens frame.

Ask the students, without touching the tens frames, to discuss how they can add the six to the eight.

Invite a student who says that fourteen is the answer to come and demonstrate how they got the answer.

Record on the board or in the modelling book:

8 + 6 = (8 + 2) + 4

= 10 + 4

= 14

Examples: Word problems and recording for: 5 + 6, 9 + 7, 8 + 5, 7 + 6, 8 + 7, 4 + 8, 3 + 9 …

#### Using imaging with tens frames

When using the tens frame, present a problem relevant to your students, such as: Tash has eight books and gets given six more. How many books does Tash have now? Build the numbers on the tens frame behind a shield. Say: “Tell your partner what the tens frame looks like behind this shield.” “Now tell your partner what I am doing as I move things around to make ten. What does the tens frame look like now? How would we record what we just did on the tens frames?” For those students who do not make the connections, have them fold back to showing the materials to work through the problem.

#### Using Number Properties

Examples. Word stories and recording for: 75 + 8, 9 + 48, 6 + 67, 75 + 7, 74 + 7, 94 + 7, 9 + 89....