diff --git a/src/gates/insertion.rs b/src/gates/insertion.rs
index 7cdd0242..ea1d37a7 100644
--- a/src/gates/insertion.rs
+++ b/src/gates/insertion.rs
@@ -25,14 +25,73 @@ impl InsertionGate {
         GateRef::new(gate)
     }
 
-    pub fn get<F: Extendable<D>, const D: usize>() -> GateRef<F, D> {
-
-        GateRef::new(InsertionGate)
+    pub fn wires_insertion_index() -> Range<usize> {
+        0..D
     }
 
-    pub const CONST_INPUT: usize = 0;
+    pub fn wires_list_item(i: usize) -> Range<usize> {
+        let start = (i + 1) * D;
+        start..start + D
+    }
 
-    pub const WIRE_OUTPUT: usize = 0;
+    fn start_of_intermediate_wires() -> usize {
+        (i + 2) * D
+    }
+
+    fn wires_per_round() -> {
+        // D wires needed for each of cur_index, insert_here, equality_dummy, new_item, new_item_plus_old_item,
+        // already_inserted, and not_already_inserted
+        7 * D
+    }
+
+    /// The wires corresponding to the "cur_index" variable in the gadget (non-gate) insert function.
+    pub fn cur_index_for_round_r(r: usize) -> Range<usize> {
+        let intermediate_index = 0;
+        let start = start_of_intermediate_wires() + r * wires_per_round() + D * intermediate_index;
+        start..start + D
+    }
+
+    /// The wires corresponding to the "insert_here" variable in the gadget (non-gate) insert function.
+    pub fn insert_here_for_round_r(r: usize) -> Range<usize> {
+        let intermediate_index = 1;
+        let start = start_of_intermediate_wires() + r * wires_per_round() + D * intermediate_index;
+        start..start + D
+    }
+
+    /// The wires corresponding to the "equality_dummy" variable in the gadget (non-gate) insert function.
+    pub fn equality_dummy_for_round_r(r: usize) -> Range<usize> {
+        let intermediate_index = 1;
+        let start = start_of_intermediate_wires() + r * wires_per_round() + D * intermediate_index;
+        start..start + D
+    }
+
+    /// The wires corresponding to the "new_item" variable in the gadget (non-gate) insert function.
+    pub fn new_item_for_round_r(r: usize) -> Range<usize> {
+        let intermediate_index = 2;
+        let start = start_of_intermediate_wires() + r * wires_per_round() + D * intermediate_index;
+        start..start + D
+    }
+
+    /// The wires corresponding to the "new_item_plus_old_item" variable in the gadget (non-gate) insert function.
+    pub fn new_item_plus_old_item_for_round_r(r: usize) -> Range<usize> {
+        let intermediate_index = 3;
+        let start = start_of_intermediate_wires() + r * wires_per_round() + D * intermediate_index;
+        start..start + D
+    }
+
+    /// The wires corresponding to the "already_inserted" variable in the gadget (non-gate) insert function.
+    pub fn already_inserted_for_round_r(r: usize) -> Range<usize> {
+        let intermediate_index = 4;
+        let start = start_of_intermediate_wires() + r * wires_per_round() + D * intermediate_index;
+        start..start + D
+    }
+
+    /// The wires corresponding to the "not_already_inserted" variable in the gadget (non-gate) insert function.
+    pub fn not_already_inserted_for_round_r(r: usize) -> Range<usize> {
+        let intermediate_index = 5;
+        let start = start_of_intermediate_wires() + r * wires_per_round() + D * intermediate_index;
+        start..start + D
+    }
 }
 
 impl<F: Extendable<D>, const D: usize> Gate<F, D> for InsertionGate {
@@ -41,9 +100,28 @@ impl<F: Extendable<D>, const D: usize> Gate<F, D> for InsertionGate {
     }
 
     fn eval_unfiltered(&self, vars: EvaluationVars<F, D>) -> Vec<F::Extension> {
-        let input = vars.local_constants[Self::CONST_INPUT];
-        let output = vars.local_wires[Self::WIRE_OUTPUT];
-        vec![output - input]
+        let insertion_index = vars.get_local_ext_algebra(Self::wires_insertion_index());
+        let mut list_items = Vec::new();
+        for i in 0..self::vec_size {
+            list_items.push(vars.get_local_ext_algebra(Self::wires_list_item(i)));
+        }
+
+        let mut constraints = Vec::new();
+
+        for r in 0..self::vec_size {
+            let this_round_cur_index = vars.get_local_ext_algebra(Self::cur_index_for_round_r(r));
+            // TODO: set value of cur_index
+
+            let this_round_insert_here = vars.get_local_ext_algebra(Self::insert_here_for_round_r(r));
+            // enforce "insert_here = is_equal(cur_index, insertion_index)"
+            let this_round_equality_dummy = vars.get_local_ext_algebra(Self::equality_dummy_for_round_r(r));
+            let computed_insert_here = (this_round_cur_index - insertion_index) * this_round_equality_dummy;
+            constraints.extend(computed_insert_here - this_round_insert_here).to_basefield_array());
+
+
+        }
+
+        constraints
     }
 
     fn eval_unfiltered_recursively(
@@ -51,9 +129,7 @@ impl<F: Extendable<D>, const D: usize> Gate<F, D> for InsertionGate {
         builder: &mut CircuitBuilder<F, D>,
         vars: EvaluationTargets<D>,
     ) -> Vec<ExtensionTarget<D>> {
-        let input = vars.local_constants[Self::CONST_INPUT];
-        let output = vars.local_wires[Self::WIRE_OUTPUT];
-        vec![builder.sub_extension(output, input)]
+        todo!()
     }
 
     fn generators(
@@ -70,11 +146,14 @@ impl<F: Extendable<D>, const D: usize> Gate<F, D> for InsertionGate {
     }
 
     fn num_wires(&self) -> usize {
-        1
+        let num_input_wires = self.vec_size + 1; // the original vector, and the insertion index
+        let num_output_wires = self.vec_size + 1; // the final vector, with the inserted element
+        let num_intermediate_wires = 6 * self.vec_size; // six intermediate variables needed for each element of the vector
+        self.vec_size + 1
     }
 
     fn num_constants(&self) -> usize {
-        1
+        0
     }
 
     fn degree(&self) -> usize {